This application claims priority to Australian Provisional Patent application AU2022900513, filed on 3 Mar. 2022 and titled, ‘Methods for qubit readout’, the entire content of which is incorporated herein in its entirety.
Aspects of the present disclosure are related to advanced processing systems and in particular to methods for readout in advanced processing systems.
The developments described in this section are known to the inventors. However, unless otherwise indicated, it should not be assumed that any of the developments described in this section qualify as prior art merely by virtue of their inclusion in this section, or that those developments are known to a person of ordinary skill in the art.
Large-scale quantum processing systems hold the promise of a technological revolution, with the prospect of solving problems which are out of reach with classical machines. To date, a number of different structures, materials, and architectures have been proposed to implement quantum processing systems and to fabricate their basic information units (quantum bits or qubits). Qubits may be understood as a two-level quantum system, where non-degenerate spin states represent the two levels.
Qubit readout—i.e., determining or measuring the state or encoded information in a qubit—is a fundamental quantum operation in quantum computing. To yield reliable readout results, it is important to measure qubit states with reasonable fidelities (usually above 99% fidelity) and to perform the readout at a speed that is faster than the spin relaxation time of the qubit. Although there are several current readout techniques, they are often prone to errors and may not yield reliable results.
Accordingly, improved techniques for measuring qubit states in quantum processing systems are desirable.
According to an aspect of the present disclosure there is provided a method for readout of a singlet-triplet qubit in a donor based quantum processing element, the method comprising the steps of: initialising the singlet-triplet qubit in a ground state |G; performing a shelving readout; using a final measured charge configuration of the singlet-triplet qubit to determine information about a current Zeeman energy difference; and using the information about the current Zeeman energy difference to adjust mapping of the shelving readout.
In one example, the determined information about the current Zeeman energy difference is the sign of the Zeeman energy difference, i.e., whether it is negative or positive.
The method of the first aspect further comprising performing a qubit operation.
In some embodiments, the donor based quantum processing element comprises: a semiconductor substrate, a dielectric material forming an interface with the semiconductor substrate, one or more gate electrodes, and a double dot system comprising two dopant dots embedded in the semiconductor substrate, each dopant dot comprising one or more dopant atoms and two or more electrons or holes confined in the double dot system.
In some examples, the two or more electrons are loaded on to the donor dots via at least one gate electrode of the one or more gate electrodes.
Further, in some embodiments, the donor atoms are phosphorus atoms.
In an example, the semiconductor substrate is silicon and the dielectric is silicon dioxide. Preferably, the semiconductor substrate is isotopically purified silicon-28 and the dielectric is silicon dioxide.
Further still, the gate of the one or more gate electrodes may be manufactured within the semiconductor substrate to control the donor dots.
In some embodiments, the spin of the two or more electrons are entangled to form a singlet state and three triplet states. Further, the singlet-triplet qubit may be encoded in the |S singlet state and a |T0
triplet state.
In some embodiments, performing the shelving readout comprises: starting the singlet-triplet qubit in a (1,1) charge configuration, moving the singlet-triplet qubit from the (1, 1) charge configuration to a (1,2) charge configuration by applying potentials to the one or more gate electrodes; moving the singlet-triplet qubit back to the (1,1) charge configuration by applying potentials to the one or more gate electrodes; and adiabatically changing ϵ to move the singlet-triplet qubit to a (0,2) charge configuration.
While the invention is amenable to various modifications and alternative forms, specific embodiments are shown by way of example in the drawings and are described in detail. It should be understood, however, that the drawings and detailed description are not intended to limit the invention to the particular form disclosed. The intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the present invention as defined by the appended claims.
As described above, it is important to establish reliable readout method for reading out the state of a singlet-triplet qubit.
Generally speaking, quantum computers provide means to solve certain computing problems that cannot be solved in a reasonable period of time using conventional, classical computers. These problems include factoring very large numbers into their primes (which on a quantum computer can be accomplished relatively quickly using Shor's algorithm), and searching large, unstructured data sets (which can be done on a quantum computer using Grover's search algorithm). These algorithms are well-understood in terms of operations that need to be performed over a few qubits.
As described previously, a number of different techniques exist to fabricate the basic information units (quantum bits or qubits) of quantum processing systems or quantum computers. One way of fabricating qubits, for example, is to use the nuclear or the electron spin of phosphorus donor atoms in silicon such that the nuclear/electron spin of each phosphorus donor atom acts as a qubit. Spin qubits based on phosphorus donors in silicon have demonstrated excellent coherence and relaxation times. These long coherence times, together with the mature fabrication technology based on scanning tunnelling microscopy, makes silicon-phosphorus systems a promising semiconductor platform for quantum information processing.
While implementation and operation of single electron qubits in Si:P using magnetic means is well established, there is still high interest in alternative qubit systems which can be controlled purely by electrical means, which can simplify the task of scaling up quantum computers.
One such electrically controllable processing element is a singlet-triplet qubit. The use of electrical control in these qubits simplifies the task of scaling up to a large-scale quantum computer as there is no need for micro-magnets to be included on the chip for magnetic addressability in such qubits. In singlet-triplet qubits, two electrostatically-defined or donor-based quantum dots, occupied by two or more electrons, are formed side-by-side and tuned so that they can be tunnel coupled. Information can be stored in the relative spin and spatial symmetry states of the two electrons, further reducing coupling of the qubit to its environment. Singlet-triplet qubits of this type typically include two electrons localized within a double quantum dot (QD) and coupled by the exchange interaction between them.
The qubit 100 includes a pair of tunnel-coupled donor atom clusters 106, 108 and two electrons 109 and 110 bound to the pair of donor atom clusters 106, 108. There may be additional electrons in the qubit 100. In certain embodiments, the donor atom clusters 106, 108 are placed in the silicon substrate 102 with atomic-scale precision using scanning tunneling lithography techniques.
The left and right quantum dots 128, 130 can each tunnel to the SET 132 via tL and tR respectively. The two quantum dots 128, 130 are also tunnel coupled via t0 allowing the electrons 140, 142 to form singlet and triplet states across both quantum dots. In general each dot 128, 130 can be occupied by an odd number of electrons. In such cases, only the behaviours of one unpaired, highest energy electron in each dot contributes to the singlet-triplet qubit formation. The SET 132 serves as an electron reservoir for the donor dots 128, 130 and is used as a charge sensor. The surrounding gates 122, 124, 126 control the electrostatic environment of the dots.
In certain embodiments, each donor cluster 106, 108 may have a single donor atom and the donor atom may be a phosphorous (P) atom such that the qubit 100 is a 1P-1P system. In other embodiments, the qubit 100 may be an nP-mP system and the donor atom clusters 106, 108 may have any other number of phosphorous donor atoms, where n=m or n≠m.
For a two-electron qubit 100 there are four possible combined spin states. Each electron has two possible spin states, spin-down and spin-up, denoted |↓ and |↑
, respectively. Combining the two spin states of each electron yields four new states. There is one singlet state with total spin angular momentum 0. This state is:
Where the first arrow and second arrow in each combination indicate the spin direction of the first and second electron respectively. There are three triplet states, each with total spin angular momentum 1:
Here, the T+ triplet states corresponds to both electrons being in the spin-up state.
Of the four possible relative spin states of the electrons (S, T0, T+, T−), information is generally stored in the S (singlet state) and T0 (a triplet state) states (the so-called ‘logical subspace’). This choice is generally motivated by two advantages. First, the two qubit states remain unaffected by changes in magnetic field (with magnetic quantum number, m=0), which further decouples them from the environment. Second, due to the Pauli Exclusion principle, in the singlet state, one electron has an orbital wavefunction hybridized between the two donors dots, and in the triplet states both electrons are confined to separate donor dots. Therefore, by tuning the relative electrochemical potentials of the two dots, the charge distribution of electrons can be tuned.
Multiple realisations of singlet-triplet qubit have been implemented in double QD and quantum dot-donor systems. Crucially, for large-scale implementations, singlet-triplet qubits 100 can be measured and/or controlled via a single gate—thereby allowing for high density scaling of the qubits. This minimal gate density allows for the qubits to be closer together and minimises the classical electronics required to operate the quantum computer.
Typically, the singlet-triplet qubits are measured using dispersive readout. Dispersive readout works by applying a radio frequency voltage signal to a nearby gate that moves the electrons between the quantum dots. The movement of the electrons creates a changing capacitance which can be detected using a resonant circuit connected to the same gate or a reservoir. This dispersive readout allows for minimal gate densities, i.e., less gates than dots, and the possibility for frequency multiplexed qubit measurements which can be useful for large quantum systems.
To realize purely electrical control of the singlet-triplet qubit, the two quantum dots 106, 108 need to be characterized by different spin Zeeman splittings, which is caused by the interaction between a magnetic field and a magnetic dipole moment. That Zeeman energy difference, ΔEz, allows coupling between the singlet and triplet states and therefore the ability to perform qubit rotations.
In electrostatically-defined quantum dots, ΔEz can be produced by a nuclear spin bath, micro-magnets, spin-orbit interaction or difference of g-factors in two quantum dots. However, in donor-based devices the same coupling can be achieved using hyperfine interaction between electron and nuclear spins inherently present in the system. For example, each of the phosphorous donors 106 and 108 have a nuclear spin that interacts with the two electron spins. The electron-nuclear hyperfine interaction can be described as an effective magnetic field experienced by the electrons. The magnetic field can be treated as homogeneous if the hyperfine interaction is same at both dots. Alternatively, if the interaction differs between the dots then it is the magnetic field gradient that causes a difference in the Zeeman splitting, ΔEz.
Although ΔEz is desirable as it is necessary for fast singlet-triplet qubit operation, it is also a source of triplet relaxation. That is, it provides an energy pathway for the T0 triplet state to relax into another state, i.e., singlet S(0,2). The fast relaxation is the most prominent in context of the singlet-triplet qubit readout, significantly limiting the visibility of the standard Pauli spin-blockade readout (PSB). Additionally, in donor-based devices, ΔEz can change in time together with nuclear spin polarization of the donors 106 and 108, as nuclear spins can undergo uncontrolled flips. As such, these processes need to be accounted for when designing and interpreting readout outcomes for singlet-triplet qubits in donor-based devices.
One widely used singlet-triplet readout technique is called Pauli spin-blockade readout (PSBR). This method gives relatively small contrast between the singlet and triplet states since it relies on measuring the charge distribution within the double quantum dot. The PSBR method also suffers from fast triplet relaxation when singlet-triplet state mixing is present in the system.
Alternative singlet-triplet readout methods have been developed to address the shortcomings of PSBR and adjust the readout process to the needs of specific quantum dot architectures. The improved visibility of the new readout methods in comparison to PSBR is achieved via either mapping the triplet state to some metastable state which minimizes relaxation, or mapping the (1,1) and (0,2) charge configurations to states differing in total number of electrons.
One alternative readout method that may be used to overcome the limitations of PSBR is called shelving. Shelving has been demonstrated to be efficient for gate-defined quantum dot devices. In particular, the shelving readout method for donor-based devices has improved readout fidelity in comparison to the standard PSBR. Moreover, shelving is well-suited for singlet-triplet qubits subject to large magnetic field gradients, typically of the order of a few mT (ten-hundredths of MHz) of ΔEz, where ΔEz changes in time, which is a characteristic very specific to the donor-based system (in gate-defined quantum dots, ΔEz is either constant in time due to use of micro-magnets or the changes in ΔEz are not widely discussed).
Shelving readout operates in the charge occupation subspace comprising the (1,1), (0,2) and (1,2) configurations. The electron distribution between the dots is controlled with detuning ϵ while loading of additional electrons from the SET 132 is determined with a parameter γ, which represents the global energy shift of both quantum dots (QDs). Both ϵ and γ can be controlled by the leads surrounding the double-dot system. In some examples gates 122, 124, and 126 can be used to control these parameters.
The shelving readout method maps the two-electron spin states |↑↓ and |↓↑
to different charge configurations, namely (0,2) and (1,1). In particular, the shelving protocol starts in the (1,1) charge configuration region. Further, the shelving protocol starts at high detuning ϵ where the exchange is negligible and ΔEz sets the eigenstates to approximately:
|G=|↑↓
|E=|↓↑
.
As referred to here, a high detuning refers to a detuning value where exchange J gets much smaller than Zeeman energy difference ΔEz (as exchange depends on detuning while Zeeman energy difference is constant). The exact value of detuning depends on the specific values of Zeeman energy difference and how exchange depends on detuning and that the exchange detuning dependency is mainly impacted by tunnelling between the quantum dots T0. Typically, if ΔEz is hundreds of MHz and T0 is of the order of 1 GHz, detuning would be tens-hundreds GHz.
The first step, step 1, is to ramp non-adiabatically along the γ-axis in a set time period, tin, to, γmax 204 to the (1,2) charge configuration region and stay there for a second time period twait. The potentials created by control gates (e.g., gates 122, 124 and 126) are changing so that γ is effectively ramped (from some initial γ in (1,1) region to γmax in (1,2) region.
If γmax is set such that the energy level of the |↓S lies between the |↓↑
and the |↓↓
states) (see
→|↓S
→|↓↓
(indicated by the arrows denoted 2 in
state is mapped to the metastable triplet state |T−
.
The transition takes place due to the spin-down electron |↓ tunnelling from the SET 132 to the right quantum dot 130 and the spin-up electron |↑
tunnelling back to the SET 132. At the same time, the |↑↓
energy level does not undergo any transition as the |↑S
state is energetically inaccessible and no electron can tunnel from the SET 132 to the right dot 130.
At step 2, the system is brought back to the (1,1) charge configuration region 202. Then by adiabatic change of detuning ϵ, the system is moved to the Pauli-blocked region in the (0,2) charge configuration region at step 3. The potentials created by control gates (e.g., gates 122, 124 and 126) are changed such that γ is effectively ramped from γmax in (1,2) region to some γ in (1,1) region.
This is the Pauli-blocked region and is a part of (0,2) region between ϵ=0 line and the dashed line 208 below it in and |T+
) can tunnel to (0,2) and cannot be distinguished from singlet anymore.
In the absence of a magnetic field gradient, ΔEz=0, the states |G and |E
are split by the exchange interaction J and form singlet S(1,1) and triplet T0(1, 1) states, respectively. ΔEz mixes singlet and triplet states and in the limit of ΔEz>>J sets |G
=|↑↓
and |E
=|↓↑
. Otherwise, the opposite states are set for |G
and |E
for ΔEz<0.
In an intermediate regime, where J and ΔEz are comparable, the mixing of |S and |T0
(or |↓↑
and |↑↓
) strongly depends on the relative amplitudes of exchange J and ΔEz. As the exchange J is controllable with the detuning ϵ between the S(1,1) and S(0,2) states, the singlet-triplet mixing can be modulated by the detuning ϵ.
The shelving process causes |↑↓ to be mapped to the singlet (0,2) state—see
state is mapped to the blocked triplet state |T−
—of charge configuration (1,1).
Due to the long relaxation time of the |T− state, the final (0,2) and (1,1) charge configurations can be measured with better visibilities compared to the standard PSBR method. The mapping obtained via the shelving procedure can be also conveniently used with dispersive readout, which can be performed using just a single gate and thus minimizes the device complexity.
In practice, even for large detuning ϵ the |↓↑ and |↑↓
states are mixed due to the non-zero exchange J. The admixtures of the opposite states cause leakage, lowering the total readout visibility. However, the shelved readout method solves the problem of fast relaxation due to singlet-triplet mixing, as the operation takes place in (1,1)-(1,2) region where the singlet (0,2) is energetically inaccessible.
In quantum dots using a micro-magnet, the magnetic field gradient, and thus ΔEz, can be deterministically set at the beginning of the measurements and kept constant throughout the experiment. However, there are also issues with accurately designing micro-magnets with the optimal magnetic field gradient. Further, these micro-magnets take up precious space on the physical chip.
In donor-based devices, however, ΔEz originates from the different hyperfine interaction of the electron spins to each donor dot nuclei and is likely to change during the experiment. Due to the presence of nuclear spin flips, ΔEz can change both value and sign which crucially can result in a reversed mapping of the |G and |E
states.
and |T+
after shelving as a function of detuning ϵ on the x-axis and Zeeman energy difference ΔEz on the y-axis. Here γmax=0. The left plot 302 corresponds to simulations starting from the ground state |G
and the right plot 304 corresponds to simulations starting from the excited state |E
. Darker regions in both plots indicate lower probabilities of blocked triplet states and lighter regions in both plots indicate higher probability of block triplet states.
For the simulations shown in
and finish
where γmax is set exactly at the (1,1)/(1,2) transition line for every detuning, i.e., black line between regions (1,1) and (1,2) in is mapped to |T−
and eventually to the (1,1) charge configuration. While for negative values of ΔEz, the ground state |G
is mapped to |T−
.
The visibility of the readout is calculated as FG+FE−1, where FG(FE) is a final probability of charge configurations corresponding to |G (|E
) state when the initial state of the simulation has been set to |G
(|E
). For shelving, F is calculated as a sum of final probabilities of S02, |G
and |E
states FG=PS02+PG+PE, as we assume all of those states will be mapped to (0,2) charge configuration when we decrease detuning to Pauli blockaded (0,2) region and wait T0 relaxation time. FE is calculated as a sum of blocked triplet states T− and T+ probabilities.
As seen in and |↑↓
states mixing and hence less leakage.
The visibility reaches 0 for ΔEz=0 because both the |G and |E
states, now corresponding to singlet (1,1) and triplet states, respectively, can transfer to |↓S
state equally fast. The visibility is also reduced for small detuning ϵ, as in this region the exchange interaction dominates over ΔEz (the x-axis limits ϵ=0 and 100 GHz correspond to exchange J values of 2 GHz and 40 MHz, respectively).
A quasistatic nuclear polarization is assumed, which means that the nuclear spins are not flipping during single qubit operations and shelving readout. However, as the full experiment time usually reaches minutes or even hours, the nuclear spins will likely flip multiple times. In the system of two donor quantum dots we can express all possible values of ΔEz as:
Where i and j enumerate nuclear spins in left and right dots 128, 130, with total donor numbers NL, NR, respectively. ALi(ARj) is the hyperfine constant of the i-th (j-th) donor in the left (right) dots. IL
Additionally, the inventors of the present invention have found that even if nuclear polarization is changing slower than the total experiment time, it is important to know the sign of ΔEz to ensure a proper mapping of |G and |E
to (0,2) and (1,1) charge configurations. Knowing the sign of ΔEz before a qubit operation means the overall readout visibility is increased.
To overcome the readout visibility issue with conventional shelving readout techniques and to determine the sign of ΔEz to ensure a proper mapping of |G and |E
to (0,2) and (1,1) charge configurations, aspects of the present disclosure provide an improved shelving readout method. In particular, the presently disclosed shelving readout method includes a calibration step that improves the total readout visibility.
First, at step 402, a double quantum dot system (e.g., the double quantum dot 100) is loaded with electrons (e.g., from the SET 132). In some examples, there is only one electron per quantum dot (e.g., 128, 130). In other examples there may be multiple electrons per quantum dot.
At step 404 the double quantum dot system 100 is initialised in the (1,1) ground state |G. This may be done by an adiabatic sweep from negative to positive detuning starting from the (0,2) state to (1,1) state.
At step 406, a shelving readout process (similar to that described above with respect to or |↑↓
state, respectively. Thus, the sign of ΔEz can be determined. For example, if the final configuration measured after the shelving operation is (0, 2) then it can be determined that ΔEz>0. Alternatively, if the final configuration measured after the shelving operation is (1,1), then it can be determined that ΔEz<0.
Steps 402, 404 and 406 together form the calibrations step.
The calibration step is ideally performed before every qubit operation, to provide the correct mapping for the shelving readout of the qubit. However, it can be performed less frequently (every ith qubit operation) if the nuclear spin flips are significantly slower than the time of a single measurement.
Once the calibration steps 402, 404, 406 has been performed. The current sign of ΔEz can be determined for use in subsequent shelving readout processes. The following qubit operation can use this information via a feed-forward protocol to map the final readout results.
At step 412, the qubit or the double quantum dot system 100 is reinitialised in either the ground state or the excited state.
At step 414, a qubit operation is performed on the qubit. It will be appreciated that any qubit operation may be performed. For example, a rotation operation or a SWAP gate operation may be performed.
The qubit operation time needs to be faster than the time it takes for the nuclear spin polarisation to change. However, phosphorus donors in silicon have long nuclear spin coherence times—so the time required to perform the qubit operation is realistic. The longest coherence times for single phosphorus donors reach values of the order of seconds or even tens of seconds, while qubit operation for singlet-triplet qubits is less than a microsecond. The exact time scales required are also device dependent and may differ based on the number of donors and electrons in the systems.
For the system shown in
At step 416, shelving readout is performed with the current knowledge of the sign of ΔEz such that the correct mapping is used. The obtained sign of ΔEz can be used to apply the correct mapping for the subsequent qubit operation. That is, the qubit operation is performed (initialisation, control, shelving readout) and then it is mapped to the final measured charge configuration appropriately:
Shelving readout solves the problem of triplet relaxation, as it maps one of the states to a metastable triplet T− state in (1,1) charge configuration, and another state to (0,2) singlet. Therefore, it can significantly improve readout fidelity in comparison to PSBR.
However, for donor-based devices the magnetic field gradient (coming from the effective hyperfine interaction) is changing in time, as the nuclear spins tend to flip multiple times within the timescale of the experiment. The effective ΔEz is thus uncontrollably changing both value and sign during the experiment. The interpretation of measured (1,1) and (0,2) charge configurations depend on the sign of ΔEz (with opposite mappings for opposite signs). Thus, without knowledge about the current nuclear spin state, the average visibility of the readout over time (or over all the nuclear configurations) will reach 0%.
The calibration step described herein provides information about the current sign of ΔEz, allowing to employ correct shelving readout mapping for every single qubit operation. This procedure allows the efficient use of shelving readout for singlet-triplet qubits in donor-based devices, even if the effective ΔEz uncontrollably changes in time.
The term “comprising” (and its grammatical variations) as used herein are used in the inclusive sense of “having” or “including” and not in the sense of “consisting only of”.
It will be appreciated by persons skilled in the art that numerous variations and/or modifications may be made to the invention as shown in the specific embodiments without departing from the spirit or scope of the invention as broadly described. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive.
Number | Date | Country | Kind |
---|---|---|---|
2022900513 | Mar 2022 | AU | national |