Patent Application
20190347576
The disclosure relates in general to the field of quantum processing devices and operation thereof. In particular, it is directed to methods of operating quantum processing devices with fixed frequency quantum circuits (e.g., superconducting qubits), coupled to a frequency-tunable coupler, as well as related devices.
Recent advances in quantum computing are making such a technology ever more relevant to industrial applications. Quantum computing makes direct use of quantum-mechanical phenomena, such as superposition and entanglement to perform operations on entangled quantum bits, i.e., states stored in quantum bits. Superconducting circuits are relatively easy to manufacture with current technologies and are thus promising candidates to further scale quantum information technologies. Today, it can be envisioned that in the near term a small quantum computer, based on a couple of hundreds of superconducting qubits with limited to no error correction, will be able to simulate quantum systems intractable to conventional computers.
Possible applications on quantum machines include the solving of hard optimization problems that are beyond the reach of classical algorithms. For example, quantum optimizations based on the variational principle are particularly appealing. In this approach, an objective function is minimized by varying a trial state which depends on a few parameters. Applications to quantum chemistry, metrology tasks or efficient error-syndrome measurements in error correction codes can notably be contemplated. Such examples of applications require the creation of initial states, as in many quantum algorithms. E.g., the initial states need be entangled over many qubits, which so far is typically achieved by applying a sequence of single and two-qubit gate operations to a ground state.
However, despite improvements in engineering quantum systems, superconducting qubits can reliably store quantum information only for a finite time, which is known as the coherence time. When the duration of the state preparation and (algorithmic) manipulation is comparable to or larger than the coherence time, the system can no longer be operated. Thus, the total time needed to run the algorithm should be shorter than the coherence time for such qubit systems. Now, the current gate operations consume a substantial amount of the coherence time of the qubits. This preparation limits the number of qubits that can be used in practice because the duration of the state preparation increases with the number of qubits, since only two qubits can typically be entangled at the same time, which conflicts with the finite coherence time available. It is therefore desirable to create states (be they initial states or subsequent states) and manipulate such states in shorter times, using a hardware-efficient multi-qubit entangling gate.
Quantum computing ideally needs a rapid and high-fidelity generation of highly entangled multi-qubit states. Shorter state preparation times would allow a quantum computer to perform with less error and be scaled to a larger number of qubits. More generally, one understands that the preparation time of the initial state of any type of computational quantum circuits should be reduced as possible.
In the field of superconducting qubits, the multi-qubit, single-step state preparation problem was so far not an issue. Indeed, the size of the systems was until recently limited to a few qubits, for which two-qubit entangling gates are affordable. For example, two-qubit gates are known, which are implemented with transmon qubits, where the qubits are coupled via a frequency tunable coupler element. In contrast to other approaches, this implementation takes advantage of the high coherence of fixed frequency qubits to generate entangled two qubit states with fidelities of more than 97%.
In particular, an architecture has been proposed, wherein two qubits are connected to a single tunable coupler (TC), by David C. McKay and co-workers (Phys. Rev. Appl. 6, 064007 (2016)). This architecture allows transitions between two states of the two qubits to be parametrically driven, by modulating the TC energy at a frequency that corresponds to the difference of the energy between the two states.
According to a first aspect, the present invention is embodied as a method of operating a quantum processing device. The device comprises n fixed-frequency quantum circuits (e.g., superconducting qubits) of distinct frequencies, where n≥3. The device further comprises a frequency-tunable coupler, designed in such a manner that its frequency can be concomitantly modulated at m frequencies, where m≥2, and wherein said m frequencies correspond, each, to a difference of energy between a respective pair of quantum states spanned by the quantum circuits. The quantum circuits are, each, coupled to the tunable coupler. The method relies on modulating the frequency of the tunable coupler concomitantly at said m frequencies. This is done so as to drive m energy transitions between connected pairs of states spanned by the quantum circuits, i.e., distinct pairs that nevertheless connect two-by-two via a same state of the system. This way, an entangled state of the quantum circuits can efficiently be achieved as a superposition of l states spanned by the quantum circuits, where l≥m.
According to another aspect, the present invention is embodied as a quantum processing device. Consistently with the above method, this device comprises n fixed-frequency quantum circuits of distinct frequencies, n≥3, as well as a frequency-tunable coupler, to which the n quantum circuits are coupled. The coupler is again designed so that its frequency can be concomitantly modulated at m frequencies, m≥2, wherein said frequencies correspond, each, to a difference of energy as defined above. The device further includes a controller, which is configured in the device so as to modulate the frequency of the tunable coupler concomitantly at said m frequencies. This way, m energy transitions between connected pairs of states spanned by the quantum circuits can be driven, in operation of the device, so as to achieve an entangled state of the quantum circuits as a superposition of l states spanned by the quantum circuits, where l≥m.
According to yet another aspect, the present invention is embodied as a quantum processing chip, where the chip comprises a plurality of cells, each including n fixed-frequency quantum circuits and a frequency-tunable coupler as in the above device. The chip further includes a controller system, which is configured in the chip to selectably modulate a frequency of signals applied to the tunable coupler of the cells. That is, the controller system is configured to concomitantly modulate the frequency of signals applied to the coupler of each cell, at m frequencies, so as to drive m energy transitions between connected pairs of states spanned by the quantum circuits in selected ones of the cells. This way, for each of the selected cells, an entangled state of the quantum circuits of this cell can be achieved as a superposition of l states spanned by the quantum circuits, l≥m, in operation of the chip.
Quantum processing devices, chips, and methods embodying the present invention will now be described, by way of non-limiting examples, and in reference to the accompanying drawings.
The accompanying figures, where like reference numerals refer to identical or functionally similar elements throughout the separate views, and which together with the detailed description below are incorporated in and form part of the present specification, serve to further illustrate various embodiments and to explain various principles and advantages all in accordance with the present disclosure, in which:
The accompanying drawings show simplified representations of devices or parts thereof, as involved in embodiments. Similar or functionally similar elements in the figures have been allocated the same numeral references, unless otherwise indicated.
The architecture previously proposed by McKay and co-workers, wherein two qubits are connected to a single tunable coupler (TC), allows transitions between two states of the two qubits to be parametrically driven, by modulating the TC energy at a frequency that corresponds to the difference of the energy between the two states. Using a system as proposed by McKay and co-workers, a transition between the states |01TM and |10TM can be accomplished by making the energy of the TC oscillate at a frequency fΔ that matches the energy difference between the two states. Similarly, transitions between the states |11TM and |00TM can be driven by using a frequency fΣ corresponding to the energy difference between |11TM and |00TM. Such oscillations of the TC energy is achieved by modulating a flux line positioned in close proximity with the TC. The solution proposed by McKay et al. accordingly allows two transitions between disconnected pairs of states (i.e., on the one hand |01TM and |10TM and, on the other hand, |11TM and |00TM) to be achieved by using distinct frequencies to modulate the frequency of the tunable coupler.
As present Inventors have discovered, novel architectures and methods of operation can be achieved, which make it possible to couple more than two quantum circuits (QCs), via a tunable coupler (TC) that can concomitantly be modulated at two or more frequencies. Interestingly, this approach allows two or more transitions to be achieved between connected pairs of states of the QC system and bring the system into a superposition of three or more of such states. Using three or more QCs allows, together with transitions between connected pairs of states of the system, more flexibility and large combinations of superpositions of states to be achieved in short times.
Various methods and devices embodying the invention are described in the following description, which is structured as follows. First, general embodiments and high-level variants are described (sect. 1). The next section addresses more specific embodiments and technical implementation details (sect. 2).
Referring to
The present “quantum circuits” 11-14, 1j are meant to be used as computational qubits. On the contrary, the tunable coupler 20 is here not meant to be used as a computational QC in the processing device, even though the coupler 20 can practically be embodied as a qubit, as discussed later. Rather, the role of the coupler 20 is merely to couple the computational QCs, to achieve the desired transitions.
At least three QCs are involved (n≥3), which are, each, coupled to the tunable coupler 20. The latter is designed so that its frequency can be concomitantly modulated at several frequencies. At least one tunable coupler 20 is involved. Yet, the entanglement circuit may possibly involve a larger array of quantum circuits, which may include more couplers 20 and/or more QCs, as discussed later, in reference to
Basically, the present method revolves around concomitantly (e.g., simultaneously) modulating (see step S20 in the flowchart of
System states refer to states spanned altogether by the QCs of the system, e.g., like the state |001TM in a system comprising three QCs, whereas states |0TM and |1TM refer to individual states of the QCs, as discussed later in detail. The pairs of states between which the transitions selectably occur are connected two-by-two, i.e., via a common state, as illustrated in the diagrams of
As exemplified later, the transitions involved are bidirectional, such that a transition between states |ATM and |BTM concurrently involves both an excitation of population from state |ATM to state |BTM and a de-excitation of population from state |BTM to state |ATM. Triggering transitions between connected pairs of multi-QC states eventually allows an entanglement between all the computational QCs involved to be achieved, as opposed to transitions between unconnected pairs of states.
Direct energy transitions between multi-QC states are contemplated. I.e., such transitions result in direct population transfers between two multi-QC states, even if they are mediated through the tunable coupler. Such transitions will normally occur concomitantly, as per the concomitant modulation of the frequency of the tunable coupler (hereafter TC). Yet, there is no reason for such transitions to be perfectly synchronous, owing to the physics involved.
The present approach leverages the high-coherence of the fixed frequency circuits and short operation times allowed by the concomitant transitions, to achieve high gate rates. This way, a number of fixed frequency QCs can be entangled within a single, short operation, such that shorter state preparation can be obtained. Namely, an entangled state of the system formed by the QCs is achieved S40 as a superposition of l states spanned by the QCs (l≥m). Examples of such entangled states are discussed later. This, in turn, makes it possible for a quantum processing device to be to be scaled to a larger number of QCs. In addition, the present approach may be leveraged for a quantum computer to perform with less error or a quantum sensor to provide a better sensitivity.
As noted above, the QCs have distinct frequencies, which makes it possible to selectively address the desired state transitions of the system, by appropriately choosing the driving frequencies. Such frequencies correspond, each, to a difference of energy between a respective pair of states of the system. I.e., such frequencies may exactly match respective energy differences or, in variants, be close enough to such differences, for the desired transitions to take place. That is, the driving of a transition can be resonant (i.e., the energy difference exactly matches the drive frequency) or slightly off-resonant (i.e., the energy difference is slightly off the drive frequency). However, since an off-resonant transition affects the fidelity of the entangled state, the drive frequency should preferably match the energy difference as exactly as possible.
As evoked above, the quantum states of the multi-QC system must be distinguished from individual quantum states of the QCs. Each of the QCs can be associated to at least two distinct, individual quantum states |aTM. E.g., each QC may be associated to an individual state that correspond to a ground state |0TM or a first excited state |1TM of this QC. On the other hand, the states spanned by the multi-QC system can be regarded as tensor products |abc . . . TM of individual QC states. However, the system states referred to above and in the following description do not involve individual quantum states of the tunable coupler. I.e., the present methods are agnostic to the actual quantum state of the coupler 20, which is not meant to be used as a computational qubit. Instead, the tunable coupler is used to mediate transitions between multi-QC states of the system.
Assuming that each QC has (at least) two distinct states, then 2n states (at least) of the multi-QC system can potentially be populated. Now, in embodiments described herein, the QCs are mostly assumed to behave as two-level subsystems, such that each QC can be in one of two states, which typically are the ground state |0TM and the first excited state |1TM of this subsystem. One may therefore consider that only 2n states of the multi-QC system can potentially be populated. For instance, each of
In practice, one may typically seek to obtain a superposition of l=m=n states of the multi-QC system. I.e., the number l of states eventually involved in the superposition would be equal to both the number n of QCs and the number m of transitions in that case. However, there are many exceptions. For example, m transitions from a same initial state (e.g., the ground state) of the QCs may lead to a superposition of l=m+1 states, this including the initial state in addition to the m target states as selectively caused by the m driving frequencies. In addition, larger superpositions can be achieved when starting from an initial state that is already a superposition (e.g., |000TM+|001TM, as discussed later in reference to
As it may be realized, the present methods make it possible to easily and quickly achieve complex multi-partite, initial entangled states of n QCs, thanks to the concomitant modulation at m frequencies. In practice, an initial entangled state may typically be achieved within less than 300 ns, i.e., in a time comparable to the time needed for a single, multi-QC state transition. The present approach can be used for various applications, such as evoked in the background section. In particular, it can be used in quantum sensing and quantum computing devices.
As illustrated in the diagrams of
Thus, at a given manifold k, C(n, k) states are potentially available for transitions with a state of another manifold. For example, at the k=2 manifold, there are C(3, 2)=3 states available for transitions with the ground state |000TM, as exemplified in
For instance, in embodiments that are later referred to as “sum transitions” and “difference transitions”, the frequency of the TC 20 is concomitantly modulated S20 at a restricted number m of frequencies. I.e., m is respectively restricted to the range C(n, k)≥m≥2 or C(C(n, k), 2) m≥2, respectively, where n corresponds to the number of QCs and n−1≥k≥1. Yet, complex entanglement operations can be contemplated, which concurrently involve sum transitions and difference transitions and require a larger number m of transitions. All this is explained in detail in the following.
For difference transitions, the selected transitions restrict to transitions permitted within a same k-excitation manifold (for n−1≥k≥1). The number of permitted transitions is limited by C(C(n, k), 2), which is the number of pairs of states available within that given manifold. Alternatively, only C(n, k) states are potentially available for sum transitions (i.e., transitions that may occur to/from a same manifold k, for n−1≥k≥1). It is noted that each of the conditions C(C(n, k), 2)≥C(n, k) and C(n, k)≥2 is systematically verified when n≥3 and n−1≥k≥1.
In detail, one may for instance select m=C(n, k) frequencies to create C(n, k) transitions, when starting from a state distinct from the C(n, k) target states of the target manifold k. This is exemplified in
The example of
In each of the examples of
In more detail, in
On the contrary, in
Note that in
In the example of
For difference transitions (i.e., intra-manifold transitions restricted within a same manifold k, as in
In the examples of
Now, mechanisms can be devised, which intermingle parallel and anti-parallel transition of individual QC states. That is, the frequency of the TC may be modulated in such a manner that some of the driven S30 energy transitions involve parallel transitions, whereas other energy transitions involve anti-parallel transitions from individual states of the QC. This point is further discussed in sect. 2.3.
In practice, the m energy transitions can be driven by applying S10 harmonic microwave signals to the TC 20, where the signals are modulated S20 so as to modulate the frequency of the TC 20 at said m frequencies. In practice, this can be achieved by combining signals so as to form pulses that are applied for a certain duration. In fact, one may set S10 the amplitudes, phases and duration of the signals applied to the TC 20, so as to control the complex weights ai (i.e., the probability amplitudes in Eq. 1, see sect. 2) of the l states in the entangled state to be eventually achieved S40. Each complex weight encompasses both an amplitude and a phase of a coefficient in the linear combination of states sought. That is, one can change the duration of the TC modulation signals, in addition to their amplitudes and phases. A suitably chosen duration of the TC modulation signals applied allows a specific entangled state to be achieved.
In practice, in order to achieve a specific entangled state, one may perform a measurement such as depicted in the LHS of
Another aspect of the invention is now described, which concerns a quantum processing device 1, 2, 3. The main features of this device have already been described in reference to the present methods and are therefore only briefly reminded here.
A. minima, this device 1, 2, 3 includes n fixed-frequency QCs 11-14, 1j, each having a distinct frequency, in addition to a tunable coupler 20, to which the QCs are coupled. At least 3 QCs are involved (n≥3). The coupler 20 is designed so that its frequency can be concomitantly modulated S20 at m frequencies, m≥2. Again, the quantum circuits are meant to be used as computational qubits, contrary to the coupling element 20. In addition, the device includes at least one controller 30, which is configured in the processing device 1, 2, 3 to modulate the frequency of the TC 20 concomitantly at said m frequencies, wherein each of the frequencies corresponds to a difference of energy between a respective pair of system states, as explained earlier. This makes it possible, in turn, to drive S30 m energy transitions between connected pairs of states spanned by the QCs and achieve an entangled state, as already discussed in reference to the present methods.
The controller 30 typically includes a control line 30 (i.e., a physical wire), to apply the signals. The controller allows multi-frequency signals to be applied and, if necessary, to suitably set amplitudes and phases of the applied signals.
As illustrated in
In all cases, the TC 20 may be capacitively coupled to each of the QCs 11-14, 1j. For example, and as illustrated in which forms a superconducting quantum interference device (SQUID) loop. In the example of
The coupling is performed by modulating the frequency of the TC 20 near or at the frequency corresponding to the desired transitions. The coupler can be regarded as formed by one or more electrodes, as well as the SQUID loop (the latter containing the two Josephson junctions). I.e., the TC 20 may for instance couple to the three (or more) transmons 11-14 via separate electrodes (the latter separated by the SQUID loop) or via a single electrode, with the SQUID loop coupling to the ground.
A final aspect of the invention is now described in reference to
A controller system 30 is used to modulate a frequency of signals applied to each TC 20, e.g., via respective control lines 30, so as to drive energy transitions in selected cells. I.e., cells can be independently operated, via a respective control line 30. However, the operation of the cells follows a logic implemented by the controller system, e.g., so as to achieve a desired superposition, which in turn allows more complex operations to be performed by the quantum processing chip 3.
This section describes several mechanisms in detail, which allows complex entangled initial states to be created in a short time. In the prior art known to the Inventors the preparation of these states is achieved, e.g., starting from the qubit's system ground state |000 . . . TM, by applying a sequence of single and two-qubit gates, in order to achieve a desired initial state |STM, i.e., a superposition of multi-qubit states. As an example of application: in order to model electronic properties of an atom or molecule, for which 4 orbitals are considered and where 2 orbitals are doubly occupied in the ground state of the system, the initial quantum state |STM of the system need be brought into a superposition of states, noted |0011TM, |0101TM, |1001TM, |0110TM, |1010TM and |1100TM, with
|STM=a1|0011TM+a2|0101TM+a3|1001TM+a4|0110TM+a5|1010TM+a6|1100TM,
where a1 . . . a6 are complex weights (i.e., probability amplitudes) that need be varied by the algorithm, e.g., to achieve an energy minimum. In an architecture with only single- and two-qubit gates, the preparation of such a state |STM, starting from the ground state |0000TM, requires a relatively large number of gate operations, which need be applied sequentially and therefore consume a significant amount of time. More generally, one understands that, in a non-error corrected hardware, the time needed for state preparation may severely limits the fidelity of the initial state.
The present section describes in detail solutions to create a selectable multi-qubit entangled state in short time, using a hardware-efficient method. To that aim, use is made of an architecture where multiple qubits (n>2) are connected to a single tunable coupler (TC), which allows m transitions between states of the coupled qubits to be parametrically driven, m≥2. This is achieved by modulating the TC energy at frequencies matching the differences in energy between the desired states of the system, by modulating a flux line close to the TC. I.e., the coupler is concomitantly modulated at m frequencies, so as to achieve the m transitions between connected pairs of states of the system and bring the latter into a superposition of l≥m states, as explained in the previous section. Of interest is that the proposed mechanism allows transitions between connected pairs of states to be achieved, whereby corresponding states can be efficiently entangled. The solutions discussed herein eventually allow more flexibility and larger combinations of superpositions of states to be achieved in short time.
With these parameters, the TC 20 can be driven at a frequency corresponding to |101TM-|000TM=8.4939 GHz to bring the |000TM state into a |101TM state (and vice versa). Similarly, a drive frequency at 9.0615 GHz=|011TM−|000TM allows a transition between the |000TM state and the |011TM state, and a drive at 9.3678 GHz=|110TM−|000TM couples the |000TM state to the |110TM state.
Simulations performed by the Inventors have shown that transitions between two selectable states can be achieved, where the selection is made by the choice of the frequency. The present solutions make use of the possibility to modulate the TC at more than one frequency simultaneously. I.e., the TC energy, noted ETC, is modulated at m different frequencies fi with amplitudes ci according to
E
TC
=E
TC,0(1+Σi=1mci exp(i2πfit)) (1)
By suitably choosing fi and ci, different transitions between the states spanned by the n qubits can be driven simultaneously, so as to create entangled states within short times. In practice, the way the flux line modulates ETC is slightly more complex than what Eq. (1) may suggest, due to the nonlinear dependence of ETC on the flux. This, however, does not affect the description that follows.
The present approach is first exemplified in
Interestingly, and as evoked earlier in sect. 1, the weights ai can be controlled by the complex amplitudes ci of the TC modulation frequencies. The individual, direct coupling strengths gQi,TC (see
More generally, n qubits in a state |..0..0TM can be driven into a superposition of m states |..1..1..TM by simultaneous application of m different frequencies to a TC, where each of the latter states has two qubits in the excited |1TM states, while all others qubits remain in the |0TM states. This can be achieved via a controllable probability density of the states by appropriately choosing the frequencies, amplitudes and phases of the signals applied, as discussed earlier. The m different frequencies preferably match (as exactly as possible) the energy difference between the states involved, i.e., |..1..1..TM and |..0..0..TM, which happens to be close to the sum of two intermediate transitions (i.e., from |..0..0..TM to |..1..0..TM and |..0..0..TM to |..0..1..TM), whence the terminology of “sum transitions”. Such transitions are characterized by parallel (de-) excitations of individual states of the qubits.
Using the above approach, the creation of the superposition state is achieved within a time that corresponds to a single 2-qubit operation (which was estimated to amount to approximately 270 ns in the example of
In the previous example, individual TC frequencies fi were chosen at energy differences of states Ai and Bi that differ in two individual qubit states, which are, say, |1TM for Ai and |0TM for Bi. In a similar way, simultaneous transitions between states Ai and Bi can be driven, which now involve anti-parallel transitions between individual qubit states. Again, individual TC frequencies fi can be chosen to match energy differences between states Ai and Bi that differ in two individual qubit states, which are now, e.g., |1TM and |0TM for Ai and |0TM and |1TM for Bi, i.e. Ai=|..1..0..TM and Bi=|..0..1..TM. Such transitions are referred to as difference transitions. Also in this scheme, the population in the states Bi can be simultaneously transferred to the states Ai and vice versa. An example is given in
Interestingly, the present approach is not restricted to either |..0..0..TM-| 1..1..TM (sum) or to |..1..0..TM-|..0..1..TM (difference) transitions. As it may be realized, both kinds of transitions can actually be driven simultaneously, facilitating the generation of even more complex superposition states in short time. As an example,
Another mode of operation is to drive transitions between any states Ai and Bi where Ai and Bi differ in two qubits. For example, m=5 transitions between Ai=|0011TM, |0101TM, |1001TM, |0110TM and |1010TM and Bi=|1100TM can be driven simultaneously to prepare arbitrary superposition states of the form a1|0011TM+a2|0101TM+a3|1001TM+a4|0110TM+a5|1010TM+a6|1100TM.
As disclosed, for example, a method of operating a quantum processing device may be provided. Related quantum processing devices and processing chips may be provided.
While the present invention has been described with reference to a limited number of embodiments, variants and the accompanying drawings, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the scope of the present invention. In particular, a feature (device-like or method-like) recited in a given embodiment, variant or shown in a drawing may be combined with or replace another feature in another embodiment, variant or drawing, without departing from the scope of the present invention. Various combinations of the features described in respect of any of the above embodiments or variants may accordingly be contemplated, that remain within the scope of the appended claims. In addition, many minor modifications may be made to adapt a particular situation or material to the teachings of the present invention without departing from its scope. Therefore, it is intended that the present invention not be limited to the particular embodiments disclosed, but that the present invention will include all embodiments falling within the scope of the appended claims. In addition, many other variants than explicitly touched above can be contemplated.
