The following description relates to applying two-qubit quantum gates in a superconducting quantum processing unit.
Quantum computers can perform computational tasks by storing and processing information within quantum states of quantum systems. For example, qubits (i.e., quantum bits) can be stored in, and represented by, an effective two-level sub-manifold of a quantum coherent physical system. A variety of physical systems have been proposed for quantum computing applications. Examples include superconducting circuits, trapped ions, spin systems, and others.
In some aspects of what is described here, a superconducting quantum processing unit includes two qubit devices operably coupled to each other by a coupler device. In some examples, the two qubit devices include at least one tunable-frequency qubit device which has a transition frequency that can be tuned by applying a qubit flux bias. In some implementations, the tunable-frequency qubit device includes a superconducting circuit loop with one or more Josephson junctions and a shunt capacitor. An interaction between the two qubit devices can be controlled by communicating control signals to the superconducting quantum processing unit. In some implementations, control signals communicated to the superconducting quantum processing unit include a flux modulation signal, which is communicated to the tunable-frequency qubit device on a flux bias control line coupled to the tunable-frequency qubit device. The flux modulation signal modulates the qubit flux bias (e.g., in the superconducting circuit loop of the tunable-frequency qubit device) at a flux modulation frequency and a flux modulation amplitude causing the transition frequency of the tunable-frequency qubit device to be modulated. As such, two-qubit quantum logic gates can be applied to a pair of qubits defined by the two qubit devices by communicating the control signals to the superconducting quantum processing unit.
In some implementations, an entangling gate between two qubit devices can be activated by applying the flux modulation signal to the tunable-frequency qubit device such that a time average of the transition frequency of the tunable-frequency qubit device over a duration of the flux modulation signal is on resonance with a transition frequency of a second qubit device in the superconducting quantum processing unit. In some implementations, a flux modulation frequency of the flux modulation signal can be set to a value that is not equal to a subharmonic of the difference between the time average of the transition frequency of the first tunable-frequency qubit device and the transition frequency of the second qubit device. The value of the flux modulation frequency does not activate any interaction with its neighboring qubit devices except for the interaction between the target qubit devices. In some instances, the value of the flux modulation frequency is greater than a threshold frequency value that activates interactions (e.g., sideband interaction) between the first tunable-frequency qubit device and the second qubit device. In some implementations, a flux modulation amplitude of the flux modulation signal is set to a value at which the first tunable-frequency qubit device and the second qubit device are on resonance according to a resonant condition.
When the first tunable-frequency qubit device and the second qubit device are coupled through a tunable-frequency coupler device, the value of the flux modulation frequency of the flux modulation signal applied on the first tunable-frequency qubit device does not activate an interaction between the first tunable-frequency qubit device and the tunable-frequency coupler device. In some implementations, the value of the flux modulation frequency does not activate a sideband parametric two-qubit quantum logic gate between the first tunable-frequency qubit device and the tunable-frequency coupler device. In other words, the sidebands of the first tunable-frequency qubit device under flux modulation is not on resonance with the tunable-frequency coupler device, and there is no exchange of energy between the first tunable-frequency qubit device and the tunable-frequency coupler device.
In some implementations, the systems and techniques described here can provide technical advantages and improvements. For example, the system and techniques disclosed here can allow activation of two-qubit quantum logic gates on different qubit devices using a single flux modulation frequency. As such, the systems and techniques described can compensate variations in transition frequencies of qubit devices caused by nonuniformities of fabrication processes. In some cases, the systems and techniques described here can operate two-qubit quantum logic gates without significantly reducing the effective qubit-qubit coupling; enable two-qubit quantum logic gates that are less sensitive to the frequency-dependent transfer function; and improve performance of quantum logic gates (e.g., higher gate fidelities and faster gates) for quantum computation. In some cases, a combination of these and potentially other advantages and improvements may be obtained.
The example computing system 101 includes classical and quantum computing resources and exposes their functionality to the user devices 110A, 110B, 110C (referred to collectively as “user devices 110”). The computing system 101 shown in
The example computing system 101 can provide services to the user devices 110, for example, as a cloud-based or remote-accessed computer system, as a distributed computing resource, as a supercomputer or another type of high-performance computing resource, or in another manner. The computing system 101 or the user devices 110 may also have access to one or more other quantum computing systems (e.g., quantum computing resources that are accessible through the wide area network 115, the local network 109, or otherwise).
The user devices 110 shown in
In the example shown in
The local data connection in
In the example shown in
The remote data connection in
The example servers 108 shown in
As shown in
The classical processors 111 can include various kinds of apparatus, devices, and machines for processing data, including, by way of example, a microprocessor, a central processing unit (CPU), a graphics processing unit (GPU), an FPGA (field programmable gate array), an ASIC (application specific integrated circuit), or combinations of these. The memory 112 can include, for example, a random-access memory (RAM), a storage device (e.g., a writable read-only memory (ROM) or others), a hard disk, or another type of storage medium. The memory 112 can include various forms of volatile or non-volatile memory, media, and memory devices, etc.
Each of the example quantum computing systems 103A, 103B operates as a quantum computing resource in the computing system 101. The other resources 107 may include additional quantum computing resources (e.g., quantum computing systems, quantum simulators, or both) as well as classical (non-quantum) computing resources such as, for example, digital microprocessors, specialized co-processor units (e.g., graphics processing units (GPUs), cryptographic co-processors, etc.), special purpose logic circuitry (e.g., field programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), etc.), systems-on-chips (SoCs), etc., or combinations of these and other types of computing modules.
In some implementations, the servers 108 generate programs, identify appropriate computing resources (e.g., a QPU or QVM) in the computing system 101 to execute the programs, and send the programs to the identified resources for execution. For example, the servers 108 may send programs to the quantum computing system 103A, the quantum computing system 103B, or any of the other resources 107. The programs may include classical programs, quantum programs, hybrid classical/quantum programs, and may include any type of function, code, data, instruction set, etc.
In some instances, programs can be formatted as source code that can be rendered in human-readable form (e.g., as text) and can be compiled, for example, by a compiler running on the servers 108, on the quantum computing systems 103, or elsewhere. In some instances, programs can be formatted as compiled code, such as, for example, binary code (e.g., machine-level instructions) that can be executed directly by a computing resource. Each program may include instructions corresponding to computational tasks that, when performed by an appropriate computing resource, generate output data based on input data. For example, a program can include instructions formatted for a quantum computer system, a simulator, a digital microprocessor, co-processor or other classical data processing apparatus, or another type of computing resource.
In some cases, a program may be expressed in a hardware-independent format. For example, quantum machine instructions may be provided in a quantum instruction language such as Quil, described in the publication “A Practical Quantum Instruction Set Architecture,” arXiv:1608.03355v2, dated Feb. 17, 2017, or another quantum instruction language. For instance, the quantum machine instructions may be written in a format that can be executed by a broad range of quantum processing units or simulators. In some cases, a program may be expressed in high-level terms of quantum logic gates or quantum algorithms, in lower-level terms of fundamental qubit rotations and controlled rotations, or in another form. In some cases, a program may be expressed in terms of control signals (e.g., pulse sequences, delays, etc.) and parameters for the control signals (e.g., frequencies, phases, durations, channels, etc.). In some cases, a program may be expressed in another form or format. In some cases, a program may utilize Quil-T, described in the publication “Gain deeper control of Rigetti quantum processors with Quil-T,” available at https://medium.com/rigetti/gain-deeper-control-of-rigetti-quantum-processors-with-quil-t-ea8943061e5b dated Dec. 10, 2020, which is hereby incorporated by reference in the present disclosure.
In some implementations, the servers 108 include one or more compilers that convert programs between formats. For example, the servers 108 may include a compiler that converts hardware-independent instructions to binary programs for execution by the quantum computing systems 103A, 103B. In some cases, a compiler can compile a program to a format that targets a specific quantum resource in the computer system 101. For example, a compiler may generate a different binary program (e.g., from the same source code) depending on whether the program is to be executed by the quantum computing system 103A or the quantum computing system 103B.
In some cases, a compiler generates a partial binary program that can be updated, for example, based on specific parameters. For instance, if a quantum program is to be executed iteratively on a quantum computing system with varying parameters on each iteration, the compiler may generate the binary program in a format that can be updated with specific parameter values at runtime (e.g., based on feedback from a prior iteration, or otherwise); the parametric update can be performed without further compilation. In some cases, a compiler generates a full binary program that does not need to be updated or otherwise modified for execution.
In some implementations, the servers 108 generate a schedule for executing programs, allocate computing resources in the computing system 101 according to the schedule, and delegate the programs to the allocated computing resources. The servers 108 can receive, from each computing resource, output data from the execution of each program. Based on the output data, the servers 108 may generate additional programs that are then added to the schedule, output data that is provided back to a user device 110, or perform another type of action.
In some implementations, all or part of the computing environment operates as a cloud-based quantum computing (QC) environment, and the servers 108 operate as a host system for the cloud-based QC environment. The cloud-based QC environment may include software elements that operate on both the user devices 110 and the computer system 101 and interact with each other over the wide area network 115. For example, the cloud-based QC environment may provide a remote user interface, for example, through a browser or another type of application on the user devices 110. The remote user interface may include, for example, a graphical user interface or another type of user interface that obtains input provided by a user of the cloud-based QC environment. In some cases, the remote user interface includes, or has access to, one or more application programming interfaces (APIs), command line interfaces, graphical user interfaces, or other elements that expose the services of the computer system 101 to the user devices 110.
In some cases, the cloud-based QC environment may be deployed in a “serverless” computing architecture. For instance, the cloud-based QC environment may provide on-demand access to a shared pool of configurable computing resources (e.g., networks, servers, storage, applications, services, quantum computing resources, classical computing resources, etc.) that can be provisioned for requests from user devices 110. Moreover, the cloud-based computing systems 101 may include or utilize other types of computing resources, such as, for example, edge computing, fog computing, etc.
In an example implementation of a cloud-based QC environment, the servers 108 may operate as a cloud provider that dynamically manages the allocation and provisioning of physical computing resources (e.g., GPUs, CPUs, QPUs, etc.). Accordingly, the servers 108 may provide services by defining virtualized resources for each user account. For instance, the virtualized resources may be formatted as virtual machine images, virtual machines, containers, or virtualized resources that can be provisioned for a user account and configured by a user. In some cases, servers 108 include a container management and execution system that is implemented, for example, using KUBERNETES® or another software platform for container management. In some cases, the cloud-based QC environment is implemented using a resource such as, for example, OPENSTACK®. OPENSTACK® is an example of a software platform for cloud-based computing, which can be used to provide virtual servers and other virtual computing resources for users.
In some cases, the server 108 stores quantum machine images (QMI) for each user account. A quantum machine image may operate as a virtual computing resource for users of the cloud-based QC environment. For example, a QMI can provide a virtualized development and execution environment to develop and run programs (e.g., quantum programs or hybrid classical/quantum programs). When a QMI operates on the server 108, the QMI may engage either of the quantum processor units 102A, 102B, and interact with a remote user device (110B or 110C) to provide a user programming environment. The QMI may operate in close physical proximity to, and have a low-latency communication link with, the quantum computing systems 103A, 103B. In some implementations, remote user devices connect with QMIs operating on the servers 108 through secure shell (SSH) or other protocols over the wide area network 115.
In some implementations, all or part of the computing system 101 operates as a hybrid computing environment. For example, quantum programs can be formatted as hybrid classical/quantum programs that include instructions for execution by one or more quantum computing resources and instructions for execution by one or more classical resources. The servers 108 can allocate quantum and classical computing resources in the hybrid computing environment, and delegate programs to the allocated computing resources for execution. The quantum computing resources in the hybrid environment may include, for example, one or more quantum processing units (QPUs), one or more quantum virtual machines (QVMs), one or more quantum simulators, or possibly other types of quantum resources. The classical computing resources in the hybrid environment may include, for example, one or more digital microprocessors, one or more specialized co-processor units (e.g., graphics processing units (GPUs), cryptographic co-processors, etc.), special purpose logic circuitry (e.g., field programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), etc.), systems-on-chips (SoCs), or other types of computing modules.
In some cases, the servers 108 can select the type of computing resource (e.g., quantum or classical) to execute an individual program, or part of a program, in the computing system 101. For example, the servers 108 may select a particular quantum processing unit (QPU) or other computing resource based on availability of the resource, speed of the resource, information or state capacity of the resource, a performance metric (e.g., process fidelity) of the resource, or based on a combination of these and other factors. In some cases, the servers 108 can perform load balancing, resource testing and calibration, and other types of operations to improve or optimize computing performance.
Each of the example quantum computing systems 103A, 103B shown in
In some implementations, a quantum computing system can operate using gate-based models for quantum computing. For example, the qubits can be initialized in an initial state, and a quantum logic circuit comprised of a series of quantum logic gates can be applied to transform the qubits and extract measurements representing the output of the quantum computation. Individual qubits may be controlled by single-qubit quantum logic gates, and pairs of qubits may be controlled by two-qubit quantum logic gates (e.g., entangling gates that are capable of generating entanglement between the pair of qubits). In some implementations, a quantum computing system can operate using adiabatic or annealing models for quantum computing. For instance, the qubits can be initialized in an initial state, and the controlling Hamiltonian can be transformed adiabatically by adjusting control parameters to another state that can be measured to obtain an output of the quantum computation.
In some models, fault-tolerance can be achieved by applying a set of high-fidelity control and measurement operations to the qubits. For example, quantum error correcting schemes can be deployed to achieve fault-tolerant quantum computation. Other computational regimes may be used; for example, quantum computing systems may operate in non-fault-tolerant regimes. In some implementations, a quantum computing system is constructed and operated according to a scalable quantum computing architecture. For example, in some cases, the architecture can be scaled to a large number of qubits to achieve large-scale general purpose coherent quantum computing. Other architectures may be used; for example, quantum computing systems may operate in small-scale or non-scalable architectures.
The example quantum computing system 103A shown in
In some instances, all or part of the quantum processing unit 102A functions as a quantum processor, a quantum memory, or another type of subsystem. In some examples, the quantum processing unit 102A includes a quantum circuit system. The quantum circuit system may include qubit devices, readout devices, and possibly other devices that are used to store and process quantum information. In some cases, the quantum processing unit 102A includes a superconducting quantum circuit, and the superconducting quantum circuit includes two qubit devices operatively coupled to each other by a coupler device. In certain examples, the two qubit devices include at least one tunable-frequency qubit device and a second qubit device. The tunable-frequency qubit device is implemented as a superconducting quantum circuit device that include Josephson junctions, for example, in Superconducting Quantum Interference Device (SQUID) loops or other arrangements, and are controlled by radio-frequency signals, microwave signals, and flux bias signals delivered to the quantum processing unit 102A.
In some examples, the second qubit device may be implemented as a tunable-frequency qubit device with a tunable transition frequency, or a fixed-frequency qubit device with a fixed transition frequency. In some examples, each ach of the two qubit devices can be a floating qubit device with two respective qubit electrodes electrically floating at a certain potential (without being conductively connected to a ground plane, or to a grounded electrode of a qubit device). In some instances, the coupler device can be a tunable-frequency coupler device with a tunable transition frequency or a fixed-frequency coupler device. In some examples, when the coupler device is a tunable-frequency coupler device, the effective coupling strength between the two qubit devices can be calibrated and tuned to activate or deactivate the coupling between the two qubit devices. In some instances, the tunable-frequency coupler devices have two coupler electrodes electrically floating at a certain potential, without being conductively connected to the ground plane.
In some implementations, control signals are communicated to the quantum circuit devices of the superconducting quantum circuit for performing quantum logic operations. Values of control parameters of the control signals are determined according to device parameters of the quantum circuit devices, which can be obtained by performing a calibration process (e.g., with respective to operations in the example process 1500 in FIG. or another process. For example, a range of operating frequencies (e.g., a tunable range of the transition frequency on which the tunable-frequency qubit device operates) and anharmonicities of the tunable-frequency qubit device, a transition frequency of the second qubit device (e.g., when the second qubit device is a fixed-frequency qubit device), a tunable range of transition frequency of the second qubit device (e.g., when the second qubit device is a tunable-frequency qubit device), a range of transition frequency of the coupler device (e.g., when the coupler device is a tunable-frequency coupler device) can be obtained and further used to determine the control parameters of the control signals.
In some implementations, a flux modulation signal configured to modulate a transition frequency of the tunable-frequency qubit device in the quantum processing unit 102 is generated by, and communicated from, the example control system 105 to the tunable-frequency qubit device of the quantum processing unit 102 on respective signal lines. The flux modulation signal modulates the magnetic flux bias applied in the superconducting circuit loop of the tunable-frequency qubit device causing a modulation of the transition frequency of the tunable-frequency qubit device. The flux modulation signal is characterized by a flux modulation frequency and a flux modulation amplitude. A value of the flux modulation frequency can be determined such that a time average of the transition frequency of the tunable-frequency qubit device over a duration when the flux modulation signal is applied is on resonance with a transition frequency of the second qubit device of the quantum processing unit 102. In some implementations, the flux modulation frequency of the flux modulation signal applied on the tunable-frequency qubit device has a value greater than a threshold frequency value that activates interactions between the first tunable-frequency qubit device and the second qubit device. In some implementations, the flux modulation frequency of the flux modulation signal applied on the tunable-frequency qubit device has a value not equal to a subharmonic of the difference between the time average of the transition frequency of the first tunable-frequency qubit device and the transition frequency of the second qubit device. In some implementations, other control parameters for performing a two-qubit quantum logic gate can be also determined, for example, a gate time for the two-qubit quantum logic gate, parking, and gate-activating values of a coupler flux bias applied on the coupler device, and other control parameters.
In some cases, the quantum processing unit 102A includes an ion trap system, and the qubit devices are implemented as trapped ions controlled by optical signals delivered to the quantum processing unit 102A. In some cases, the quantum processing unit 102A includes a spin system, and the qubit devices are implemented as nuclear or electron spins controlled by microwave or radio-frequency signals delivered to the quantum processing unit 102A. The quantum processing unit 102A may be implemented based on another physical modality of quantum computing.
The quantum processing unit 102A may include, or may be deployed within, a controlled environment. The controlled environment can be provided, for example, by shielding equipment, cryogenic equipment, and other types of environmental control systems. In some examples, the components in the quantum processing unit 102A operate in a cryogenic temperature regime and are subject to very low electromagnetic and thermal noise. For example, magnetic shielding can be used to shield the system components from stray magnetic fields, optical shielding can be used to shield the system components from optical noise, thermal shielding and cryogenic equipment can be used to maintain the system components at controlled temperature, etc.
In some implementations, the example quantum processing unit 102A can process quantum information by applying control signals to the qubits in the quantum processing unit 102A. The control signals can be configured to encode information in the qubits, to process the information by performing quantum logic gates or other types of operations, or to extract information from the qubits. In some examples, the operations can be expressed as single-qubit quantum logic gates, two-qubit quantum logic gates, or other types of quantum logic gates that operate on one or more qubits. A quantum logic circuit, which includes a sequence of quantum logic operations, can be applied to the qubits to perform a quantum algorithm. The quantum algorithm may correspond to a computational task, a hardware test, a quantum error correction procedure, a quantum state distillation procedure, or a combination of these and other types of operations.
The example control system 105A includes controllers 106A and signal hardware 104A. Similarly, control system 105B includes controllers 106B and signal hardware 104B. All or part of the control systems 105A, 105B can operate in a room-temperature environment or another type of environment, which may be located near the respective quantum processing units 102A, 102B. In some cases, the control systems 105A, 105B include classical computers, signaling equipment (microwave, radio, optical, bias, etc.), electronic systems, vacuum control systems, refrigerant control systems, or other types of control systems that support operation of the quantum processing units 102A, 102B.
The control systems 105A, 105B may be implemented as distinct systems that operate independent of each other. In some cases, the control systems 105A, 105B may include one or more shared elements; for example, the control systems 105A, 105B may operate as a single control system that operates both quantum processing units 102A, 102B. Moreover, a single quantum computer system may include multiple quantum processing units, which may operate in the same controlled (e.g., cryogenic) environment or in separate environments.
The example signal hardware 104A includes components that communicate with the quantum processing unit 102A. The signal hardware 104A may include, for example, waveform generators, amplifiers, digitizers, high-frequency sources, DC sources, AC sources, etc. The signal hardware may include additional or different features and components. In the example shown, components of the signal hardware 104A are adapted to interact with the quantum processing unit 102A. For example, the signal hardware 104A can be configured to operate in a particular frequency range, configured to generate and process signals in a particular format, or the hardware may be adapted in another manner.
In some instances, one or more components of the signal hardware 104A generate control signals, for example, based on control information from the controllers 106A. The control signals can be delivered to the quantum processing unit 102A during operation of the quantum computing system 103A. For instance, the signal hardware 104A may generate signals to implement quantum logic operations, readout operations, or other types of operations. As an example, the signal hardware 104A may include arbitrary waveform generators (AWGs) that generate electromagnetic waveforms (e.g., microwave or radio-frequency) or laser systems that generate optical waveforms. The waveforms or other types of signals generated by the signal hardware 104A can be delivered to devices in the quantum processing unit 102A to operate qubit devices, readout devices, bias devices, coupler devices, or other types of components in the quantum processing unit 102A.
In some instances, the signal hardware 104A receives and processes signals from the quantum processing unit 102A. The received signals can be generated by the execution of a quantum program on the quantum computing system 103A. For instance, the signal hardware 104A may receive signals from the devices in the quantum processing unit 102A in response to readout or other operations performed by the quantum processing unit 102A. Signals received from the quantum processing unit 102A can be mixed, digitized, filtered, or otherwise processed by the signal hardware 104A to extract information, and the information extracted can be provided to the controllers 106A or handled in another manner. In some examples, the signal hardware 104A may include a digitizer that digitizes electromagnetic waveforms (e.g., microwave or radio-frequency) or optical signals, and a digitized waveform can be delivered to the controllers 106A or to other signal hardware components. In some instances, the controllers 106A process the information from the signal hardware 104A and provide feedback to the signal hardware 104A; based on the feedback, the signal hardware 104A can in turn generate new control signals that are delivered to the quantum processing unit 102A.
In some implementations, the signal hardware 104A includes signal delivery hardware that interfaces with the quantum processing unit 102A. For example, the signal hardware 104A may include filters, attenuators, directional couplers, multiplexers, diplexers, bias components, signal channels, isolators, amplifiers, power dividers, and other types of components. In some instances, the signal delivery hardware performs preprocessing, signal conditioning, or other operations to the control signals to be delivered to the quantum processing unit 102A. In some instances, signal delivery hardware performs preprocessing, signal conditioning, or other operations on readout signals received from the quantum processing unit 102A.
The example controllers 106A communicate with the signal hardware 104A to control operation of the quantum computing system 103A. The controllers 106A may include classical computing hardware that directly interface with components of the signal hardware 104A. The example controllers 106A may include classical processors, memory, clocks, digital circuitry, analog circuitry, and other types of systems or subsystems. The classical processors may include one or more single- or multi-core microprocessors, digital electronic controllers, special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit), or other types of data processing apparatus. The memory may include any type of volatile or non-volatile memory or another type of computer storage medium. The controllers 106A may also include one or more communication interfaces that allow the controllers 106A to communicate via the local network 109 and possibly other channels. The controllers 106A may include additional or different features and components.
In some implementations, the controllers 106A include memory or other components that store quantum state information, for example, based on qubit readout operations performed by the quantum computing system 103A. For instance, the states of one or more qubits in the quantum processing unit 102A can be measured by qubit readout operations, and the measured state information can be stored in a cache or other type of memory system in or more of the controllers 106A. In some cases, the measured state information is subsequently used in the execution of a quantum program, a quantum error correction procedure, a quantum processing unit (QPU) calibration or testing procedure, or another type of quantum process.
In some implementations, the controllers 106A include memory or other components that store a quantum program containing quantum machine instructions for execution by the quantum computing system 103A. In some instances, the controllers 106A can interpret the quantum machine instructions and perform hardware-specific control operations according to the quantum machine instructions. For example, the controllers 106A may cause the signal hardware 104A to generate control signals that are delivered to the quantum processing unit 102A to execute the quantum machine instructions.
In some instances, the controllers 106A extract qubit state information from qubit readout signals, for example, to identify the quantum states of qubits in the quantum processing unit 102A or for other purposes. For example, the controllers may receive the qubit readout signals (e.g., in the form of analog waveforms) from the signal hardware 104A, digitize the qubit readout signals, and extract qubit state information from the digitized signals. In some cases, the controllers 106A compute measurement statistics based on qubit state information from multiple shots of a quantum program. For example, each shot may produce a bitstring representing qubit state measurements for a single execution of the quantum program, and a collection of bitstrings from multiple shots may be analyzed to compute quantum state probabilities.
In some implementations, the controllers 106A include one or more clocks that control the timing of operations. For example, operations performed by the controllers 106A may be scheduled for execution over a series of clock cycles, and clock signals from one or more clocks can be used to control the relative timing of each operation or groups of operations. In some implementations, the controllers 106A may include classical computer resources that perform some or all of the operations of the servers 108 described above. For example, the controllers 106A may operate a compiler to generate binary programs (e.g., full or partial binary programs) from source code; the controllers 106A may include an optimizer that performs classical computational tasks of a hybrid classical/quantum program; the controllers 106A may update binary programs (e.g., at runtime) to include new parameters based on an output of the optimizer, etc.
The other quantum computer system 103B and its components (e.g., the quantum processing unit 102B, the signal hardware 104B, and controllers 106B) can be implemented as described above with respect to the quantum computer system 103A; in some cases, the quantum computer system 103B and its components may be implemented or may operate in another manner.
In some implementations, the quantum computer systems 103A, 103B are disparate systems that provide distinct modalities of quantum computation. For example, the computer system 101 may include both an adiabatic quantum computer system and a gate-based quantum computer system. As another example, the computer system 101 may include a superconducting circuit-based quantum computer system and an ion trap-based quantum computer system. In such cases, the computer system 101 may utilize each quantum computing system according to the type of quantum program that is being executed, according to availability or capacity, or based on other considerations.
In the example shown in
In some implementations, the control system 202 interfaces with the superconducting quantum processing unit 204 through a signal delivery system that includes connector hardware elements. For example, the connector hardware elements of the control system 202 can include signal lines, signal processing hardware, filters, feedthrough devices (e.g., light-tight feedthroughs, etc.), and other types of components. In some implementations, the control system connector hardware can span multiple different temperature and noise regimes. For example, the connector hardware elements can include a series of temperature stages operating at different temperatures, e.g., 60 Kelvin (K), 3 K, 800 milli Kelvin (mK), 150 mK, that decrease between a higher temperature regime of the example control system 202 and a lower temperature regime of the example superconducting quantum processing unit 204.
In some implementations, the qubit devices 212 are housed between neighboring pairs of the coupler devices 214 in a device array within the superconducting quantum processing unit 204. Quantum states (e.g., qubits) of respective qubit devices 212 can be manipulated by control signals, or read by readout signals, generated by the control system 202. The qubit devices 212 can be controlled individually, for example, by delivering control signals to the respective qubit devices 212. In some cases, a set of neighboring quantum circuit devices (e.g., the qubit devices 212B, 212C and the coupler device 214C) is controlled jointly by delivering control signals to the set. In some cases, readout devices can detect the states of the qubit devices 212, for example, by interacting directly with the respective qubit devices 212.
In the example shown in
In some examples, the transition frequency of a qubit device 212 is not tunable by application of an offset field and is independent of magnetic flux experienced by the qubit device 212. For instance, a fixed-frequency qubit device may have a fixed transition frequency that is defined by an electronic circuit of the qubit device. As an example, a fixed-frequency qubit device (e.g., a fixed-frequency transmon qubit device) may be implemented without a SQUID loop. In some examples, the fixed-frequency qubit device includes one Josephson junction and a shunt capacitor, and the transition frequency of the fixed-frequency qubit device is defined at least in part by a Josephson energy of the Josephson junction and a capacitance of the shunt capacitor, which is independent of a magnetic flux experienced by the fixed-frequency qubit device. In some implementations, the qubit devices 212 may be implemented as the fixed-frequency qubit devices 514
In certain instances, the qubit device 212 includes one qubit electrode. In this case, the qubit device 212 is considered a “grounded” qubit device when the one or more Josephson junctions of the qubit device 212 are connected between the qubit electrode and a ground plane (e.g., two or more Josephson junctions may be connected in parallel between the qubit electrode and a ground plane); and the shunt capacitor is defined by capacitance between the qubit electrode and the ground plane. In other instances, the qubit device 212 includes two qubit electrodes. In this case, the qubit device 212 is considered a “floating” qubit device when the one or more Josephson junctions of the qubit device 212 are connected between the two qubit electrodes that are not directly connected to ground (e.g., two or more Josephson junctions may be connected in parallel between the two qubit electrodes, as in the examples shown in
The coupler devices 214A, 214B, 214C, 214D, 214E may be implemented by transmon qubit devices, flux qubit devices, flatsonium qubit devices, fluxonium qubit devices, or other types of tunable-frequency qubit devices. In some implementations, the coupler device 214 is a tunable-frequency coupler device. In certain examples, a tunable-frequency coupler device may include a superconducting circuit loop (e.g., a SQUID loop), which can receive a coupler flux bias that tunes the transition frequency of the tunable-frequency coupler device. In some instances, a tunable-frequency coupler device includes two coupler electrodes; the two Josephson junctions of the tunable-frequency coupler device are connected in parallel between the two coupler electrodes; the shunt capacitor is caused by the two coupler electrodes. In this case, the tunable-frequency coupler device is a tunable-frequency “floating” coupler device. In some implementations, the coupler devices 214 may be implemented as the tunable-frequency coupler device 1916, 2206 shown in
As a particular example,
In certain examples, an offset field can be, for example, a magnetic flux bias, a DC electrical voltage, or another type of field. In some implementations, the tunability of the qubit devices 212A, 212B, 212C, 212D, in the superconducting quantum processing unit 204 allows pairs of qubit devices to be selectively coupled on-demand to perform multi-qubit quantum logic gates, to entangle pairs of qubits defined by pairs of qubit devices 212, or to perform other types of control operations. The qubit devices can have a high “on/off” ratio, which refers to the ratio of the effective coupling strength provided by control of the tunable-frequency coupler device. In some implementations, the coupler devices 214A, 214B, 214C, 214D, 214E, when activated or deactivated, can enable or disable coupling between two neighboring qubit devices 212, respectively.
In some instances, information is encoded in the qubit devices in the superconducting quantum processing unit 204, and the information can be processed by operation of the qubit devices 212A, 212B, 212C, 212D. For instance, input information can be encoded in the computational states or computational subspaces defined by some or all of the qubit devices 212 in the superconducting quantum processing unit 204. The information can be processed, for example, by applying a quantum algorithm or other operations to the input information. The quantum algorithm may be decomposed as quantum logic gates or instruction sets that are performed by the qubit devices 212 and coupler devices 214 over a series of clock cycles. For instance, a quantum algorithm may be executed by a combination of single-qubit quantum logic gates and two-qubit quantum logic gates. In some cases, information is processed in another manner. Processing the information encoded in the qubit devices 212 can produce output information that can be extracted from the qubit devices 212. The output information can be extracted, for example, by performing state tomography or individual readout operations. In some instances, the output information is extracted over multiple clock cycles or in parallel with the processing operations.
In some aspects of operation, the control system 202 communicates control signals to the qubit devices 212 in the superconducting quantum processing unit 204. The control signals can be configured to modulate, increase, decrease, or otherwise manipulate the transition frequencies of the qubit devices 212A, 212B, 212C, 212D (e.g., when the qubit devices are tunable-frequency qubit devices). In some implementations, a control signal 206 includes a flux bias signal that varies a magnetic flux experienced by the tunable-frequency qubit device, and varying the magnetic flux can change the transition frequency of the tunable-frequency qubit device. A control signal 206 includes a flux modulation signal that is configured to modulate a transition frequency of a tunable-frequency qubit device at a certain flux modulation frequency and a certain flux modulation amplitude. A control signal 206 includes a microwave drive signal that is configured to drive the qubit at the transition frequency in order to apply a two-qubit quantum logic gate. A control signal 206 can be a direct current (DC) signal communicated from the control system 202 to the individual qubit device 212. In some implementations, a control signal can be an alternating current (AC) signal communicated from the control system 202 to the individual qubit device 212. In some cases, the AC signal may be superposed with a direct current (DC) signal. Other types of control signals may be used.
In the example shown in
In some implementations, the control signals 206 are configured to generate interactions that perform quantum logic gates on the qubits defined by the qubit devices. For example, in some cases, one or more of the control signals 206 generate an interaction that applies a two-qubit quantum logic gate to a pair of qubits defined by two of the qubit devices 212 coupled through a coupler device 214 in the superconducting quantum processing unit 204. A control signal 206 may be a current signal, a voltage signal, or another type of electrical signal which can be used to control a control line, for example with a flux bias element, to modulate a flux bias signal so as to modulate a magnetic flux and generate a modulated magnetic flux (e.g., a modulated flux bias). In this case, the control signals 206 activate two-qubit quantum logic gates by modulating a transition frequency of a qubit device 212, and/or tuning a transition frequency of the coupler device 214C.
In some cases, when a qubit device 212C is a tunable-frequency qubit device, the control line (which receives the control signal 206) may include a flux bias element that is inductively coupled to a superconducting circuit loop of the qubit device 212C to control the magnetic flux through the superconducting circuit loop in the qubit device 212C. The control signal 206 may cause the flux bias element to modulate the magnetic flux at a flux modulation frequency. In some instances, the control line and the superconducting circuit loop are implemented as the control line 518 and the superconducting circuit loop 524 shown in
In some instances, the control system 202 identifies a quantum logic gate to be applied to a pair of qubits in the superconducting quantum processing unit 204. The pair of qubits includes, for example, a first qubit defined by the qubit device 212B and a second qubit defined by the qubit device 212C in the qubit device array through the coupler device 214C. The control signal 206 can be configured to turn on the coupler device 214C (e.g., when the coupler device 214C is a tunable-frequency coupler device) to enable the coupling between the qubit devices 212B and 212C. The control signal 206 can be further configured to perform a control operation (e.g., two-qubit quantum logic gate) on the qubit devices 212B, 212C. The control system 202 can perform the quantum logic gate by communicating the control signal 206 to a control line that is coupled to the coupler device 214C in the superconducting quantum processing unit 204. In some implementations, the control signal 206 can be further configured to perform a calibration process to determine device parameters and control parameters for activating the quantum logic gate; for enabling and disabling the coupling between the two qubit devices 212, and for other control operations.
The control parameters of the control signal 206 can be selected to achieve a specified multi-qubit quantum logic gate. In some systems, applying the two-qubit quantum logic gate to the pair of qubits defined by a pair of tunable-frequency qubit devices may include applying any quantum logic gate from the XY family of gates, the controlled-phase family of gates, the iSWAP family of gates, or another family of gates. In some cases, applying the two-qubit quantum logic gate to the pair of qubits includes applying a controlled-phase gate (e.g., a controlled-Z gate) to the pair of qubits. In some cases, applying the two-qubit quantum logic gate to the pair of qubits includes applying a Bell-Rabi gate, a square-root-of-Bell-Rabi gate, or another two-photon gate to the pair of qubits.
In some implementations, the control system 202, or another type of system associated with the quantum computing system 200, determines control parameters for applying two-qubit quantum logic gates in the superconducting quantum processing unit 204. For example, values of the control parameters for the control signal 206 may be determined by a gate calibration process defined in software, firmware, or hardware or a combination thereof. In some cases, the control system 202 executes a gate calibration process when the superconducting quantum processing unit 204 is first installed for use in the quantum computing system 200, and the gate calibration process may be repeated at other times (e.g., as needed, periodically, according to a calibration schedule, etc.). For instance, a gate calibration module may execute a calibration process that obtains values of device parameters of the qubit devices 212 and the coupler devices 214 in the superconducting quantum processing unit 204. For example, the device parameters include a range of qubit operating frequency and anharmonicity of the qubit devices 212 (e.g., when the qubit devices 212 are tunable-frequency qubit devices), an operating frequency and anharmonicity of the qubit devices 212 (e.g., when the qubit devices 212 are fixed-frequency qubit devices), and a coupling between the qubit devices and the tunable-frequency coupler devices, or another parameter.
In some instances, the values of the device parameters are used to determine values of control parameters for the control signal. In some implementations, the parameters for the control signal 206 may include the relative duration, relative phase, flux modulation frequency, flux modulation amplitude, or another parameter. When the qubit devices 212B, 212C are tunable-frequency qubit devices, the control signal with the determined parameters can be applied to one or more of the qubit devices 212B, 212C to bring the qubit devices 212B, 212C on resonance with each other. The control signal 206 can vary values of the magnetic flux applied to the coupler device 214C (e.g., when the coupler device 214C is a tunable-frequency coupler device) to determine a parking value which causes a total coupling strength of the qubit devices 212B, 212C to vanish or to be less than or equal to a predetermined threshold value. The control signal 206 can vary values of the magnetic flux applied to the coupler device 214C to determine a gate-activating value which corresponds to a maximal value of the total coupling strength. For example, the control parameters of the control signal for activating a two-qubit quantum logic gate (e.g., bringing the two qubit devices 212B, 212C on resonance) can be identified with respect to the example process 1500 shown in
In some cases, the parking value of the coupler flux bias is determined based on a threshold value of the coupling strength between the qubits. The threshold value can be determined based on target operating parameters of the superconducting quantum processing unit or target operating parameters for processes (e.g., quantum logic gates or other operations) to be performed by the superconducting quantum processing unit 204. In some cases, the threshold value represents a maximum value of the coupling strength that is small enough to allow single-qubit gates (or other types of quantum logic gates) to be performed at or above a target gate fidelity. Zero coupling strength is often ideal, but a non-zero value of the coupling strength can be effectively equal to zero when it is small enough to still allow single-qubit gates to be performed at or above the target gate fidelity. In such cases, target control parameters may be achieved by using a parking value that minimizes the magnitude of the coupling strength or otherwise causes the magnitude of the coupling strength to be less than the threshold value (effectively equal to zero). Thus, a threshold value of the coupling strength can define a maximum value of the coupling strength that still preserves single-qubit gate fidelities above a target gate fidelity. Other types of gate fidelities and/or other criteria may be used to define a threshold value of the coupling strength.
In some implementations, one or more operations in the example process 300 can be performed by a computer system, for instance, by a digital computer system having one or more digital processors (e.g., a microprocessor or other data processing apparatus) that execute instructions (e.g., instructions stored in a digital memory or other computer-readable medium), or by another type of digital, quantum, or hybrid computer system. As an example, in some cases the superconducting quantum processing unit can be deployed as the superconducting quantum processing unit 102 shown in
At 302, a flux modulation signal is generated. The flux modulation signal is configured to modulate a transition frequency of a first qubit device such that a time average of the transition frequency of the first qubit device over a duration of the flux modulation signal is on resonance with a transition frequency of a second qubit device. In some implementations, the first qubit device is a tunable-frequency qubit device; and the second qubit device may be a tunable-frequency qubit device or a fixed frequency qubit device. The first and second qubit devices are operably coupled to each other through a coupler device, e.g., a fixed-frequency coupler device or a tunable-frequency coupler device.
When the superconducting quantum processing unit includes a first tunable-frequency qubit device and a second tunable-frequency qubit device, the first and second tunable-frequency qubit devices can be brought on resonance with each other by tuning a transition frequency of the first tunable-frequency qubit device, for example, by modulating a flux bias in a first superconducting circuit loop associated with the first tunable-frequency qubit device. In some instances, the first tunable-frequency qubit device has a higher transition frequency than that of the second tunable-frequency qubit device. In some implementations, the qubit flux bias in the first superconducting circuit loop can be modulated by modulating the flux bias signal at a flux modulation frequency and a flux modulation amplitude, which causes a modulation of the transition frequency. In some implementations, when the qubit flux bias is modulated such that a time average of the transition frequency of the first tunable-frequency qubit device is on resonance with a transition frequency of the second tunable-frequency qubit device (e.g., a maximum transition frequency or another frequency of the second tunable-frequency qubit device), a two-qubit quantum logic gate is activated.
When the superconducting quantum processing unit includes a tunable-frequency qubit device and a fixed-frequency qubit device, the tunable-frequency and fixed-frequency qubit devices can be brought on resonance with each other by tuning the transition frequency of the tunable-frequency qubit device. In some implementations, when the qubit flux bias in a superconducting circuit loop associated with the tunable-frequency qubit device is modulated such that a time average of the transition frequency of the tunable-frequency qubit device is on resonance with a transition frequency of the fixed-frequency qubit device, a two-qubit quantum logic gate is activated.
In some implementations, the transition frequency of the first qubit device is modulated by communicating a flux modulation signal to the first qubit device via a respective flux bias control line. In some instances, the first qubit device includes a superconducting circuit loop and a flux bias element that applies a magnetic flux to the superconducting circuit loop of the first qubit device. When the flux modulation signal is communicated to the first qubit device, the flux modulation signal is communicated to the flux bias element on the flux bias control line such that the magnetic flux to the superconducting circuit loop is modulated. In some implementations, the flux modulation signal is characterized by a flux modulation frequency and a flux modulation amplitude. In some implementations, to activate a two-qubit quantum logic gate (e.g., iSWAP, CZ02, CZ20, and another two-qubit quantum logic gate), the flux modulation frequency of the flux modulation signal applied on the first qubit device has a value that is not equal to a subharmonic of the difference between the time average of the transition frequency of the first tunable-frequency qubit device and the transition frequency of the second qubit device. In some implementations, to activate a two-qubit quantum logic gate, the flux modulation frequency has a value that is greater than a threshold frequency value that activates interactions between the first qubit device and the second qubit device.
In some implementations, the first qubit device is communicably coupled with other quantum circuit devices in the quantum processing unit. For example, the first qubit device may have a connectivity of four (e.g., the tunable-frequency qubit device 1802E in
In some instances, a two-qubit quantum logic gates can be operated at a frequency value (e.g., tens of MHz or another value) away from the maximum transition frequency (e.g., DC flux insensitive point) of the first qubit device to reduce the dephasing time of the first qubit device.
In some implementations, control parameters for control signals (e.g., the flux modulation frequency, flux modulation amplitude of the flux modulation signal to the first qubit device) are determined by operation of a control system based on device parameters. The device parameters representing the quantum circuit devices in a superconducting quantum processing unit can be determined by performing a measurement or characterization process, a calibration process, or another type of process. For example, a calibration process can be executed in a quantum computing system to obtain the device parameters for each of the quantum circuit devices in the superconducting quantum processing unit. In some instances, a calibration process can characterize the quantum circuit devices that a quantum logic gate operation is to be applied to. In some cases, the calibration process can also characterize neighboring qubit devices in the superconducting quantum processing unit. In certain examples, the process for obtaining the device parameters of the quantum circuit devices is executed by the control system 202 of
In some implementations, the device parameters may include one or more of the device parameters of the tunable-frequency qubit devices (e.g., floating or grounded), the fixed-frequency qubit device, and the coupler device (e.g., floating or grounded, fixed-frequency or tunable-frequency) in the superconducting quantum processing unit. For example, device parameters, such as a range of operating frequencies (e.g., minimal and a maximal frequencies), and anharmonicity of each of the tunable-frequency qubit devices and the tunable-frequency coupler device involved in the interaction, the transition frequency of the fixed-frequency qubit device, or another qubit device parameter, may be obtained. In certain cases, the values of the device parameters may be used to determine values of control parameters for control signals.
At 304, a two-qubit quantum logic gate is applied to a pair of qubits defined by the first and second qubit devices. In the example shown, applying the two-qubit quantum logic gate includes communicating the flux modulation signal (generated at 302) to a flux bias control line coupled to the first qubit device. In some instances, when the two-qubit quantum logic gate is applied, a microwave drive signal can be generated, for example by operation of the control system 202 according to the determined control parameters of the microwave drive signal; and the microwave drive signal is communicated to the first qubit device on a respective qubit drive line. In some instances, when the two-qubit quantum logic gate is applied, a flux bias signal can be generated by operation of the control system; and the flux bias signal can be communicated to the coupler device (e.g., a tunable-frequency coupler device) for activating the coupling between the first and second qubit devices. In some implementations, other control signals are also communicated to other quantum circuit devices, when the two-qubit quantum logic gate is applied. For example, when the first and second qubit devices are operably coupled by a tunable-frequency a coupler flux bias signal can be communicated to the tunable-frequency coupler device to shift the transition frequency from a parking value to a gate-activating value to activate the coupling between the first and second qubit devices. For another example, when the second qubit device is a tunable-frequency coupler device, qubit flux bias signal and qubit drive signal can be generated according to the control parameters and communicated to the second qubit devices.
In some implementations, the two qubits defined by the first and second qubit devices can be described by the Hamiltonian as below,
where |0, |1
, |2
are the first three energy levels of each qubit, ωk is the transition frequency of respective qubit devices; ηk is the anharmonicity; g01 is the coupling rate between |10
and |01
; g02 and g20 are coupling rates between |11
and |02
, and |11
and |20
, respectively; and k={1, 2} representing the first (k=1) and the second (k=2) qubit devices.
In some implementations, the first qubit device is a tunable-frequency qubit device, and the second qubit device is a fixed-frequency qubit device. In this case, a transition frequency of the tunable-frequency qubit device can be modulated by applying a flux bias of the form
Φ(t)=Φdc+Φac(t)cos(ωmt+ϕ) (2)
where Φdc is a static flux bias and Φac(t) is a flux modulation amplitude, ωm is a flux modulation frequency, and ϕ is a flux modulation phase. In the limit where the parking value of the flux bias (e.g., the static flux bias Φdc) and when Φac≤Φ0/2, the transition frequency of the tunable-frequency qubit device can be modulated, which can be expressed in an approximate form given by:
ωT
where
the interaction Hamiltonian can be written as
H={tilde over (g)}
01(t)|1010|+{tilde over (g)}02(t)|11
02|+{tilde over (g)}20(t)|11
20|+h.c. (5)
where |FT represents the state F defined by the fixed-frequency qubit device and the state T defined by the tunable-frequency qubit device, and
where Δ are the detunings between two states of the two qubits, e.g., Δ= and |01
, and {tilde over (g)}02 and {tilde over (g)}20 are the normalized coupling rates between |11
and |02
, and |11
and |20
, respectively, and n is an integer.
As shown in Equation (6) above, the coupling rates are normalized by the Bessel function of the first kind (Jn). In particular, when |n|≥1, the value of the Bessel function of the first kind is approximately 0.7, e.g., Jn=0.7, causing the normalized coupling rates between the first and second qubit devices become less than the respective coupling rates; and when n=0, the normalized coupling rates shown in Equation (6) can be simplified and re-written in equations below:
In the example shown in
In the example shown in
In some instances, the fixed-frequency qubit device 514 and the tunable-frequency qubit device 512 can be also coupled together through a tunable-frequency coupler device. The tunable-frequency coupler device may include one or more tunable-frequency transmon qubit devices, tunable-frequency fluxonium qubit devices, or another type of tunable-frequency qubit device. The tunable-frequency coupler device may be capacitively coupled to each of the fixed-frequency qubit device 514 and the tunable-frequency qubit device 512 with respective coupling strengths. In some instances, an effective coupling between the fixed-frequency qubit device 514 and the tunable-frequency qubit device 512 is determined by the capacitance value of the capacitor 552.
In some implementations, the fixed-frequency qubit device 514 has a transition frequency ωF
As shown in
In some implementations, when the two qubit devices 512, 514 are coupled through a tunable-frequency coupler device, the effective coupling between the two qubit devices 512, 514 can be enabled by tuning a magnetic field applied on the tunable-frequency coupler device. For example, a separate control signal (e.g., a DC or an AC current) can be applied on a control line to tune the magnetic flux threading to the tunable-frequency coupler device, for example with a superconducting circuit loop, to turn on the coupling. When the tunable-frequency coupler device is turned on, the flux modulation signal can be applied on the flux bias element so as to apply the modulated flux bias to the tunable-frequency qubit device 512 to activate a two-qubit quantum logic gate. In some cases, the control signal applied on the tunable-frequency coupler device can be also modulated. In another instances, operation of the tunable-frequency coupler device that is used to couple the fixed-frequency qubit device 514 and the tunable-frequency qubit device 512 can be implemented with respect to the operations in the example process 1500 shown in
→|1
transition frequency of 3.7 GHz and anharmonicity of 202 MHz. Qubit device Q2 represents the tunable-frequency qubit device 512, which has a |0
→|1
transition frequency (at zero flux bias) of 4.00 GHz (e.g., a maximum value of the transition frequency ωmax/2π=4.00 GHz), a |1
→|2
transition frequency (at zero flux bias) of 3.05 GHz (a minimum value of the transition frequency ωmin/2π=3.05 GHz), and anharmonicity (at zero flux bias) of 239 MHz.
0→|1
transition (
f01T
) of the tunable-frequency qubit device 512 is brought on resonance with the transition frequency of the |0
→|1
transition (f01F) of the fixed-frequency qubit device 514 (e.g., at operating point 710 between the tunable |0
→|1
transition frequency of the tunable-frequency qubit device represented by curve 722 and the fixed |0
→|1
transition frequency of the fixed-frequency qubit device represented by curve 724). The time average of the transition frequency of the |0
→|1
transition of the tunable-frequency qubit device over a duration (e.g., a period τ) is defined by
where τ is a period, e.g., τ=2π/ωm and ωm is the flux modulation frequency. In some cases, to activate an iSWAP gate, the transition frequency of the tunable-frequency qubit device can be modulated at any available frequency that can be provided by a signal source (e.g., a flux pulse source as part of the signal hardware 104B of the control system 105B in
Similarly, a CZ02 gate is activated when the time average of the modulated |1→|2
transition frequency of the tunable-frequency qubit device is brought on resonance with the |0
→|1
transition frequency of the fixed-frequency qubit device (e.g., at operating point 712 between the tunable |1
→|2
transition frequency of the tunable-frequency qubit device represented by curve 726 and the fixed |0
→|1
transition frequency of the fixed-frequency qubit device represented by curve 724); and a CZ20 gate is activated when the time average of the modulated |0
→|1
transition frequency of the tunable-frequency qubit device is brought on resonance with the |1
→|2
transition frequency of the fixed-frequency qubit device (e.g., at operating point 714 between the tunable |0
→|1
transition frequency of the tunable-frequency qubit device represented by curve 722 and the fixed |1
→|2
transition frequency of the fixed-frequency qubit device represented by curve 728).
In some implementations, a value of the flux modulation amplitude can be tuned to activate a respective two-qubit quantum logic gate. As shown in plot 720 of
In some examples, the first and second tunable-frequency qubit devices 812, 814 and the tunable-frequency coupler device 816 may be implemented by other types of systems, and the features and components represented in
Each of the first and second tunable-frequency qubit devices 812, 814 and the tunable-frequency coupler device 816 includes a superconducting circuit loop that has two Josephson junctions connected in parallel. Particularly, the first tunable-frequency qubit device 812 includes a first superconducting circuit loop 832; the second tunable-frequency qubit device 814 includes a second superconducting circuit loop 834; and the tunable-frequency coupler device 816 includes a third superconducting circuit loop 836. In some implementations, each of the first, second, and third superconducting circuit loops 832, 834, and 836 can be inductively coupled to (has a mutual inductance with) a respective control line, which can individually tune a magnetic flux in a respective superconducting circuit loop. The control lines are connected to an external control system (e.g., the control system 202 in
As shown in
In some examples, a shunt capacitor can be formed between two qubit electrodes from the same superconducting quantum circuit device. As shown in the example equivalent circuit 900 of the example superconducting quantum processing unit 800, the shunt capacitors 922, 924, 926 are caused by the two qubit electrodes 822A/822B, 824A/824B, and the coupler electrode/ground 826/828 in the first and second tunable-frequency qubit devices 902, 904, and the tunable-frequency coupler device 906, respectively. In some instances, a residual capacitor can be formed between two qubit electrodes from two distinct superconducting quantum circuit devices forming a capacitive coupling between the two distinct superconducting quantum circuit devices. As shown in the example equivalent circuit 900 of the example superconducting quantum processing unit 800, a residual capacitor can be formed between a coupler electrode 826 of the tunable-frequency coupler device 816 and each of the qubit electrodes of first or second tunable-frequency qubit devices 812, 814. In some instances, a residual capacitor can be formed between a qubit electrode of the first tunable-frequency qubit device 812 and a qubit electrode of the second tunable-frequency qubit device 814. Therefore, a static capacitive coupling (g12) between the first and second tunable-frequency qubit devices 902, 904 includes two components, e.g., a direct capacitive coupling component and an indirect capacitive coupling component. In some instances, the direct capacitive coupling component is caused by the capacitance formed between qubit electrodes 822A/822B of the first tunable-frequency qubit device 812 and qubit electrodes 824A/824B of the second tunable-frequency qubit device 314. In some instances, the indirect capacitive coupling component is a capacitive coupling mediated by the tunable-frequency coupler device 806. The indirect capacitive coupling component is caused by the capacitances formed between coupler electrode 826 of the tunable-frequency coupler device 806 and qubit electrodes 822A/822B/824A/824B of the first and second tunable-frequency qubit devices 802, 804.
The example superconducting quantum processing unit 800 shown in
The electrodes 822A, 822B, 824A, 824B, and 826 and the ground plane 828 include superconductive materials and can be formed by patterning one or more superconductive (e.g. superconducting metal) layers or other materials on the surface of the substrate 802. In some implementations, each of the one or more superconductive layers include a superconducting metal, such as aluminum (Al), niobium (Nb), tantalum (Ta), titanium (Ti), vanadium (V), tungsten (W), zirconium (Zr), or another superconducting metal. In some implementations, each of the one or more superconductive layers may include a superconducting metal alloy, such as molybdenum-rhenium (Mo/Re), niobium-tin (Nb/Sn), or another superconducting metal alloy. In some implementations, each of the superconductive layers may include a superconducting compound material, including superconducting metal nitrides and superconducting metal oxides, such as titanium-nitride (TiN), niobium-nitride (NbN), zirconium-nitride (ZrN), hafnium-nitride (HfN), vanadium-nitride (VN), tantalum-nitride (TaN), molybdenum-nitride (MoN), yttrium barium copper oxide (Y—Ba—Cu—O), or another superconducting compound material. In some instances, the electrodes 822A, 822B, 824A, 824B, and 826 and the ground plane 828 may include multilayer superconductor-insulator heterostructures.
In some implementations, the electrodes 822A, 822B, 824A, 824B, and 826 and the ground plane 828 are fabricated on the top surface of the substrate 802 and patterned using a microfabrication process or in another manner. For example, the electrodes 822A, 822B, 824A, 824B, and 826 and the ground plane 828 may be formed by performing at least some of the following fabrication steps: using chemical vapor deposition (CVD), physical vapor deposition (PVD), atomic layer deposition (ALD), spin-on coating, and/or other suitable techniques to deposit respective superconducting layers on the substrate 802; and performing one or more patterning processes (e.g., a lithography process, a dry/wet etching process, a soft/hard baking process, a cleaning process, etc.) to form openings in the respective superconducting layers.
In the example shown in
The second tunable-frequency qubit device 904 includes two Josephson junctions, e.g., a third Josephson junction 934A and a fourth Josephson junction 934B. The third and fourth Josephson junctions 934A, 934B having Josephson energies EJS2 and EJL2 are connected in parallel with each other to form a second superconducting circuit loop 914. The second tunable-frequency qubit device 904 also includes a shunt capacitor 924 with a capacitance C2, which is connected in parallel with the two Josephson junctions 934A, 934B. The shunt capacitor 924 is caused by two qubit electrodes of the second tunable-frequency qubit device 904, e.g., the two qubit electrodes 824A, 824B as shown in the second tunable-frequency qubit device 814 in
The tunable-frequency coupler device 906 includes two Josephson junctions, e.g., a fifth Josephson junction 936A and a sixth Josephson junction 936B. The fifth and sixth Josephson junctions 936A, 936B having Josephson energies EJSC and EJLC are connected in parallel with each other to form a third superconducting circuit loop 916. The tunable-frequency coupler device 906 also includes a shunt capacitor 926 with a capacitance CC, which is connected in parallel with the two Josephson junctions 936A, 936B. The shunt capacitor 926 is caused by one electrode of the tunable-frequency coupler device 906 and the ground plane, e.g., the coupler electrode 826 and the ground plane 828 as shown in the tunable-frequency coupler device 816 in
In the example shown in
As shown in
In some implementations, control operations can be performed on the superconducting circuit by providing control signals to the first and second tunable-frequency qubit devices 902, 904 and the tunable-frequency coupler device 906 via control lines. The control lines can receive the control signals, for example, from an external control system. In some implementations, each of the control lines can be connected to a conductor, an inductor, or another type of circuit component configured to carry a respective current I, which generates a respective magnetic flux Φ(t) through the superconducting circuit loops 912, 914 or 916. For instance, the control line may include an inductor (e.g., a partial loop, a single loop, or multiple loops of a conductor) that has a mutual inductance with the superconducting circuit loop 912, 914, or 916. In the example shown, the transition frequency of the first tunable-frequency qubit device 902 is tuned by tuning a magnetic flux Φe1 in the first superconducting circuit loop 912; the transition frequency of the second tunable-frequency qubit device 904 is tuned by tuning a magnetic flux Φe2 in the second superconducting circuit loop 914; and the transition frequency of the tunable-frequency coupler device 906 is tuned by tuning a magnetic flux Φec in the third superconducting circuit loop 916. In some instances, the transition frequencies may be controlled in another manner, for instance, by another type of control signal. In some implementations, the control lines may be connected to an inductance loop or another type of flux bias element that is coupled (e.g., conductively, capacitively, or inductively) to a control port to receive control signals. In certain instances, the control signals on the control lines may cause the flux bias element to generate and modulate the magnetic flux in the superconducting circuit loop 912, 914, or 916. In some implementations, the control signals on the control line are flux bias signals or flux modulation signals, and are implemented as the control signals 206 as shown in
In some implementations, when the two tunable-frequency qubit devices 902, 904 are coupled through the tunable-frequency coupler device 906, the coupling between the two tunable-frequency qubit devices 902, 904 can be enabled/disabled by tuning a magnetic flux applied to the tunable-frequency coupler device 906. For example, a separate control signal (e.g., a DC or an AC current) can be applied to a control line to tune the magnetic flux threading to the third superconducting circuit loop 916 of the tunable-frequency coupler device 906 to adjust the transition frequency of the tunable-frequency coupler device 906. When the magnetic flux on the tunable-frequency coupler device 906 is at a parking value, the coupling between the two tunable-frequency qubit devices 902, 904 can be turned off or deactivated. When the magnetic flux on the tunable-frequency coupler device 906 is at a gate-activating value, the coupling between the two tunable-frequency qubit device 902, 904 can be activated for performing a two-qubit quantum logic gate. In some instances, operation for activating and deactivating the tunable-frequency coupler device 906 can be implemented with respect to the example process 1700 shown in
In some implementations, each of the first and second tunable-frequency qubit devices 902, 904 includes highly asymmetric Josephson junctions (e.g., EJS1«EJL1, and EJS2«EJL2) that form the respective superconducting circuit loops 912, 914. The tunable-frequency coupler device 906 includes symmetric Josephson junctions or asymmetric Josephson junctions. In some implementations, a tunable-frequency coupler device 906 with asymmetric Josephson junctions allows operating two-qubit quantum logic gates by tuning the transition frequency of the tunable-frequency coupler device 906 to a minimal value to obtain gate stability against flux fluctuations. The strong asymmetry can result in much smaller tunability of the first and second tunable-frequency qubit devices 902, 904 than that of the tunable-frequency coupler device 906. The systems and techniques presented here can reduce sensitivity of the tunable-frequency qubit devices 902, 904 to flux noise thereby improving their coherence times.
The Lagrangian of the equivalent circuit shown in
where Φj are node fluxes, {dot over (Φ)}j=∂Φj/∂t, and EJj are junction energies. The junction energies EJk defined by
where ϕj=2πΦj/Φ0, Φj are node fluxes, ϕek=2πΦek/Φ0 are reduced external flux biases applied to the respective superconducting circuit loops 912, 614, 916, and Φ0=h/2e is the flux quantum, k∈{1, 2, c}, and j∈{1, 2, . . . , 5}. The node fluxes are defined in terms of node voltages as
Φj=∫−∞tdt′Vj(t′), (12)
where Vj is the voltage at the jth node (nodes 952, 954, 956, 958, 960 in
In some implementations, new variables defined by Φ1,p/m=Φ2±Φ1, and Φ2,p/m=Φ4±Φ5 are introduced, where the canonical momenta Q k and coordinates Φk are related by Qk=L/{dot over (Φ)}k which can be written in matrix form as
Q=C{dot over (Φ)} (13)
where the charge matrix Q is given by
Q=[Q
1p
,Q
1m
,Q
c
,Q
2p
,Q
2m], (14)
and the capacitance matrix C is given by:
In some cases, the capacitance C15 between the two furthest qubit electrodes 822A, 824B of the first and second tunable-frequency qubit devices can be small compared to other capacitance and can be ignored. In some implementations, the qubit-coupler coupling capacitances C23, C34, C13, C35 and qubit-qubit coupling capacitance C24 are smaller than the capacitances between the qubit electrodes and the ground plane, e.g., [C23, C34, C24, C13, C35]<<[C01, C02, C04, C05]. In some cases, the direct qubit-qubit coupling capacitance C24 is smaller than the coupling capacitances C12 and C45. Besides, the capacitance between qubit electrodes of the same qubit device is smaller than their capacitance to the ground plane, [C12, C34]<[C01, C02, C04, C05]. The capacitances of the qubit electrodes to the ground plane are approximately the same, e.g., C01≈C02 and C04≈C05. The capacitances between each of the furthest qubit electrodes and the coupler electrode are approximately the same, and in some cases, they are very small and can be ignored, e.g., C13=C35=0.
The inverse of the capacitance matrix C−1 can be defined as
where CΣ1, CΣc, and CΣ2 are the approximate total capacitances that define the charging energies and can be expressed as:
C
Σ1
=C
12
+C
1p/4,
C
Σc
=C
cp,
C
Σ2
=C
45
+C
2p/4. (18)
In some implementations, the qubit nodes are represented by the flux variables Φ1m and Φ2m and the tunable-frequency coupler node by Φc. The nodes represented by the flux variables Φ1p and Φ2p are “free particle” rather than a harmonic oscillator because its spring constant vanishes (e.g., there are no inductance associated with these nodes). The Hamiltonian of the system is then given by
where U is the potential energy.
H=4EC1n12+4EC2n22+4E1Cn1nc+4E2Cn2nc+4E12n1n2−EJ1 cos(ϕ1+ϕ01)−EJC cos(ϕc+ϕ0c)−EJ2 cos(ϕ2+ϕ02) (20)
where nk=−i∂/∂ϕk is the Cooper-pair number of operator and ECk=e2/(2CΣk) is the charging energy. The coupling energies EJC between the qubit devices and the coupler device, and the coupling energy between the two qubit devices E12 are given by
Note that the direct qubit-qubit coupling (E12) in Equation (21) has two terms. The first term, containing C23C34, describes the coupling mediated by the tunable-frequency coupler device 906, while the second term, containing C24Ccp, is due to the direct capacitive coupling between the qubit electrodes of the two tunable-frequency qubit devices 902, 904. In some cases, since Ccp»[C23, C34], the second term can have significant contribution even if C24 is negligible compared to C23, C34. The capacitance C24 plays a key role in achieving a vanishing direct qubit-qubit coupling.
Introducing annihilation and creation operators for a harmonic oscillator as
n
k
=in
k
zpf(ak†−ak)
φk=φkzpf(ak†+ak), k∈{1,2,c} (22)
where nkzpf and φkzpf are the zero-point fluctuations and are given by
where [ak, ak†]=1. The Hamiltonian can then be expressed in the harmonic oscillator basis (up to six orders in the cosine expansion) as
where the frequencies of the first and second tunable-frequency qubit devices 902,904 and the tunable-frequency coupler device 906 are:
and the coupling rates are
where gkc are the qubit-coupler couplings and g12 is the direct qubit-qubit capacitive coupling. The qubit-coupler couplings are directly proportional to the coupling energies EJc, which in turn is proportional to C23 and/or C34. Thus, these couplings can be controlled by varying C23 and/or C34. The correction terms 1−(ξc+ξk)/8 are due to the qubits' nonlinearities. The coupling rate g12, which is positive for a grounded tunable-frequency coupler device, compensates the effective qubit-qubit coupling mediated by the coupler to achieve a vanishing qubit-qubit coupling.
Although the tunable-frequency qubit devices 902, 904 are coupled to the tunable-frequency coupler device 906, the coupling can be turned off at the idle point by tuning the transition frequency of the tunable-frequency coupler device 906 by tuning the magnetic flux to a parking value. The coupling can be tuned on, when two-qubit quantum logic gates are applied, by tuning the transition frequency of the tunable-frequency coupler device 906. In some implementations, the transition frequency is tuned by tuning the magnetic flux to a gate-activating value that maximizes the coupling or the fidelity. Approximating the first and second tunable-frequency qubit devices 902, 904 and the tunable-frequency coupler device 906 by their respective first three energy levels, the Hamiltonian of the system can be written as
where σk=|0k
1|+√{square root over (2)}|1
k
2| and ωk and ηk are the |0
→|1
transition frequency and anharmonicity of the qubit devices, respectively. Applying the Schrieffer-Wolff transformation and assuming the tunable-frequency coupler device remains in the grounded state
σzc
=−1, which is valid in the dispersive regime
the effective qubit-qubit Hamiltonian can be expressed as
where ω01,k and ω02,k are dressed qubit frequencies and the qubit-qubit coupling rates are given by
The interaction described by the Hamiltonian allows activating two-qubit quantum logic gates. The iSWAP gate is activated by modulating the transition frequency of the second tunable-frequency qubit device 904 such that a time average of the transition frequency of the second tunable-frequency qubit device 904, which has a higher maximum transition frequency, is on resonance with a transition frequency of the first tunable-frequency qubit device 902. In some cases, the transition frequency of the first tunable-frequency qubit device 902 can be tuned to a maximum frequency value (ωmax), a minimum frequency value (ωmin), or another frequency value. In the case of controlled-Z (CZ) gates, the time average of the modulated |1→|2
transition frequency of the second tunable-frequency qubit device 904 is brought on resonance with the |0
→|1
transition frequency of the first tunable-frequency qubit device 902. During operation of the two-qubit quantum logic gate, the magnetic flux applied to the tunable-frequency coupler device 906 is tuned to a gate-activating value such that the total coupling is turned on, enabled, or activated. During the idle time, the magnetic flux applied to the tunable-frequency coupler device 906 is tuned to a parking value so that the total coupling is turned off, deactivated, or vanished. In some case, the tunable-frequency coupler device 906 can be parked at a magnetic flux that gives a vanishing ZZ-coupling between the first and second tunable-frequency qubit devices 902, 904. In certain instances, the ZZ coupling can be measured by preparing both qubit devices in their excited states and measuring the accumulated phase in qubit state |11
.
When the magnetic flux on the tunable-frequency coupler device 906 is at a parking value, the total coupling of an XX coupling or a ZZ coupling between the two tunable-frequency qubit devices 902, 904 can be turned off, deactivated, or vanished (e.g., less than or equal to a predetermined threshold value). When the magnetic flux on the tunable-frequency coupler device 906 is at a gate-activating value different from the parking value, the total coupling between the two tunable-frequency qubit devices 902, 904 can be turned on, enabled, or otherwise activated for performing a two-qubit quantum logic gate or another multi-qubit quantum logic gate. In other instances, operation for determining the parking value and the gate-activating value of the magnetic flux on the tunable-frequency coupler device 906 in a superconducting quantum processing unit 900 can be implemented with respect to operation of the example process 1100 shown in
→|1
transition frequency (at zero flux bias) of 3.630 GHz (a maximum value of the transition frequency, ωmax/2π=3.630 GHz), a |1
→|2
transition frequency (at zero flux bias) of 2.924 GHz (a minimum value of the transition frequency ωmin/2π=2.924 GHz), and anharmonicity (at zero flux bias) of 205 MHz. Qubit device Q2 represents the second tunable-frequency qubit device 814, which has a |0
→|1
transition frequency (at zero flux bias) of 3.654 GHz (a maximum value of the transition frequency, ωmax/2π=3.654 GHz), a |1
→|2
transition frequency (at zero flux bias) of 3.05 GHz (a minimum value of the transition frequency, ωmin/2π=3.05 GHz), and anharmonicity (at zero flux bias) of 239 MHz. Coupler device Qc represents the tunable-frequency coupler device 816, which has a |0
→|1
transition frequency (at zero flux bias) of 5.740 GHz (a maximum value of the transition frequency, ωmax/2π=5.740 GHz). The qubit-coupler coupling √{square root over (g1Cg2C)} is 83.9 MHz and the qubit-qubit coupling g12 is 4.66 MHz. In some implementations, the device parameters and coupling rates shown in
by applying a qubit drive signal (e.g., a π pulse), while the second tunable-frequency qubit device Q2 is in its ground state. The transition frequency of the second tunable-frequency qubit device is tuned by modulating the flux bias (flux pulses) applied on the second tunable-frequency qubit device Q2 at a flux modulation frequency. In some implementations, a flux modulation frequency of the flux modulation signal applied on the second tunable-frequency qubit device Q2 is greater than a value that is required for activating activates interactions between the first tunable-frequency qubit device Q1 and the second tunable-frequency qubit device Q2. In some instances, the flux modulation frequency can be 300 MHz (e.g., as shown in plot 700 of
As shown in
For example, an iSWAP gate can be activated when the time average of the transition frequency of the |0→|1
transition (
f01T
) of the second tunable-frequency qubit device 814 under flux modulation is brought on resonance with the transition frequency of the |0
→|1
transition (a) of the first tunable-frequency qubit device 812 without flux modulation (e.g., at operating point 1310 between the tunable |0
→|1
transition frequency of the second tunable-frequency qubit device 814 represented by curve 1326 and the |0
→|1
transition frequency of the first tunable-frequency qubit device 812 represented by curve 1322).
Similarly, a CZ02 gate is activated when the time average of the modulated |0→|1
transition frequency (
f01T
) of the second tunable-frequency qubit device 814 under flux modulation is brought on resonance with the |1
→|2
transition frequency (f12T
→|1
transition frequency of the second tunable-frequency qubit device 814 represented by curve 1326 and the |1
→|2
transition frequency of the first tunable-frequency qubit device 812 represented by curve 1324.
In some cases, to activate an iSWAP gate, the transition frequency of the second tunable-frequency qubit device 814 can be modulated at any available frequency that can be provided by a signal source (e.g., a flux pulse source as part of the signal hardware 104B of the control system 105B in
In some instances, the flux modulation frequency can be fixed and the modulation amplitude can be varied to generate the chevron. For example, a flux modulation frequency of ωm/2π=300 MHz of the flux modulation signal applied to the second tunable-frequency qubit device 814 can be used to activate an iSWAP gate; a coupler flux bias of Φc=0.336Φ0 is used to enable the coupling between the first and the second tunable-frequency qubit device 812, 814; and a chevron measurement can be performed to determine the flux modulation amplitude of the flux modulation signal applied to the second tunable-frequency qubit device 812.
In some implementations, the flux modulation frequency (e.g., ωm=0) can be zero. In this case, a value of the flux modulation amplitude can be tuned to activate a respective two-qubit quantum logic gate. As shown in plot 1320 of
has been prepared. As shown in the plot 700, experimentally measured chevrons are associated with the XY interaction. The first qubit device qubit 1 (e.g., the second tunable-frequency qubit device 814 in
while the second qubit device qubit 2 (e.g., the first tunable-frequency qubit device 812 in
.
As shown in
In some implementations, one or more operations in the example process 1500 can be performed by a computer system, for instance, by a digital computer system having one or more digital processors (e.g., a microprocessor or other data processing apparatus) that execute instructions (e.g., instructions stored in a digital memory or other computer-readable medium), or by another type of digital, quantum, or hybrid computer system. As an example, in some cases the superconducting quantum processing unit can be deployed as the superconducting quantum processing unit 102 shown in
At 1502, device parameters are obtained. The device parameters representing the quantum circuit devices (e.g., the two qubit devices and the coupler device) in a superconducting quantum processing unit can be determined by performing a measurement or characterization process, a calibration process, or another type of process. In some implementations, the device parameters may include one or more of the device parameters of the two qubit devices, and the coupler device in the superconducting quantum processing unit. For example, device parameters as shown in the table 1000 of
At 1504, control parameters of control signals for applying a two-qubit quantum logic gate on qubits are determined. The qubits are defined by the two qubit devices in the quantum processing unit. In some instances, a flux modulation frequency and a flux modulation amplitude of the flux modulation signal applied on a first qubit device, a qubit flux bias applied on a second qubit device (e.g., when the second qubit device is a tunable-frequency qubit device), a coupler flux bias for coupling and decoupling the first and second qubit devices, and a gate time are determined. As shown in
At 1510, a qubit flux bias applied on the first qubit device is modulated with a flux modulation frequency and a time average of the transition frequency of the first qubit device is determined. In some instances, operation 1510 can be used to determine the curves 722, 726 of
At 1512, the flux modulation frequency of the qubit flux bias is computed as a function of a flux modulation amplitude of the first qubit device. In some implementations, the flux modulation frequencies corresponding to the iSWAP, CZ20 and CZ02 gates are determined using
At 1514, a value of the flux modulation amplitude at which the time average of the |0→|1
transition frequency of the first qubit device which is on resonance with the |1
→|2
transition frequency of the second qubit device is identified. For example, the value of the flux modulation amplitude can be determined based on the plot 1320 of
In some implementations, the value of the flux modulation amplitude of the flux modulation signal applied on the first qubit device can be determine by performing a chevron measurement. In some implementations, once the flux modulation frequency is determined, the flux modulation amplitude of the flux modulation signal can be selected according to results from a chevron measurement (e.g., the plot 1400 in
At 1516, a gate time is determined. In some instances, the gate time may be determined based on a coupler flux bias applied on the tunable-frequency coupler device. For example, a gate time can be determined according to the plot 1200 of
In some implementations, total coupling strength of the two qubit devices are measured. In some instances, the total coupling strength of the two qubit devices is measured at different values of a coupler flux bias applied to the coupler device. For example, a first value of the coupler flux bias can be applied to the coupler device to tune the frequency of the tunable-frequency coupler device to a maximal value. When the coupler device is tuned to the maximal value, a π pulse can be applied to one of the two qubit devices and an oscillation of a population of the other one of the two tunable-frequency qubit devices can be measured. In some instances, the total coupling strength at the first value of the coupler flux bias may be determined according to the oscillation period. This process is repeated as coupler flux bias is varied from the first value to a second value of the coupler flux bias causing coupler device to park at the minimal frequency. In some instances, the total coupling strength as a function of the coupler flux bias may be determined using a different control signal or in another manner. In some instances, a total XX coupling can be determined.
In some instances, a parking value of the coupler flux bias is identified. In some instances, the parking value of the coupler flux bias is identified as the value of the coupler flux bias at a vanishing total coupling strength, e.g., g=0 or g≤g01,th. In certain instances, the predetermined threshold value (e.g., g oi, th) of the total coupling strength is determined according to a performance parameter, e.g., a gate fidelity. For example, a different gate fidelity value may result in a different threshold value for the total coupling strength.
In some instances, a gate-activating value of the coupler flux bias can be also identified. In certain examples, when the frequency of the coupler device is greater or less than both of the frequencies of the two qubit devices, the gate-activating value of the coupler flux bias is a value of the coupler flux bias that causes the total coupling strength to reach a local maximal value. In some instances, when the coupler device includes asymmetric Josephson junctions and its minimum frequency is greater than both the frequencies of the two qubit devices, the gate-activating value of the coupler flux bias is a value that causes the coupler device to park at the minimal frequency or another value.
In some implementations, the values of the control parameters of the control signal that are applied to the flux bias element can be determined according to the values of the coupler flux bias to be achieved. In some instances, the values of the control parameters of the control signal that are applied to the flux bias element can be determined using a measurement process, a calibration process, or another type of process. In some implementations, the values of the control parameters of the control signal are determined according to the design of the other quantum circuit devices in the superconducting quantum processing unit.
In some instances, the control signal can be applied to the first and second qubit devices to bring the first and second qubit devices on resonance with each other, for example, by tuning the qubit flux bias on a superconducting circuit loop of one of the two qubit devices to tune the transition frequency of the one of the two qubit devices. When the control signals are applied on the first and second qubit devices, a coupling of the first and second tunable-frequency qubit devices is allowed to evolve for a predetermined time period. In some examples, a time evolution of initial states of the first and second qubit devices is determined by a unitary operation that is applied to the first and second qubit devices within the predetermined time period. The predetermined time period is an evolution time or a gate time.
In some implementations, the coupler flux bias applied to the coupler device can be optimized to minimize the leakage from the states of the qubit devices to the tunable-frequency coupler device. For example, the coupler flux bias (flux pulses) can be a bipolar flux pulse, which is shaped to have a positive amplitude for part of the gate time, and a negative amplitude for the rest of the gate time such that the qubit is insensitive to flux noise, thus improving dephasing time and performance of two-qubit quantum logic gates.
where a is the amplitude of the flux pulse (dimensionless quantity), τr is the pulse rise time in nanosecond (ns), and τp is the pulse length in ns.
In some implementations, a bipolar flux pulse can be asymmetric and has net-zero flux during a period. As shown in
In some other implementations, one or two tunable-frequency qubit devices are modulated with two tones (e.g., bichromatic modulation). The bichromatic modulation generates dynamical sweet spots where the qubit is first order insensitive to slow flux noise and as a consequence where the dephasing time is not limited by slow flux noise. A two-qubit quantum logic gate can be activated at dynamical sweet spots by optimizing the bichromatic parameters to get the time average of the transition frequencies of a tunable-frequency qubit device on resonance with the transition frequency of another tunable-frequency qubit device or a fixed-frequency qubit device. This two-qubit quantum logic gate is protected from slow flux noise and can reach high fidelity. In certain implementations, the bichromatic modulation is optimized to maximize the sideband weight in order to minimize the gate time. In some other implementations, the flux pulse is optimized to maximize the gate fidelity of the two-qubit quantum logic gate.
In some implementations, the superconducting quantum processing unit may include a superconducting circuit that includes quantum circuit devices. The quantum circuit devices may include, for example, tunable-frequency qubit devices, fixed-frequency qubit device, tunable-frequency coupler devices, readout resonator devices, control lines, connections (e.g., capacitive coupling, galvanic coupling, inductive coupling, or combinations thereof), and other types of circuit devices. For instance, the example process 1700 shown in
In some implementations, one or more operations in the example process 1700 can be performed by a computer system, for instance, by a digital computer system having one or more digital processors (e.g., a microprocessor or other data processing apparatus) that execute instructions (e.g., instructions stored in a digital memory or other computer-readable medium) to perform the example process 1700, or by another type of digital, quantum, or hybrid computer system. As an example, in some cases the superconducting quantum processing unit can be deployed as the superconducting quantum processing unit 102 shown in
At 1702, the tunable-frequency coupler device is tuned by changing a coupler flux bias from a parking value to a gate-activating value. In some instances, the parking value and the gate-activating value of the coupler flux bias applied to the tunable-frequency coupler device may be obtained with respect to operations of the example process 1500 shown in
At 1704, a two-qubit quantum logic gate is applied. The two-qubit quantum logic gate is applied on qubits defined by the first tunable-frequency qubit device and the second tunable-frequency qubit device. In some instances, values of control parameters for a control signal are obtained and stored in a database. For example, control parameters of control signals (e.g., flux modulation frequency and amplitude of a flux modulation signal applied on the second tunable-frequency qubit device, a qubit flux bias applied on the first tunable-frequency qubit device, and a coupler flux bias applied on the tunable-frequency coupler device, or other control parameters) can be obtained with respect to operations of the example process 1500 in
In some implementations, the control information may be converted to one or more control signals by operation of a processing unit. The control signal, which can be implemented as the control signals 206, can be communicated by operation of a control system, e.g., the control system 202 in
In some implementations, the control signal may be used to operate devices in the superconducting quantum processing unit, including the tunable-frequency qubit devices, the tunable-frequency coupler devices, readout resonator devices, bias devices, flux bias elements, or another type of component in the superconducting quantum processing unit, e.g., the superconducting quantum processing unit 102 of the quantum computing system 103 as shown in
In some implementations, the control signal is a current signal, a voltage signal, or another type of electrical signal that is used to control the magnetic flux applied to tunable-frequency qubit devices in a superconducting quantum processing unit, e.g., the tunable-frequency qubit device 512, 812, 814, 902, 904, 1912, 1914 in
At 1706, the tunable-frequency coupler device is tuned by changing the coupler flux bias from the gate-activating value to the parking value, after applying the two-qubit quantum logic gate. In some implementations, the tunable-frequency coupler devices are tuned by changing the coupler flux bias to its parking value which causes the tunable-frequency coupler device to park at a designated frequency value (e.g., the maximum) of the transition frequency of the tunable-frequency coupler device. In this case, the control signals are used to control a coupler flux bias applied to the tunable-frequency coupler device (e.g., the tunable-frequency coupler device 816, 906, 1916 in
Qubit electrodes of the tunable-frequency qubit devices 1802A, 1802B, 1802C, 1802D, 1802E are configured to form couplings with different superconducting circuit elements as shown in the example superconducting quantum processing unit 1800. For example, the qubit electrodes of the tunable qubit devices 1802A, 1802B, 1802C, 1802D, 1802E are configured to form couplings with the respective tunable-frequency coupler devices 1804A, 1804B, 1804C, 1804D in both X and Y directions. In some instances, the qubit electrodes are also configured to form coupling with other superconducting circuit elements, for example, Purcell filter devices, readout resonator devices, etc. The qubit electrodes of the tunable-frequency qubit devices 1802A, 1802B, 1802C, 1802D, 1802E and the coupler electrodes of the tunable-frequency coupler devices 1804A, 1804B, 1804C, 1804D may be implemented as the respective electrodes 822A, 822B, 824A, 824B, and 826 in
In the example shown in
In some implementations, when operating a two-qubit quantum logic gate in the example superconducting quantum processing unit 1800, the tunable-frequency coupler device is tuned by changing the coupler flux bias applied to the tunable-frequency coupler device from a parking value to a gate-activating value. While the coupler flux bias is at the gate-activating value, one or more control signals can be applied to one or more of the first and second tunable-frequency qubit devices to perform the two-qubit quantum logic gate on qubits defined by the first and second tunable-frequency qubit devices. After the two-qubit quantum logic gate is performed, the tunable-frequency coupler device is tuned by changing the coupler flux bias from the gate-activating value to the parking value. In some implementations, operations of the superconducting quantum processing unit to perform a quantum logic gate may be performed using operations in the example process 1700 shown in
In some examples, the first and second tunable-frequency qubit devices 1912, 1914 and the tunable-frequency coupler device 316 may be implemented by other types of systems, and the features and components represented in
Each of the first and second tunable-frequency qubit devices 1912, 1914 and the tunable-frequency coupler device 1916 includes a superconducting circuit loop that has two Josephson junctions connected in parallel. Particularly, the first tunable-frequency qubit device 1912 includes a first superconducting circuit loop 1932; the second tunable-frequency qubit device 1914 includes a second superconducting circuit loop 1934; and the tunable-frequency coupler device 1916 includes a third superconducting circuit loop 1936. In some implementations, each of the first, second, and third superconducting circuit loops 1932, 1934, and 1936 can be inductively coupled to (has a mutual inductance with) a respective control line, which can individually tune a magnetic flux in a respective superconducting circuit loop. The control lines are connected to an external control system (e.g., the control system 202 in
As shown in
In some examples, a shunt capacitor can be formed between two qubit electrodes from the same superconducting quantum circuit device. In some instances, a residual capacitor can be formed between two qubit electrodes from two distinct superconducting quantum circuit devices forming a capacitive coupling between the two distinct superconducting quantum circuit devices. In some instances, a residual capacitor can be formed between a qubit electrode of the first tunable-frequency qubit device 1912 and a qubit electrode of the second tunable-frequency qubit device 1914. Therefore, a static capacitive coupling (g12) between the first and second tunable-frequency qubit devices 1912, 1914 includes two components, e.g., a direct capacitive coupling component and an indirect capacitive coupling component. In some instances, the direct capacitive coupling component is caused by the capacitance formed between qubit electrodes 1922A/1922B of the first tunable-frequency qubit device 1912 and qubit electrodes 1924A/1924B of the second tunable-frequency qubit device 1914. In some instances, the indirect capacitive coupling component is a capacitive coupling mediated by the tunable-frequency coupler device 1906. The indirect capacitive coupling component is caused by the capacitances formed between coupler electrodes 1926A/1926B of the tunable-frequency coupler device 1916 and qubit electrodes 1922A/1922B/1924A/1924B of the first and second tunable-frequency qubit devices 1912, 1914.
The example superconducting quantum processing unit 1900 shown in
The example superconducting quantum processing unit 2000 may include additional or different features and components, which may be configured in another manner. For example, the example superconducting quantum processing unit 2000 includes other superconducting quantum circuit devices, e.g., readout resonator devices associated with each of the multiple tunable-frequency qubit devices 2002 for performing readout operations. For another example, the example superconducting quantum processing unit 2000 may include control lines (e.g., flux bias control lines and/or qubit drive lines) for providing control signals (e.g., to activate or deactivate coupling between a pair of neighboring tunable-frequency qubit devices 2002) and performing multi-qubit quantum logic gates. In some implementations, each of the multiple tunable-frequency qubit devices 2002 has a dedicated flux bias control line. In some instances, each of the multiple tunable-frequency qubit devices has the flux bias control line combined with a qubit drive line. In some implementations, the tunable-frequency qubit devices 2004 and the tunable-frequency coupler devices 2004 in the example superconducting quantum processing unit 2000 may be operated with respect to the operations described in the example process 300, 1500, 1700 as shown in
In some implementations, the tunable-frequency qubit devices 2102 and the tunable-frequency coupler devices 2104 in the example superconducting quantum processing unit 2100 may be operated with respect to the operations described in the example process 300, 1500, 1700 as shown in
In some instances, the methods and techniques presented here can be used to improve the performance of parametrically activated multi-qubit quantum logic gates by reducing the gate time while taking advantage of the selectivity of parametric gates. The methods and techniques presented in this disclosure enable activation of two-qubit quantum logic gates without a reduction of the coupling rates. In some implementations, all the two-qubit quantum logic gates as well as other types of multi-qubit quantum logic gates on different qubit devices can be activated at a single flux modulation frequency value. In this case, sensitive to the frequency dependent transfer function that could lead to chevron distortion which can negatively impact the performance of the multi-qubit quantum logic gates can be reduced.
In the example shown in
The tunable-frequency coupler device 2206 includes two Josephson junctions, e.g., a third Josephson junction 2236A and a fourth Josephson junction 2236B. The third and fourth Josephson junctions 2236A, 2236B having Josephson energies EJSC and EJLC are connected in parallel with each other to form a third superconducting circuit loop 2216. The tunable-frequency coupler device 2206 also includes a shunt capacitor 2226 with a capacitance CC, which is connected in parallel with the two Josephson junctions 2236A, 2236B. The shunt capacitor 2226 is caused by two electrodes of the tunable-frequency coupler device 2206. In this case, each of the two electrodes of the tunable-frequency coupler device 2206 is a capacitively coupled to the ground plane; and the tunable-frequency coupler device 2206 is electrically floating.
The fixed-frequency qubit device 2204 includes one Josephson junctions, e.g., a fifth Josephson junction 2234. The fifth Josephson junction 2234 having a Josephson energy Ej2 are connected in parallel with a shunt capacitor 2224 with a capacitance C2. The shunt capacitor 2224 is caused by two qubit electrodes of the fixed-frequency qubit device 2204.
In the example shown in
As shown in
In some implementations, control operations can be performed on the superconducting circuit by providing control signals to the tunable-frequency qubit device 2202 and the fixed-frequency qubit device 2204 and the tunable-frequency coupler device 2206 via control lines. The control lines can receive the control signals, for example, from an external control system. In some implementations, each of the control lines can be connected to a conductor, an inductor, or another type of circuit component configured to carry a respective current I from a respective current source 2254A, 2254B, which generates a respective magnetic flux Φ(t) through the superconducting circuit loops 2212, 2216. For instance, the control line may include an inductor 2256A, 2256B (e.g., a partial loop, a single loop, or multiple loops of a conductor) that has a mutual inductance with the respective superconducting circuit loop 2212, 2216. In the example shown, the transition frequency of the tunable-frequency qubit device 2202 is tuned by tuning a magnetic flux in the first superconducting circuit loop 2212; and the transition frequency of the tunable-frequency coupler device 2206 is tuned by tuning a magnetic flux in the second superconducting circuit loop 2216. In some instances, the transition frequencies may be controlled in another manner, for instance, by another type of control signal. In some implementations, the control lines may be connected to an inductance loop or another type of flux bias element that is coupled (e.g., conductively, capacitively, or inductively) to a control port to receive control signals. In certain instances, the control signals on the control lines may cause the flux bias element to generate and modulate the magnetic flux in the superconducting circuit loop 2212, 2216. In some implementations, the control signals on the control line are flux bias signals or flux modulation signals, and are implemented as the control signals 206 as shown in
In some implementations, when the tunable-frequency qubit device 2202 and the fixed-frequency qubit device 2204 are coupled through the tunable-frequency coupler device 2206, the coupling between the tunable-frequency qubit device 2202 and the fixed-frequency qubit device 2204 can be enabled/disabled by tuning a magnetic flux applied to the tunable-frequency coupler device 2206. For example, a separate control signal (e.g., a DC or an AC current) can be applied to a control line to tune the magnetic flux threading to the superconducting circuit loop 2216 of the tunable-frequency coupler device 2206 to adjust the transition frequency of the tunable-frequency coupler device 2206. When the magnetic flux on the tunable-frequency coupler device 2206 is at a parking value, the coupling between the two tunable-frequency qubit devices 2202, 2204 can be turned off or deactivated. When the magnetic flux on the tunable-frequency coupler device 906 is at a gate-activating value, the coupling the tunable-frequency qubit device 2202 and the fixed-frequency qubit device 2204 can be activated for performing a two-qubit quantum logic gate. In some instances, operation for activating and deactivating the tunable-frequency coupler device 2206 can be implemented with respect to the example process 1700 shown in
In some implementations, the tunable-frequency qubit device 2202 includes highly asymmetric Josephson junctions (e.g., EJS1«EJL1) that form the superconducting circuit loop 2212. The tunable-frequency coupler device 2206 includes symmetric Josephson junctions or asymmetric Josephson junctions. In some implementations, a tunable-frequency coupler device 2206 with asymmetric Josephson junctions allows operating two-qubit quantum logic gates by tuning the transition frequency of the tunable-frequency coupler device 2206 to a minimal value to obtain gate stability against flux fluctuations. The strong asymmetry can result in much smaller tunability of the tunable-frequency qubit device 2202 than that of the tunable-frequency coupler device 2206. The systems and techniques presented here can reduce sensitivity of the tunable-frequency qubit device 2202 to flux noise thereby improving their coherence times.
In some implementations, when the tunable-frequency coupler device 2206 is in the ground state, the net qubit-qubit system can be described by the following Hamiltonian:
where g is the effective qubit-qubit coupling; g12 is the direct qubit-qubit coupling via the residual capacitor 2258; g1c is the coupling between the tunable-frequency coupler device 2206 and the tunable-frequency qubit device 2204 via the residual capacitor 2248A; g2c is the coupling between the tunable-frequency coupler device 2206 and the fixed-frequency qubit device 2204 via the residual capacitor 2248B; and ωj (j=1, 2, c) are the respective transition frequencies of the tunable-frequency qubit device 2202, the fixed-frequency qubit device 2204, and the tunable-frequency coupler device 2206.
In some implementations, a two-qubit quantum logic gate can be applied to qubits defined by the tunable-frequency qubit device 2202 and the fixed-frequency qubit device 2204 of the example superconducting quantum processing unit 2200. In some instances, a flux modulation signal can be generated and communicated to the tunable-frequency qubit device 2202. The flux modulation signal is configured to modulate a transition frequency of the tunable-frequency qubit device 2202 such that an average frequency of the tunable-frequency qubit device 2202 over a duration of the flux modulation signal is on resonance with the transition frequency of the fixed-frequency qubit device 2204 in the superconducting quantum logic circuit 2200. In some instances, the tunable-frequency coupler device can be tuned from a parking value (operating point 2304 as shown in
For example, an iSWAP gate can be activated when the time average of the transition frequency of the |0→|1
transition of the tunable-frequency qubit device 2202 under flux modulation is brought on resonance with the transition frequency of the |0
→|1
transition of the fixed-frequency qubit device 2204 (e.g., at operating point 2410 between the tunable |0
→|1
transition frequency of the tunable-frequency qubit device 2202 represented by curve 2426 and the |0
→|1
transition frequency of the fixed-frequency qubit device 2204 represented by curve 2422).
Similarly, a CZ20 gate is activated when the time average of the modulated |0→|1
transition frequency of the tunable-frequency qubit device 2202 under flux modulation is brought on resonance with the |1
→|2
transition frequency of the fixed-frequency qubit device 2204 (e.g., at operating point 2412 between the tunable |0
→|1
transition frequency of the tunable-frequency qubit device 2202 represented by curve 2426 and the |1
→|2
transition frequency of the fixed-frequency qubit device 2204 represented by curve 2424).
In some cases, to activate an iSWAP gate, the transition frequency of the tunable-frequency qubit device 2202 can be modulated at any available frequency that can be provided by a signal source (e.g., a flux pulse source as part of the signal hardware 104B of the control system 105B in
In some instances, the flux modulation frequency can be fixed and the modulation amplitude can be varied to generate the chevron. For example, a flux modulation frequency of ωm/2π=300 MHz of the flux modulation signal applied to the second tunable-frequency qubit device 814 can be used to activate an iSWAP gate; a coupler flux bias of Φc=0.336Φ0 is used to enable the coupling between the first and the second tunable-frequency qubit device 812, 814; and a chevron measurement can be performed to determine the flux modulation amplitude of the flux modulation signal applied to the second tunable-frequency qubit device 812.
In some implementations, a value of the flux modulation amplitude can be tuned to activate a respective two-qubit quantum logic gate. As shown in plot 2420 of
In some other implementations, a two-qubit quantum logic gate between the tunable-frequency qubit device 2202 and the fixed-frequency qubit device 2204 coupled via the tunable-frequency coupler device 2206 can be activated by modulating the transition frequency of the tunable-frequency coupler device 2202 at a frequency value that does not activate any sideband gate. For example, a flux modulation signal can be generated by and communicated from an AC+DC flux bias source (e.g., the current source 2254A in
Some of the subject matter and operations described in this specification can be implemented in digital electronic circuitry, or in computer software, firmware, or hardware, including the structures disclosed in this specification and their structural equivalents, or in combinations of one or more of them. Some of the subject matter described in this specification can be implemented as one or more computer programs, i.e., one or more modules of computer program instructions, encoded on a computer storage medium for execution by, or to control the operation of, data-processing apparatus. A computer storage medium can be, or can be included in, a computer-readable storage device, a computer-readable storage substrate, a random or serial access memory array or device, or a combination of one or more of them. Moreover, while a computer storage medium is not a propagated signal, a computer storage medium can be a source or destination of computer program instructions encoded in an artificially generated propagated signal. The computer storage medium can also be, or be included in, one or more separate physical components or media.
Some of the operations described in this specification can be implemented as operations performed by a data processing apparatus on data stored on one or more computer-readable storage devices or received from other sources.
The term “data-processing apparatus” encompasses all kinds of apparatus, devices, and machines for processing data, including by way of example a programmable processor, a computer, a system on a chip, or multiple ones, or combinations, of the foregoing. The apparatus can include special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit). The apparatus can also include, in addition to hardware, code that creates an execution environment for the computer program in question, e.g., code that constitutes processor firmware, a protocol stack, a database management system, an operating system, a cross-platform runtime environment, a virtual machine, or a combination of one or more of them.
A computer program (also known as a program, software, software application, script, or code) can be written in any form of programming language, including compiled or interpreted languages, declarative or procedural languages, and it can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, object, or other unit suitable for use in a computing environment. A computer program may, but need not, correspond to a file in a file system. A program can be stored in a portion of a file that holds other programs or data (e.g., one or more scripts stored in a markup language document), in a single file dedicated to the program, or in multiple coordinated files (e.g., files that store one or more modules, sub programs, or portions of code). A computer program can be deployed to be executed on one computer or on multiple computers that are located at one site or distributed across multiple sites and interconnected by a communication network.
Some of the processes and logic flows described in this specification can be performed by one or more programmable processors executing one or more computer programs to perform actions by operating on input data and generating output. The processes and logic flows can also be performed by, and apparatus can also be implemented as, special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit).
In a general aspect, forming, activating, and calibrating two-qubit quantum gates are performed in a superconducting quantum processing unit.
In a first example, a flux modulation signal is generated, by operation of a control system. The flux modulation signal is configured to modulate a transition frequency of a first tunable-frequency qubit device in a superconducting quantum processing unit such that a time average of the transition frequency of the first tunable-frequency qubit device over a duration of the flux modulation signal is on resonance with a transition frequency of a second qubit device in the superconducting quantum processing unit. A two-qubit quantum logic gate is applied to a pair of qubits in the superconducting quantum processing unit. When the two-qubit quantum logic gate is applied, the flux modulation signal is communicated to a flux bias control line coupled to the first tunable-frequency qubit device. The pair of qubits includes a first qubit defined by the first tunable-frequency qubit device and a second qubit defined by the second qubit device.
Implementations of the first example may include one or more of the following features. The first tunable-frequency qubit device includes a superconducting circuit loop, and a flux bias element that applies a magnetic flux to the superconducting circuit loop. When the flux modulation signal is communicated to the flux bias control line coupled the first tunable-frequency qubit device, the flux modulation signal is communicated to the flux bias element such that the magnetic flux to the superconducting circuit loop is modulated. The second qubit device includes a fixed-frequency qubit device; and the superconducting quantum processing unit includes a fixed-frequency coupler device coupled between the first tunable-frequency qubit device and the fixed-frequency qubit device. The second qubit device includes a second tunable-frequency qubit device. The superconducting quantum processing unit includes a tunable-frequency coupler device coupled between the first tunable-frequency qubit device and the second tunable-frequency qubit device. The transition frequency of the second qubit device is a maximum transition frequency of the second tunable-frequency qubit device. When the two-qubit quantum logic gate is applied, a flux bias signal is communicated to a flux bias control line coupled to the second tunable-frequency qubit device. The flux bias signal is configured to tune the transition frequency of the second tunable-frequency qubit device to the maximum transition frequency.
Implementations of the first example may include one or more of the following features. The first tunable-frequency qubit device further includes a qubit drive line. When the two-qubit quantum logic gate is applied to the pair of qubits, a microwave drive signal is generated by operation of the control system; and the microwave drive signal is communicated to the first tunable-frequency qubit device on the qubit drive line. The first tunable-frequency qubit device includes a tunable-frequency transmon device.
Implementations of the first example may include one or more of the following features. The flux modulation signal is defined by a flux modulation amplitude and a flux modulation frequency. When the flux modulation signal is generated, a value of the flux modulation frequency and a value of the flux modulation amplitude of the flux modulation signal is determined by operation of the control system. The superconducting quantum processing unit includes a third qubit device. The third qubit device is operably coupled to the first tunable-frequency qubit device. The value of the flux modulation frequency does not activate an interaction between the first tunable-frequency qubit device and the third qubit device. The value of the flux modulation frequency is not equal to a subharmonic of the difference between the time average of the transition frequency of the first tunable-frequency qubit device and the transition frequency of the second qubit device. The value of the flux modulation frequency is greater than a threshold frequency value that activates interactions between the first tunable-frequency qubit device and the second qubit device.
Implementations of the first example may include one or more of the following features. The superconducting quantum processing unit comprises a tunable-frequency coupler device coupled between the first tunable-frequency qubit device and the second qubit device. The flux modulation signal is defined by a flux modulation amplitude and a flux modulation frequency. Before the flux modulation signal is generated, a value of the flux modulation frequency and a value of the flux modulation amplitude of the flux modulation signal are determined by operation of the control system. The value of the flux modulation frequency does not activate an interaction between the first tunable-frequency qubit device and the tunable-frequency coupler device.
Implementations of the first example may include one or more of the following features. Prior to generating the flux modulation signal, a calibration process for the two-qubit quantum logic gate is performed. When the calibration process is performed, values of device parameters of the superconducting quantum processing unit are determined. When the values of the device parameters are determined, values of at least one of a range of operating frequencies and anharmonicities of the first tunable-frequency qubit device are determined. While the first and second tunable-frequency qubit devices are on resonance with each other, values of a coupling strength of the first and second tunable-frequency qubit devices are measured to determine an operating value and a parking value of a magnetic flux applied on the tunable-frequency coupler device. When the flux modulation signal is generated, a gate time for the two-qubit quantum logic gate is determined.
In a second example, a quantum computing system includes a superconducting quantum processing unit and a control system. The superconducting quantum processing unit includes a first tunable-frequency qubit device and a second qubit device. The control system is communicably coupled to the superconducting quantum processing unit. The control system is configured to perform one or more operations of the first example.
While this specification contains many details, these should not be understood as limitations on the scope of what may be claimed, but rather as descriptions of features specific to particular examples. Certain features that are described in this specification or shown in the drawings in the context of separate implementations can also be combined. Conversely, various features that are described or shown in the context of a single implementation can also be implemented in multiple implementations separately or in any suitable sub-combination.
Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. In certain circumstances, multitasking and parallel processing may be advantageous. Moreover, the separation of various system components in the implementations described above should not be understood as requiring such separation in all implementations, and it should be understood that the described program components and systems can generally be integrated together in a single product or packaged into multiple products.
A number of embodiments have been described. Nevertheless, it will be understood that various modifications can be made. Accordingly, other embodiments are within the scope of the following claims.
This application is a continuation of PCT/US2021/065086, filed Dec. 23, 2021, entitled “Applying Two-qubit Quantum Logic Gates in a Superconducting Quantum Processing Unit” which claims priority to U.S. Provisional Application No. 63/130,053 filed on Dec. 23, 2020, and entitled “Parametric Resonance Gates.” The above-referenced priority applications are hereby incorporated by reference.
Number | Date | Country | |
---|---|---|---|
63130053 | Dec 2020 | US |
Number | Date | Country | |
---|---|---|---|
Parent | PCT/US2021/065086 | Dec 2021 | US |
Child | 18338601 | US |