Error suppression technology

Abstract

A method for suppressing errors in quantum computing, wherein the method comprises: performing (S101) an operation on the state of a qubit in a set of qubits multiple times, the operation having a first error rate, each execution of the operation comprising: performing a first operation, the first operation comprising: a gate operation, a symmetry operation, and a first basic operation; or performing a second operation, the second operation comprising: a gate operation, a symmetry operation, and a second basic operation; wherein the first basic operation and the second basic operation are different basic operations selected from a set of basic operations; and measuring the state of the qubit; wherein the probability of performing the first operation is a first probability and the probability of performing the second operation is a second probability; and obtaining (S102) a symmetry measurement of the set of qubits using the symmetry operation after each execution of the operation, wherein the set of qubits comprises a plurality of qubits ; wherein the symmetry measurement is a first symmetry result if the number of errors is an even number, or a second symmetry result if the number of errors is an odd number; obtaining (S103) a first state measurement by determining an average state of the qubits for the first symmetry result; obtaining (S104) a second state measurement by determining an average state of the qubits for the second symmetry result; fitting (S105) the first state measurement to a first curve of the form #imgabs0#; fitting the second state measurement to a second curve of the form #imgabs1#; wherein n is the error rate and A and γ are fitting parameters; and extrapolating (S106) the average state of the qubits at the second error rate using the first fit curve and the second fit curve; wherein the second error rate is lower than the first error rate.

Description

Technical Field

[0001] The present invention relates to quantum computing, and in particular to error suppression technology. Background Art

[0002] Quantum computers can be used to compute "observables," that is, properties of a system. To measure an observable, the output state of a qubit can be measured after performing a sequence of quantum operations on the qubit. The same sequence of quantum operations is typically repeated many times, and the average of the measured output states can be calculated to estimate the expected value of the observable.

[0003] However, the sequence of quantum operations performed on qubits is subject to errors, and therefore the estimated expected value is also subject to errors. Reducing or even eliminating these errors is the goal of quantum computing. However, a more realistic approach for near-term quantum devices or quantum devices of the noisy intermediate-scale quantum (NISQ) era is to aim to suppress these errors using analytical methods. In this way, the error-free or noise-free expected value of the observable can be estimated.

[0004] Error suppression techniques use additional measurements to extract the noise-free expected value from the noisy measurement results. Some existing error suppression techniques include symmetry verification, quasi-probability, and error extrapolation. Symmetry verification uses known properties of the system to determine whether an error has occurred without measuring (and therefore collapsing) the state of the qubit. Quasi-probability uses additional gates determined by modeling the errors associated with components in the circuit. Error extrapolation involves increasing the noise level by physically changing the hardware and predicting the noise-free expected value based on the higher noise level measurement. Each of these error suppression techniques can be used to suppress different types of noise.

[0005] Symmetry verification is simple to perform, but circuit operation that passes the symmetry verification test cannot be considered error-free because errors can combine in such a way that the total error cannot be detected using symmetry.

[0006] Quasi-probability can eliminate errors. However, error elimination is very costly and requires a large number of repetitions.

[0007] Error extrapolation requires that the noise level be increased by the experimenter. Accurate prediction of a noise-free observable after measurements at an increased noise level requires that the additional noise comes from the same noise model as the original noise.

[0008] It is hoped that better error suppression techniques will be developed. Summary of the Invention

[0009] One aspect of the present invention provides a method for suppressing errors in quantum computing. The method includes: performing an operation on the state of a qubit in a group of qubits multiple times. The operation has a first error rate, and each execution of the operation includes: performing a first operation or performing a second operation and measuring the state of the qubit. The first operation includes: a gate operation, a symmetry operation, and a first basic operation. The second operation includes: a gate operation, a symmetry operation, and a second basic operation. The first basic operation and the second basic operation are different basic operations selected from a set of basic operations. The probability of performing the first operation is a first probability, and the probability of performing the second operation is a second probability. The method further includes: obtaining a symmetry measurement of the group of qubits using the symmetry operation after each execution of the operation, wherein the group of qubits includes a plurality of qubits; wherein if the number of errors is an even number, the symmetry measurement is a first symmetry result, or if the number of errors is an odd number, the symmetry measurement is a second symmetry result. The method further includes: obtaining a first state measurement by determining the average state of the qubits of the first symmetry result; and obtaining a second state measurement by determining the average state of the qubits of the second symmetry result. The method further includes: fitting the first state measurement to a form of The first curve of the second state measurement is fitted into the form of wherein n is the error rate, and A and γ are fitting parameters; and using the first and second fitting curves to extrapolate the average state of the qubit at the second error rate; wherein the second error rate is lower than the first error rate.

[0010] Advantageously, the error suppression method yields an improved estimate of an observable quantity for a reduced cost. The cost is given by the number of operations performed. The method combines quasi-probabilistic, symmetry verification, and error extrapolation error suppression techniques in a synergistic manner.

[0011] The first state measurement and the second state measurement are fitted to a first curve and a second curve, respectively. The combination of the first state measurement and the second state measurement can be modeled by an exponential decay curve. Using an exponential decay curve is advantageous because it has been found to be a good model for the relationship between an observable and an error rate. Optionally, the exponential decay curve is a multi-exponential decay curve comprising a sum of two or more exponentials. Compared to a single exponential decay curve, a multi-exponential decay curve generally has a higher cost, but can advantageously provide an improved model of the change in the expected value of the observable as a function of the error rate.

[0012] Typically, the gate operation may include any quantum logic gate operation, for example, a Pauli gate, a Hadamard gate, a SWAP gate, a controlled NOT (CNOT) gate, or a controlled Z gate. The gate operation may include a sequence of operations. The first basic operation and the second basic operation may be performed after the gate operation. Typically, the basic operation is selected from a basic operation set. The basic operation set may include 16 basic operations. Advantageously, any single qubit operation (a single qubit operation may be represented as a 4x4 matrix) may be represented as a linear combination of the 16 basic operations. In general, the number of basic operations in the basic operation set may be larger to accommodate a larger number of qubits. The basic operation set may include Pauli basic operations. Typically, for n qubits, the basic operation set may include at least 4 n Thus, each of the first and second basic operations may be one of the Pauli basic operations.

[0013] Alternatively, the execution of the operation may include executing a j-th operation, the j-th operation comprising: a gate operation, a symmetry operation, and a j-th elementary operation. The number of possible operations that can be executed is preferably related to the number of elementary operations in the elementary operation set. For example, if there is one gate operation, one qubit, and three elementary operations in the set, then there may be three possible operations that can be executed. The probability of executing the j-th operation may be the j-th probability. In this way, random elementary operations can be used to modify the gate operation. This has the advantage of reducing the effective error rate of the operation. Optionally, the method can be repeated with different effective error rates. This can be achieved by varying the first probability and the second probability.

[0014] A symmetry measure of the set of qubits is obtained using a symmetry operation. The symmetry measure preferably has a set of known symmetry results that may depend on the symmetry operation and the system. The symmetry measure is a first symmetry result or a second symmetry result. Optionally, the symmetry measure is a kth symmetry result, where k may be greater than 2. In one example with two symmetry results, the first symmetry result is a pass, where the symmetry measure is consistent with the expected symmetry. In this example, the second symmetry result is preferably a fail, where the symmetry is violated. The first state measurement and the second state measurement are obtained by determining the average state of the qubits for both the pass symmetry result and the fail symmetry result. Optionally, the kth state measurement is obtained by determining the average state of the qubits for the kth symmetry result. This approach has the advantage that measurements that fail the symmetry test are constructively used when estimating the average state of the qubits at the second error rate. This advantageously reduces the cost of performing the error suppression operation.

[0015] Typically, the execution of the operation includes performing a symmetry operation. Optionally, the symmetry operation is a first symmetry operation. The execution of the operation may also include performing a second symmetry operation. The symmetry measurement using the second symmetry operation may be a third symmetry result or a fourth symmetry result, where the third symmetry result or the fourth symmetry result may be a pass or a fail, respectively. The first symmetry operation may be used to test a first symmetry of the system, and the second symmetry operation may be used to test a second symmetry of the system. In this way, multiple properties of the set of qubits may be measured simultaneously to provide additional data. Advantageously, the additional data may be used to provide a better estimate of the expected value of the observable.

[0016] Preferably, the symmetry operation and the basic operation are performed after the gate operation. Optionally, the symmetry operation is performed before the basic operation. Alternatively, the basic operation can be performed before the symmetry operation.

[0017] The method may optionally be performed with an additional error rate. The effective error rate may be determined by selecting a basic operation and a probability of selecting each basic operation in the set of basic operations. In an example, the method further comprises: performing another operation on the state of a qubit in the set of qubits multiple times, wherein the another operation has a third error rate, wherein each performance of the another operation comprises: performing another first operation, wherein the another first operation comprises: a gate operation, a symmetry operation, and another first basic operation; or performing another second operation, wherein the another second operation comprises: a gate operation, a symmetry operation, and another second basic operation; and measuring the state of the qubit; wherein the probability of performing the another first operation is another first probability, wherein the probability of performing the another second operation is another second probability; and obtaining using the symmetry operation another symmetry measurement of the set of qubits; wherein the another symmetry measurement is another first symmetry result or another second symmetry result; obtaining another first state measurement by determining an average state of the qubits for the another first symmetry result; obtaining another second state measurement by determining an average state of the qubits for the another second symmetry result; fitting the another first state measurement to another first curve and fitting the another second state measurement to another second curve; and extrapolating the average state of the qubits at a fourth error rate using the another first fit curve and the another second fit curve; wherein the fourth error rate is lower than the third error rate.

[0018] Advantageously, this method modifies the gate operation using a random selection of basic operations to achieve a different effective error rate, i.e., a third error rate. Typically, the first basic operation, the second basic operation, the further first basic operation, and the further second basic operation are selected from the same set of basic operations. Using this method, any i-th error rate can be influenced by randomly selecting basic operations from a set of basic operations with different associated probabilities. Preferably, the probabilities of selecting the basic operations are determined theoretically.

[0019] A qubit in the set of qubits may be a first qubit, and the state of another qubit may be manipulated as part of the quantum computation. Preferably, the method further comprises: performing an operation on the state of a second qubit in the set of qubits a plurality of times; obtaining a third state measurement by determining an average state of the second qubit for a first symmetry result; obtaining a fourth state measurement by determining an average state of the second qubit for a second symmetry result; fitting the third state measurement to a third curve and fitting the fourth state measurement to a fourth curve; and extrapolating the average state of the second qubit at a second error rate using the third and fourth fitted curves. There may be any number of qubits in the set of qubits, and the state of each qubit may be manipulated in a similar manner. Advantageously, the method may be performed entirely on a quantum device.

[0020] Optionally, during the execution of an operation on the state of one or more qubits in the set of qubits, one or more qubits in the set of qubits may remain idle. An identity gate operation may be used to operate on the one or more idle qubits in the set of qubits. The one or more idle qubits are typically subject to decoherence errors associated with the execution of the identity gate. A symmetry measure of the set of qubits is obtained using a symmetry operation after each operation is performed. The symmetry measure preferably includes the one or more qubits in the set of qubits that were operated on and the one or more qubits that remained idle.

[0021] The (one or more) qubits may be electron spin qubits. Preferably, if the qubit is an electron spin qubit, the state of the qubit is electron spin. Advantageously, electron spin qubits can be easily manipulated and coupled to other electron spin qubits. Preferably, the qubit is an electron spin qubit in a silicon-based device, as electron spin qubits in silicon-based devices advantageously have long coherence times and are compatible with existing technologies. Such devices may be beneficially applicable in the era of noisy, medium-scale quantum computing.

[0022] Another aspect of the present invention provides a device for performing a quantum computing operation, the device comprising: a selection module; a quantum processor; a quantum measurement device; a symmetry measurement device; and a classical processor. The selection module is configured to: select a first elementary operation from a set of elementary operations with a first probability; and select a second elementary operation from the set of elementary operations with a second probability; wherein the first elementary operation and the second elementary operation are different. The quantum processor is configured to perform an operation on the state of a qubit in a set of qubits multiple times, wherein the operation has a first error rate, wherein each execution of the operation comprises: performing a gate operation, a symmetry operation, and the selected elementary operation. The quantum measurement device is configured to measure the state of the qubit. The symmetry measurement device is configured to measure the symmetry of the set of qubits using the symmetry operation after each execution of the operation, wherein the set of qubits comprises a plurality of qubits; wherein if the number of errors is even, the symmetry measurement is a first symmetry result, or if the number of errors is odd, the symmetry measurement is a second symmetry result. The classical processor is configured to obtain a first state measurement by determining an average state of the qubits of a first symmetry result, and obtain a second state measurement by determining an average state of the qubits of a second symmetry result; and fit the first state measurement to a form of The first curve of the second state measurement is fitted into the form of wherein n is the error rate, A and γ are fitting parameters; and using the first and second fitted curves to extrapolate the average state of the qubit at a second error rate, wherein the second error rate is lower than the first error rate.

[0023] The device can be advantageously used to suppress the effects of noise on the measured expected value of an observable. The selection module is configured to, after performing a gate operation, select a first elementary operation or a second elementary operation to be performed by the quantum processor with corresponding probabilities. In this way, measurements of the states of the qubits can be recombined to estimate an error-suppressed value of the observable. The estimated error-free value of the observable using the device is advantageously accurate and cost-effective.

[0024] The selection module is preferably further configured to select the jth basic operation for 3≤j≤J, where J is preferably the total number of basic operations in the basic operation set. The set of basic operations may be determined based on a theoretically determined noise model, benchmark experiments, and / or considerations of available experimental options.

[0025] Yet another aspect of the present invention provides a computer-readable storage medium comprising instructions that, when executed by a computer, cause the computer to perform steps on a quantum computer, the steps comprising: performing an operation on a state of a qubit in a set of qubits a plurality of times, wherein the operation has a first error rate, wherein each performance of the operation comprises: performing a first operation, the first operation comprising: a gate operation, a symmetry operation, and a first elementary operation; or performing a second operation, the second operation comprising: a gate operation, a symmetry operation, and a second elementary operation; wherein the first elementary operation and the second elementary operation are different elementary operations selected from a set of elementary operations; and Measuring the state of the qubit; wherein the probability of performing the first operation is a first probability and the probability of performing the second operation is a second probability; obtaining a symmetry measurement of the group of qubits using the symmetry operation after each performance of the operation, wherein the group of qubits includes a plurality of qubits; wherein the symmetry measurement is a first symmetry result if the number of errors is even, or a second symmetry result if the number of errors is odd; obtaining a first state measurement by determining an average state of the qubits for the first symmetry result; obtaining a second state measurement by determining an average state of the qubits for the second symmetry result; fitting the first state measurement to a form of The first curve of the second state measurement is fitted into the form of wherein n is the error rate, A and γ are fitting parameters; and using the first fitting curve and the second fitting curve to extrapolate the average state of the qubit at the second error rate; wherein the second error rate is lower than the first error rate.

[0026] Advantageously, the computer-readable storage medium may be used to determine an error-suppressed value for an observable having a low estimation error.

[0027] One aspect of the present invention provides a method for suppressing errors in quantum computing. The method includes: performing an operation on the state of a qubit in a group of qubits multiple times. The operation has a first error rate, and each execution of the operation includes: performing a first operation or performing a second operation, and measuring the state of the qubit. The first operation includes: a gate operation, a symmetry operation, and a first elementary operation. The second operation includes: a gate operation, a symmetry operation, and a second elementary operation. The probability of performing the first operation is a first probability, and the probability of performing the second operation is a second probability. The method further includes: using the symmetry operation to obtain a symmetry measurement of the group of qubits; wherein the symmetry measurement is a first symmetry result or a second symmetry result. The method further includes: obtaining a first state measurement by determining the average state of the qubits for the first symmetry result; and obtaining a second state measurement by determining the average state of the qubits for the second symmetry result. The method further includes: combining the first state measurement and the second state measurement to estimate the average state of the qubit.

[0028] Advantageously, this error suppression method yields an improved estimate of an observable quantity for a reduced cost. The cost is given by the number of operations performed. The method synergistically combines quasi-probabilistic and symmetry-verified error suppression techniques. Quasi-probabilistic methods can advantageously be used to modify the form of the error in such a way that errors that would be undetectable using symmetry operations can be removed. Furthermore, knowing the relative probabilities of obtaining a first symmetry result and a second symmetry result, respectively, the first state measurement and the second state measurement can be recombined to provide an improved estimate of the error-free observable quantity.

[0029] Another aspect of the present invention provides an apparatus for performing a quantum computing operation, the apparatus comprising: a selection module; a quantum processor; a quantum measurement device; a symmetry measurement device; and a classical processor. The selection module is configured to: select a first elementary operation from a set of elementary operations with a first probability; and select a second elementary operation from the set of elementary operations with a second probability. The quantum processor is configured to perform an operation on the state of a qubit in a set of qubits multiple times, wherein the operation has a first error rate, and wherein each execution of the operation comprises: performing a gate operation, a symmetry operation, and the selected elementary operation. The quantum measurement device is configured to measure the state of the qubit. The symmetry measurement device is configured to measure the symmetry of the set of qubits using the symmetry operation; wherein the symmetry measurement is a first symmetry result or a second symmetry result. The classical processor is configured to: obtain a first state measurement by determining an average state of the qubits for the first symmetry result, and obtain a second state measurement by determining an average state of the qubits for the second symmetry result; and combine the first state measurement and the second state measurement to estimate the average state of the qubits.

[0030] The device can be advantageously used to suppress the effects of errors on the measured expected value of an observable. The selection module is configured to, after performing a gate operation, select a first elementary operation or a second elementary operation to be performed by the quantum processor with corresponding probabilities. The measurement of the state of the qubit is classified according to the result of the symmetry measurement. In this way, knowing the probabilities of the first symmetry result and the second symmetry result, the first state measurement and the second state measurement can be recombined to estimate the error-suppressed value of the observable.

[0031] Yet another aspect of the present invention provides a computer-readable storage medium comprising instructions that, when executed by a computer, cause the computer to perform steps on a quantum computer, the steps comprising: performing an operation on a state of a qubit in a set of qubits a plurality of times, wherein the operation has a first error rate, wherein each performance of the operation comprises: performing a first operation comprising: a gate operation, a symmetry operation, and a first elementary operation; or performing a second operation comprising: a gate operation, a symmetry operation, and a second elementary operation; and measuring the state of the qubit; wherein a probability of performing the first operation is a first probability and a probability of performing the second operation is a second probability; obtaining a symmetry measurement of the set of qubits using the symmetry operation; wherein the symmetry measurement is a first symmetry result or a second symmetry result; obtaining a first state measurement by determining an average state of the qubits for the first symmetry result; obtaining a second state measurement by determining an average state of the qubits for the second symmetry result; and combining the first state measurement with the second state measurement to estimate the average state of the qubits.

[0032] Advantageously, the computer-readable storage medium may be used to more accurately determine an error-rejected value for an observable.

[0033] One aspect of the present invention provides a method for suppressing errors in quantum computing. The method includes: performing a first operation on a state of a qubit, wherein the first operation has a first error rate; obtaining a first measurement of the state of the qubit; performing a second operation on the state of the qubit, wherein the second operation has the first error rate; obtaining a second measurement of the state of the qubit; calculating a first average value of the state of the qubit at the first error rate by averaging the first and second measurements; performing a third operation on the state of the qubit, wherein the third operation has a second error rate lower than the first error rate, wherein the third operation includes the first operation and a first elementary operation; obtaining a third measurement of the state of the qubit; performing a fourth operation on the state of the qubit, wherein the fourth operation has the second error rate, wherein the fourth operation includes the first operation and a second elementary operation; wherein the first and second elementary operations are different elementary operations selected from a set of elementary operations; obtaining a fourth measurement of the state of the qubit; and calculating a second average value of the state of the qubit at the second error rate by averaging the third and fourth measurements. The method further includes fitting a first average value of the state of the qubit and a second average value of the state of the qubit into a curve; and using the fitted curve to extrapolate the average state of the qubit at a third error rate, wherein the third error rate is lower than the first error rate and the second error rate.

[0034] Advantageously, this method of suppressing errors results in improved estimates of observables for reduced cost.The method combines quasi-probabilistic and error extrapolation error suppression techniques in a synergistic manner.

[0035] The first basic operation and the second basic operation are both selected from a set of basic operations. The selection is preferably random, with a weighted probability of selecting a specific basic operation. Alternatively, the probability of selecting the first basic operation is a first probability, and the probability of selecting the second basic operation is a second probability. The set of basic operations may further include additional basic operations, each of which has a corresponding probability of being selected. In this way, random basic operations can be used to modify the first operation. This has the following advantages: the effective error rate of the operation can be reduced from the first error rate to the second error rate. The second error rate may depend on the selection probability of each of the basic operations.

[0036] The first operation and the second operation both have a first error rate. The first average is calculated by averaging the first measurement and the second measurement. Preferably, the second operation is identical to the first operation. Furthermore, the first operation is typically repeated a plurality of times, and a first average of the state of the qubit at the first error rate can be calculated by averaging each of the resulting measurements. Each measurement is either +1 or -1, corresponding to the two states of the qubit, respectively. Performing the first operation multiple times has the advantage of reducing uncertainty in the expected value of the observable at the first error rate.

[0037] In addition to the first operation, the third operation and the fourth operation also include a first basic operation and a second basic operation, respectively. Optionally, the first basic operation and the second basic operation are Pauli basic operations. Pauli basic operations generally include identity operations. Further, another basic operation can be used to perform the modified operation. Each of the first basic operation, the second basic operation, and any additional basic operations can be randomly selected from the basic operation set. In this way, compared to performing the first operation in the case of random sampling of the unmodified operation, the effective error rate can be advantageously reduced.

[0038] The qubit is preferably one of a plurality of qubits in a set of qubits. The state of each qubit in the set of qubits can be transformed by performing an operation or sequence of operations. Advantageously, this error suppression method can be applied to quantum devices comprising a plurality of qubits.

[0039] The qubit can be an electron spin qubit. Preferably, if the qubit is an electron spin qubit, the state of the qubit is the electron spin. Measurement of the state of the qubit typically returns spin up |↑> or spin down |↓>. Advantageously, electron spin qubits can be easily manipulated and coupled to other electron spin qubits. Preferably, the qubit is an electron spin qubit in a silicon-based device, which advantageously provides long coherence times and is compatible with existing technologies.

[0040] The first average value and the second average value are fitted into a curve. Optionally, the curve is an exponential decay curve. Using an exponential decay curve is advantageous because it is generally a good model for the relationship between the observable quantity and the error rate. Optionally, the exponential decay curve is a multi-exponential decay curve comprising a sum of two or more exponentials. Preferably, the multi-exponential decay curve is of the form Where E is the average state of the qubit, n is the error rate, and A k and γ k Multi-exponential decay curves are generally more expensive than single-exponential decay curves, but can beneficially provide an improved model of the variation in the expected value of an observable as a function of the error rate.

[0041] Yet another aspect of the present invention provides an apparatus for performing quantum computing operations, the apparatus comprising: a selection module; a quantum processor; a quantum measurement device; and a classical processor. The selection module is configured to select a basic operation from a set of basic operations comprising a first basic operation and a second basic operation, wherein the first basic operation and the second basic operation are different. The quantum processor is configured to perform a first operation on a state of a quantum bit, wherein the first operation has a first error rate; perform a second operation on the state of the quantum bit, wherein the second operation has the first error rate; perform a third operation on the state of the quantum bit, wherein the third operation has a second error rate lower than the first error rate, wherein the third operation includes the first operation and the first basic operation; and perform a fourth operation on the state of the quantum bit, wherein the fourth operation has the second error rate, wherein the fourth operation includes the first operation and the second basic operation. The quantum measurement device is configured to obtain a first measurement, a second measurement, a third measurement, and a fourth measurement after performing the first operation, the second operation, the third operation, and the fourth operation, respectively. The classical processor is configured to: calculate a first average value of the state of the qubit at a first error rate by averaging the first measurement and the second measurement; calculate a second average value of the state of the qubit at a second error rate by averaging the third measurement and the fourth measurement; fit the first average value of the state of the qubit and the second average value of the state of the qubit to a curve; and extrapolate the average state of the qubit at a third error rate using the fitted curve, wherein the third error rate is lower than the first error rate and the second error rate.

[0042] Advantageously, the apparatus can be used to suppress the effects of errors on the measured expected value of the observable.The estimated noise-free value of the observable using the apparatus is advantageously accurate and low-cost.

[0043] Yet another aspect of the present invention provides a computer-readable storage medium comprising instructions that, when executed by a computer, cause the computer to perform steps on a quantum computer, the steps comprising: performing a first operation on a state of a qubit, wherein the first operation has a first error rate; obtaining a first measurement of the state of the qubit; performing a second operation on the state of the qubit, wherein the second operation has the first error rate; obtaining a second measurement of the state of the qubit; calculating a first average value of the state of the qubit at the first error rate by averaging the first and second measurements; performing a third operation on the state of the qubit, wherein the third operation has a second error rate lower than the first error rate, wherein the third operation comprises the first operation. The method further comprises performing a first operation and a second operation on the state of the qubit; obtaining a third measurement of the state of the qubit; performing a fourth operation on the state of the qubit, wherein the fourth operation has the second error rate, wherein the fourth operation includes the first operation and the second operation; wherein the first operation and the second operation are different operations selected from the set of operations; obtaining a fourth measurement of the state of the qubit; calculating a second average value of the state of the qubit at the second error rate by averaging the third measurement and the fourth measurement; fitting the first average value of the state of the qubit and the second average value of the state of the qubit to a curve; and using the fitted curve to extrapolate the average state of the qubit at a third error rate, wherein the third error rate is lower than the first error rate and the second error rate.

[0044] Advantageously, the computer-readable storage medium may be used to determine an error-suppressed value for an observable having a low estimation error.

[0045] Another aspect of the present invention provides a method for suppressing errors in quantum computing. The method includes: performing an operation on the state of a qubit in a set of qubits multiple times. The operation has a first error rate, and each execution of the operation includes: performing the first operation or performing the second operation, and measuring the state of the qubit. The first operation includes: a gate operation, a symmetry operation, and a first elementary operation. The second operation includes: a gate operation, a symmetry operation, and a second elementary operation. The probability of performing the first operation is a first probability, and the probability of performing the second operation is a second probability. The method further includes: using the symmetry operation to obtain a symmetry measurement of the set of qubits; wherein the symmetry measurement is a first symmetry result or a second symmetry result. The method further includes: obtaining a first state measurement by determining the average state of the qubit for the first symmetry result; and obtaining a second state measurement by determining the average state of the qubit for the second symmetry result. The method further includes: fitting the first state measurement to a first curve, fitting the second state measurement to a second curve, and using the first and second fitted curves to extrapolate the average state of the qubit at a second error rate; wherein the second error rate is lower than the first error rate.

[0046] Another aspect of the present invention provides an apparatus for performing a quantum computing operation, the apparatus comprising: a selection module; a quantum processor; a quantum measurement device; a symmetry measurement device; and a classical processor. The selection module is configured to: select a first elementary operation from a set of elementary operations with a first probability; and select a second elementary operation from the set of elementary operations with a second probability. The quantum processor is configured to perform an operation on the state of a qubit in a set of qubits multiple times, wherein the operation has a first error rate, wherein each execution of the operation comprises: performing a gate operation, a symmetry operation, and the selected elementary operation. The quantum measurement device is configured to measure the state of the qubit. The symmetry measurement device is configured to measure the symmetry of the set of qubits using the symmetry operation; wherein the symmetry measurement is a first symmetry result or a second symmetry result. The classical processor is configured to: obtain a first state measurement by determining an average state of the qubit for a first symmetry result, and obtain a second state measurement by determining an average state of the qubit for a second symmetry result; fit the first state measurement to a first curve and fit the second state measurement to a second curve; and extrapolate the average state of the qubit at a second error rate using the first and second fitted curves, wherein the second error rate is lower than the first error rate.

[0047] Yet another aspect of the present invention provides a computer-readable storage medium comprising instructions that, when executed by a computer, cause the computer to perform steps on a quantum computer, the steps comprising: performing an operation on a state of a qubit in a set of qubits a plurality of times, wherein the operation has a first error rate, wherein each performance of the operation comprises: performing a first operation, the first operation comprising: a gate operation, a symmetry operation, and a first elementary operation; or performing a second operation, the second operation comprising: a gate operation, a symmetry operation, and a second elementary operation; and measuring the state of the qubit; wherein a probability of performing the first operation is a first probability , the probability of performing the second operation is a second probability; obtaining a symmetry measurement of the set of qubits using the symmetry operation; wherein the symmetry measurement is a first symmetry result or a second symmetry result; obtaining a first state measurement by determining an average state of the qubits for the first symmetry result; obtaining a second state measurement by determining an average state of the qubits for the second symmetry result; fitting the first state measurement to a first curve and fitting the second state measurement to a second curve; and extrapolating the average state of the qubits at a second error rate using the first and second fitted curves; wherein the second error rate is lower than the first error rate.

[0048] One aspect of the present invention provides a method for suppressing errors in quantum computing. The method includes: performing a first operation on a state of a qubit, wherein the first operation has a first error rate; obtaining a first measurement of the state of the qubit; performing a second operation on the state of the qubit, wherein the second operation has the first error rate; obtaining a second measurement of the state of the qubit; calculating a first average value of the state of the qubit at the first error rate by averaging the first and second measurements; performing a third operation on the state of the qubit, wherein the third operation has a second error rate lower than the first error rate, wherein the third operation includes the first operation and a first elementary operation; obtaining a third measurement of the state of the qubit; performing a fourth operation on the state of the qubit, wherein the fourth operation has the second error rate, wherein the fourth operation includes the first operation and the second elementary operation; obtaining a fourth measurement of the state of the qubit; and calculating a second average value of the state of the qubit at the second error rate by averaging the third and fourth measurements. The method further includes fitting a first average value of the state of the qubit and a second average value of the state of the qubit into a curve; and using the fitted curve to extrapolate the average state of the qubit at a third error rate, wherein the third error rate is lower than the first error rate and the second error rate.

[0049] Another aspect of the present invention provides an apparatus for performing a quantum computing operation, the apparatus comprising: a selection module; a quantum processor; a quantum measurement device; and a classical processor. The selection module is configured to select a basic operation from a set of basic operations including a first basic operation and a second basic operation. The quantum processor is configured to perform a first operation on a state of a quantum bit, wherein the first operation has a first error rate; perform a second operation on the state of the quantum bit, wherein the second operation has the first error rate; perform a third operation on the state of the quantum bit, wherein the third operation has a second error rate lower than the first error rate, wherein the third operation includes the first operation and the first basic operation; and perform a fourth operation on the state of the quantum bit, wherein the fourth operation has the second error rate, wherein the fourth operation includes the first operation and the second basic operation. The quantum measurement device is configured to obtain a first measurement, a second measurement, a third measurement, and a fourth measurement after performing the first operation, the second operation, the third operation, and the fourth operation, respectively. The classical processor is configured to: calculate a first average value of the state of the qubit at the first error rate by averaging the first measurement and the second measurement; calculate a second average value of the state of the qubit at the second error rate by averaging the third measurement and the fourth measurement; fit the first average value of the state of the qubit and the second average value of the state of the qubit to a curve; and extrapolate the average state of the qubit at a third error rate using the fitted curve, wherein the third error rate is lower than the first error rate and the second error rate.

[0050] Yet another aspect of the present invention provides a computer-readable storage medium comprising instructions that, when executed by a computer, cause the computer to perform steps on a quantum computer, the steps comprising: performing a first operation on a state of a qubit, wherein the first operation has a first error rate; obtaining a first measurement of the state of the qubit; performing a second operation on the state of the qubit, wherein the second operation has the first error rate; obtaining a second measurement of the state of the qubit; calculating a first average value of the state of the qubit at the first error rate by averaging the first and second measurements; and performing a third operation on the state of the qubit, wherein the third operation has a first error rate lower than the first error rate. The method further comprises performing a first operation and a second operation on the state of the qubit, wherein the first operation has a second error rate, wherein the third operation includes the first operation and a first basis operation; obtaining a third measurement of the state of the qubit; performing a fourth operation on the state of the qubit, wherein the fourth operation has the second error rate, wherein the fourth operation includes the first operation and a second basis operation; obtaining a fourth measurement of the state of the qubit; calculating a second average value of the state of the qubit at the second error rate by averaging the third measurement and the fourth measurement; fitting the first average value of the state of the qubit and the second average value of the state of the qubit to a curve; and using the fitted curve to extrapolate the average state of the qubit at a third error rate, wherein the third error rate is lower than the first error rate and the second error rate. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Embodiments of the present invention will now be described with reference to the accompanying drawings, in which:

[0052] Figure 1 is a flowchart of the error suppression method according to the first embodiment;

[0053] Figure 2 is a flowchart of an error suppression method according to a second embodiment;

[0054] Figure 3 is a schematic diagram of quantum computing according to an embodiment; and

[0055] Figure 4 is a graph showing observables as a function of error rate. DETAILED DESCRIPTION

[0056] Figure 1 is a flow chart depicting an error suppression method according to an embodiment. In this embodiment, a combination of quasi-probability, symmetry verification and error extrapolation is used.

[0057] Quantum computing typically involves initializing a set of qubits, performing a sequence of quantum operations on the set of qubits, and measuring the output state of each qubit. Measurements can also be performed on the set of qubits as a whole. The sequence of quantum operations has an associated error.

[0058] In step S101, a quantum processor is used to perform an operation on the state of a qubit in a set of qubits. The operation has a first error rate and is performed multiple times. The first error rate n1 is the number of errors expected to occur each time the operation is performed. The actual number of errors occurring each time will vary, but the average number of errors over multiple operations will be approximately equal to n1. Errors, including phase shift errors and depolarization errors, may occur at multiple possible error locations M. Assuming the number of possible error locations is large, the first error rate is approximately 1, i.e., M>>1; n1~1.

[0059] Each time the operation is performed, a quantum measurement device is used to measure the state of the qubit after the operation. After performing the operation many times, the expected value of the state of the qubit can be obtained by averaging the individual measurements using a classical processor. This expected value can be mapped to a physical quantity of the system (such as position or momentum) and is sometimes called an observable.

[0060] The operations performed in step S101 include gate operations and additional operations. Gate operations include one or more quantum logic gate operations. Any quantum gate or series of quantum gates can be selected based on the experimental requirements. Additional operations are performed after the gate operations and are used to suppress errors caused by the execution of the gate operations. Additional operations include symmetry operations and basic operations; symmetry operations are used to suppress errors using symmetry verification, while basic operations are used to suppress errors using quasi-probability. Symmetry verification and quasi-probability error suppression techniques will be discussed below.

[0061] Without any error suppression, a gating operation can be used to obtain a noisy measurement of an observable. The gating operation is chosen by the experimenter based on the observable to be measured. The goal of the error suppression technique is to estimate the value of the observable in the case where the gating operation is noiseless or non-noisy. n It can be represented as a noiseless operation U0, followed by a noisy operation M, that is, U n =MU0.

[0062] In the quasi-probabilistic error suppression technique, the inverse noise M -1 It can be expressed as each basic operation B in the basic operation set j A function of , where 1≤j≤J, J is the number of elementary operations in the set. In this embodiment, Pauli elementary operations are used, where there are 4 different elementary operations J=4 in the set. The Pauli elementary operations B acting on the state s of the qubit are j Can be written as in, as well as in It is bj The transpose complex conjugate. The inverse noise can be expressed as M -1 = a1B1 + a2B2 + a3B3 + a4B4, where a j is a numerical coefficient.

[0063] To estimate the impact of noiseless operations, a basic operation can be performed after the gate operation. The basic operation is randomly selected by the selection module. In this case, for one gate operation and three basic operations, the possible operations are: B1U n 、B2U n 、B3U n and B4U n . The selection module selects the j-th basic operation with a probability proportional to |a j |.

[0064] In an alternative embodiment, additional gate operations can be performed, and different basic operations can be selected from the set of basic operations. This increases the number of possible operations that the selection module can choose. Therefore, using quasiprobability to suppress the impact of noiseless operations typically requires performing a very large number of operations.

[0065] In this embodiment, quasiprobability is used to reduce the error rather than eliminate it. The cost C of using quasiprobability to reduce the error rate from the natural error rate n to the first error rate n1 is approximately Therefore, the cost of a small reduction in error is significantly less than the cost of a large reduction or complete elimination of error.

[0066] Using quasiprobability to reduce the error rather than eliminate it is advantageously less costly and thus requires fewer operation repetitions. The noisy gate operation U n can be transformed into a gate operation U n1 with a first error rate, where the first error rate is lower than the error rate of the noisy gate operation U n n1 < n. The relationship between the original operation and the error reduction operation can be expressed as U n = NU n1 .

[0067] For j = 1, 2, 3, 4, this transformation N -1 can be expressed as a function of basic operations N -1 = p1B1 + p2B2 + p3B3 + p4B4, and each basic operation can be included in the execution of the operation with a probability proportional to |p j |. For example, if p1 = 0.1, p2 = -0.2, p3 = 0.8, and p4 = 0.3 and the operation is executed 140 times, then the first operation B1U n will be executed approximately 10 times, the second operation B2U n will be executed approximately 20 times, the third operation B3U nWill be executed about 80 times, the fourth operation B4U n Will be executed approximately 30 times.

[0068] Thus, each operation performed in step S101 includes the jth basic operation after the gate operation. The operation modified using the jth basic operation can be referred to as the jth operation. The operation is performed multiple times, and according to the probability |p j |Performing each possible modification operation multiple times. Typically, step S101 comprises performing a set of operations that modify the state of each qubit in the set of qubits.

[0069] Symmetry verification error suppression techniques involve performing symmetry operations and making symmetry measurements. In quantum computing, some properties of the system are known and can be verified. For example, the number of electrons in a system should remain constant, regardless of the specific state of each electron. If an error occurs, it may manifest as a loss or gain of electrons.

[0070] However, using symmetry verification cannot easily distinguish the occurrence of multiple errors because the symmetry operation is performed on the group of qubits as a whole. In the above example, the symmetry operation may only be able to determine whether the total number of electrons is odd or even. If the number of electrons changes by ±1, ±3, ±5, etc., the result of the symmetry measurement after performing the symmetry operation will fail. A failed symmetry test is an indication that at least one error has occurred. If the number of electrons does not change, the result will pass, but if the number changes by ±2, ±4, ±6, etc., the result will also pass. Measurements that fail the symmetry verification test are typically discarded in existing error suppression techniques because it is known that at least one error has occurred. However, it is not possible to conclude from a passed symmetry verification test that no errors have occurred.

[0071] Each operation performed in step S101 includes a symmetry operation S. A noise gate operation U n This may include errors of a form that is undetectable using the selected symmetry operation. Thus, in this embodiment, a quasi-probabilistic technique is used to remove error components that are locally undetectable using symmetry. Note from the above description of the symmetry verification technique that the remaining locally detectable errors can be recombined to form globally undetectable errors. The symmetry measurement is performed globally.

[0072] The symmetry operations and basic operations performed after the gate operation in step S101 can be performed in any order after the gate operation. A first possible operation performed on the qubits in the group of qubits includes: performing the gate operation U n, followed by executing the symmetry operation S, followed by executing a first elementary operation B1, where the first elementary operation is selected by the selection module with a first probability proportional to |p1|. The first elementary operation can change the symmetry of the system and modify the pass / fail criteria of our symmetry verification accordingly. The state of the qubit is measured by a quantum measurement device after executing the sequence of operations in the first operation.

[0073] A second possible operation to be performed on a qubit in the set of qubits includes performing the gate operation U n , followed by performing a second elementary operation B2, followed by performing a symmetry operation S, wherein the second elementary operation is selected by the selection module with a second probability proportional to |p2|. Similarly, the state of the qubit is measured by the quantum measurement device after performing the sequence of operations in the second operation.

[0074] The state of a qubit is typically a superposition of a first state, |0>, and a second state, |1>. However, when measured, the qubit's state will be either the first or second state, i.e., 0 or 1, with the first or second state corresponding to the measurement results being -1 or +1, respectively.

[0075] The first state and the second state are different depending on the type of qubit. Thus, the measured property of the qubit depends on the type of qubit. The quantum measurement device is selected to correspond to the type of qubit. For example, the first state and the second state of an electron spin qubit are spin-up and spin-down, where spin-up is recorded as +1 and spin-down is recorded as -1. Thus, a measurement of the electron spin qubit is obtained by measuring the electron spin, and the quantum measurement device is configured to measure the electron spin.

[0076] If the qubit is an electron charge qubit, the electron charge is measured, where the first state and the second state are not multiple electrons but a single electron. If the qubit is a superconducting phase qubit, the excited state is measured, where the first state and the second state are a ground state and a first excited state. Any quantum system having a first measurable state and a second measurable state can be used as a qubit. A suitable quantum measurement device that enables the first state and the second state to be distinguished is used to obtain the measurement.

[0077] By performing the operation in step S101 multiple times, the average state of the qubit can be determined. n and reduce the error operation U n1 The relationship between N -1 U n =U n1 , where N -1= p1B1+p2B2+p3B3+p4B4, it can be seen that measurements made after performing the modified operation can be computationally recombined to determine the effect of the error-reducing operation on the state of the qubit, where the error-reducing operation is expressed in terms of |p j | Proportional probability for different basic operations B j Sampling is performed. According to the coefficient p j For example, if p2 = -0.2 and SB2U is performed n If the state of the qubit is later measured to be 1, the measurement is recorded as -1.

[0078] In step S102, a symmetry operation is performed on the group of qubits using a symmetry measurement device to obtain a symmetry measurement. The group of qubits includes a plurality of qubits. A symmetry measurement S102 is obtained after each execution of operation S101. If the number of errors is an even number, the symmetry measurement is a first symmetry result, "pass", or if the number of errors is an odd number, the symmetry measurement is a second symmetry result, "fail". Examples of characteristics of a system that can be used to perform a symmetry verification test include parity, particle number, and energy. In existing symmetry verification techniques, measurements that fail the symmetry test are discarded. However, in this embodiment, each measurement is retained and classified according to its symmetry result. This reduces the cost of the error suppression technology of this embodiment. However, measurements that fail the symmetry verification test can be constructively used using the methods and analysis described below.

[0079] In this embodiment, a single symmetry operation is performed after the gate operation. In alternative embodiments, more than one symmetry operation is used. Typically, each symmetry operation is used to verify the symmetry of a different characteristic of the system and returns a pass result or a fail result.

[0080] In step S103, the first state measurement E is obtained. pass The classical processor is used to average the measurements of the state of the qubits after the operations in step S101, which are classified as "passed" after the symmetry classification in step S102. The averaged measurement is obtained from the set of j-th operations performed. According to the coefficient p determined j Possible basic operations B j The weighted sampling of experimentally recreates the theoretically determined transformation N -1 .

[0081] In step S104, the second state measurement E is obtained. fail, where the measurements classified as "failed" in step S102 are averaged using a classical processor. The first state measurement and the second state measurement will differ due to the different probabilities of an even number of errors and an odd number of errors. The probability of an even number of errors at the first error rate n1 is The probability of an odd number of errors occurring at the first error rate is The measurements obtained in steps S102, S103 and S104 may be obtained simultaneously.

[0082] In alternative embodiments where more than one symmetry operation is performed, additional status measurements may be obtained. For example, if two symmetry operations are performed and each operation has a pass or fail result, four status measurements corresponding to pass-pass, pass-fail, fail-pass, and fail-fail will be measured.

[0083] In step S105, the first state measurement and the second state measurement are fitted to a first curve and a second curve, respectively, using a classical processor of a conventional computer. This is an extrapolated error suppression technique. The expected value of the observable (i.e., the average of the individual measurements of the state of the qubit) depends on the level of noise. Assuming that the relationship between the expected value of the observable and the noise level or error rate follows a trend, the measured state measurement can be fitted to the trend and used to predict the expected value of the observable under lower noise.

[0084] In this embodiment, it is assumed that the expected value of the observable decays exponentially with increasing error rate. The first state measurement and the second state measurement are from the operation performed at the first error rate in step S101, but since the probability of passing or failing the symmetry verification test is different, the two state measurements will result in different measurement expected values. The first curve used to fit the first state measurement is of the form Where A and γ are fitting parameters and n is the error rate. The second curve used to fit the second state measurement is of the form

[0085] At this first error rate, the expected value of the state of the qubit can be expressed as E n1 =P even E pass +P odd E fail In an alternative embodiment, the probability P of the first symmetry result and the second symmetry result is used. even 、P odd With the first state measurement and the second state measurement E pass 、E fail This estimate of the expected value of the state of the qubits of the combination can be used to provide an error-suppressed value of the observable.

[0086] In this embodiment, error extrapolation is used together with the assumption that the value of the observable decays approximately exponentially with the error rate to further suppress the error. Assume that the exponential decay curve is a single exponential decay (ie, E n =Ae -γn , where E n is the average state of the qubit, n is the error rate, and A and γ are fitting parameters), two types of measurements (i.e., pass and fail measurements) performed at a single error rate can be used to determine the noise-free expectation value.

[0087] In an alternative embodiment, the curve is a multi-exponential decay curve comprising the sum of two or more exponentials, i.e. where K>1. To ensure that the fitting parameters adequately reflect the relationship between the expected value of the observable and the error rate, there should be sufficient data points. For example, a double exponential decay curve with K=2 requires a minimum of four measurements in order to determine the four free fitting parameters A1, A2, γ1, and γ2. This can be achieved using two symmetry operations and four state measurements as described above. Alternatively or additionally, operations can be performed at another error rate to obtain additional measurements of the state of the qubit under differently modified operations.

[0088] In step S106, a classical processor is used to extrapolate the average state of the qubit at a second error rate lower than the first error rate. In this embodiment, the second error rate is selected to be zero error rate so that a noise-free expected value can be estimated.

[0089] Using the first fitting curve and the second fitting curve from step S105, the first state measurement and the second state measurement E can be respectively combined by using the following equations pass and E fail To determine the noise-free expected value E0.

[0090]

[0091] Figure 2 is a flow chart depicting an error suppression method according to another embodiment. In step S201, a first operation is performed on the state of a qubit using a quantum processor. The first operation has a first error rate n1, which, in this embodiment, is typically the unsuppressed error rate of the quantum computing system. Typically, the unsuppressed error rate is the lowest experimentally achievable error rate. However, hardware variations and other environmental factors may affect the error rate.

[0092] The first operation is a gate operation selected by the experimenter. After performing the first operation, a first measurement of the state of the qubit is obtained using a quantum measurement device in step S202. Figure 1 As described, the measurement result is +1 or -1.

[0093] In step S203, the quantum processor is used to perform a second operation on the state of the qubit. The second operation also has a first error rate n1. The second operation in this embodiment is the same as the gate operation performed in step S201. After performing the second operation, in step S204, the quantum measurement device is used to obtain a second measurement of the state of the qubit.

[0094] The gate operation is typically repeated multiple times, and a measurement of the state of the qubit is obtained after each execution of the gate operation. Then, in step S205, a classical processor is used to calculate a first average value of the state of the qubit. The first average value is calculated by averaging the first measurement, the second measurement, and any additional measurements performed. The first average value represents the expected value of the observable at the first error rate.

[0095] In step S206, a third operation is performed on the state of the qubit using the quantum processor. The third operation has a second error rate n2, and the second error rate n2 is lower than the first error rate n1, i.e., n2 < n1. A quasi-probability technique as described with respect to Figure 1 is used to achieve the lower error rate. The third operation includes a first operation and a first elementary operation. The first elementary operation is one of a set of elementary operations, and the selection module is used to randomly select the first elementary operation with a first probability. After performing the third operation, in step S207, the quantum measurement device is used to obtain a third measurement of the state of the qubit.

[0096] In step S208, a fourth operation is performed on the state of the qubit. The fourth operation has a second error rate n2. The fourth operation includes a first operation and a second elementary operation. The second elementary operation is one of a set of elementary operations, and the selection module is used to randomly select the second elementary operation with a second probability. The second elementary operation is different from the first elementary operation. After performing the fourth operation, in step S208, a fourth measurement of the state of the qubit is obtained.

[0097] The modified gate operation (i.e., the first operation after randomly selecting an elementary operation) is typically repeated multiple times. The randomly selected elementary operation is selected from a set of elementary operations that includes the first elementary operation, the second elementary operation, and additional different elementary operations. In this embodiment, the set of elementary operations used is the Pauli set, and there are four different elementary operations for single-qubit operations. As described with respect to Figure 1 the selection of each of the basis operations is weighted according to coefficients determined using quasi-probability. A measurement of the state of the qubit is obtained after each execution of the modified gate operation. Thus, the error rate can be reduced by performing additional elementary operations after the gate operation.

[0098] This gate operation is typically an operation sequence and can include any typical quantum gates, such as Pauli or Hadamard gates, and the qubit is one of a set of qubits. The selection module is configured to modify each operation performed on the state of each qubit in the set of qubits. Optionally, some operations are not modified and are performed in a conventional manner. The random nature of the modification provides an unbiased statistical representation of the expected value of the state of the qubit. In this embodiment, for a set of n qubits, the selection module randomly selects basic operations from a set of 4 n basic operations.

[0099] In step S210, a second average value of the state of the qubit is calculated by averaging the third measurement, the fourth measurement, and any additional measurements performed. According to the determined coefficient p j of the possible basic operations B j weighted sampling is used to experimentally recreate the theoretically determined transformation N -1 =∑ j p j B j . In this embodiment, the correlation between an operation with a first error rate and an operation with a second error rate is: U n1 =NU n2 , where n2 < n1. The second average value represents the expected value of the observable at the second error rate. In this embodiment, the operator N is designed to change the form of the error such that the noise model is simplified.

[0100] In step S211, a classical processor is used to fit the first average value and the second average value to a curve. The selected curve can depend on the theoretical understanding of the relationship between the expected value of the state of the qubit and the error rate. In this embodiment, the curve is an exponential decay curve including a single exponent, that is, E n =Ae -γn , where E n is the average state of the qubit, n is the error rate, and A and γ are fitting parameters.

[0101] In an alternative embodiment, the curve is a multi-exponential decay curve including at least two exponents, that is, where K>1. To fit a multi-exponential decay curve, it is usually necessary to obtain further measurements of the average value of the qubit to ensure that the curve is not overfitted, thus obtaining the performance of local noise rather than the overall trend.

[0102] Having determined the form of the curve by fitting the first average and the second average, extrapolation can be used in step S212 to estimate the average state of the qubit at a third error rate. The third error rate is lower than the first error rate and the second error rate, and in this embodiment is selected to be zero. In this way, a noise-free value of an observable can be estimated using a classical processor.

[0103] Figure 3 is a schematic diagram of a first quantum computation according to an embodiment. In this embodiment, each qubit undergoes a sequence of four operations before being measured. The diagram depicts the operations for a group of three qubits, but there are typically 10 or 100 qubits in the group.

[0104] A first operation 311, a second operation 312, and a third operation 313 are performed on the states of the first qubit, the second qubit, and the third qubit, respectively. In this embodiment, the first, second, and third operations 311-313 are performed simultaneously. Each of the first, second, and third operations 311-313 is a single-qubit operation. Subsequently, a fourth operation 314 and a fifth operation 315 are performed. In this embodiment, the fourth and fifth operations 314, 315 are performed simultaneously. Fourth operation 314 is a two-qubit operation performed on the first and second qubits, and fifth operation 315 is a single-qubit operation performed on the third qubit. Thereafter, a sixth operation 316 and a seventh operation 317 are performed. In this embodiment, the sixth and seventh operations 316, 317 are performed simultaneously. Sixth operation 316 is a single-qubit operation performed on the first qubit, and seventh operation 317 is a two-qubit operation involving the interaction of the second and third qubits.

[0105] The first to seventh operations 311-317 are gate operations. The first, second, third, fifth, and sixth operations 311, 312, 313, 315, and 316 are single-qubit gate operations performed on qubits in the set of qubits. One or more of the first, second, third, fifth, and sixth operations 311, 312, 313, 315, and 316 may be identity operations. The fourth and seventh operations 314 and 317 are two-qubit gate operations performed on two qubits in the set of qubits. Any single-qubit and / or two-qubit operation may be selected based on the requirements of the experiment.

[0106] After performing the gate operation described above, in this embodiment, a first basic operation 321, a second basic operation 322, and a third basic operation 323 are performed on the states of the first qubit, the second qubit, and the third qubit, respectively. A selection module is used to randomly select each of the first, second, and third basic operations 321-323 from a basic operation set. In this embodiment, the basic operation set is a Pauli set, and there are three operations in the set. Random selection means that the first, second, and third basic operations 321-323 can all be different, or only two of them can be the same, or they can all be the same.

[0107] After performing the sequence of operations, a measurement is obtained. In this embodiment, a symmetry measurement is performed using symmetry measurement device 330. Symmetry measurement device 330 measures a characteristic of the system as a whole. The symmetry measurement in this embodiment is designed so that it does not affect the measurement of the state of each qubit in the set of qubits. For example, symmetry measurement device 330 can measure the state of an ancilla qubit that is configured to change state upon detecting a specified state change in any of the first qubit, the second qubit, and the third qubit. The measurement of the state of the ancilla qubit can advantageously be performed without destroying the states of the qubits in the set of qubits.

[0108] The quantum computation described can be performed multiple times. In embodiments that include symmetry verification, a symmetry measurement is obtained after each execution of the quantum computation using the symmetry measurement device 330. The symmetry measurement is a first symmetry result if the number of errors is even, or a second symmetry result if the number of errors is odd.

[0109] First quantum measurement device 331 measures the state of a first qubit. Second quantum measurement device 332 measures the state of a second qubit. Third quantum measurement device 333 measures the state of a third qubit.

[0110] The use of symmetry measurements is optional, and in an alternative embodiment, the state of each qubit is measured only after the operation. In another alternative embodiment, each operation performed on the set of qubits (i.e., the first, second, third, fourth, fifth, sixth, and seventh operations 311-317) can be modified using a randomly selected elementary operation.

[0111] Figure 4FIG2 is a diagram illustrating a fitting and extrapolation process according to an embodiment. The fitting and extrapolation are performed using a processor of a classical computer. Using the above method, a first measurement 41 at a first error rate 42 and a second measurement 43 at a second error rate 44 are obtained. When the first error rate 42 is greater than the second error rate 44, the first measurement 41 is less than the second measurement 43.

[0112] Using a classic processor, the form E = Ae -γn An exponential decay curve 45 is fitted to the first measurement 41 and the second measurement 43. Having determined the fitting parameters A and γ, the curve is extrapolated to a third error rate 47 using a classical processor. Here, third error rate 47 is the zero error rate n=0. The error-free value of observable 46 is estimated by extrapolating to the zero error rate. In alternative embodiments, further measurements can be performed at additional error rates to refine the estimate of the fitting parameters.

[0113] As will be appreciated, an improved error suppression method is provided in which the estimate of error-free observables is greatly improved.The combination of error suppression techniques as described results in an improved estimate of error-free observables at a reduced cost.

Claims

1. A method for suppressing errors in quantum computing, wherein: The method comprises: performing an operation a plurality of times on a state of a qubit in a set of qubits, wherein the operation has a first error rate, wherein each performance of the operation comprises: performing a first operation, wherein the first operation includes: a gate operation, a symmetry operation, and a first basic operation; or performing a second operation, the second operation comprising: the gate operation, the symmetry operation, and a second basic operation; wherein the first basic operation and the second basic operation are different basic operations selected from a basic operation set; and Measuring the state of the qubit; wherein the probability of performing the first operation is a first probability, and the probability of performing the second operation is a second probability; obtaining a symmetry measurement of the set of qubits using the symmetry operation after each performance of the operation, wherein the set of qubits comprises a plurality of qubits; wherein the symmetry measure is a first symmetry result if the number of errors is an even number, or a second symmetry result if the number of errors is an odd number; obtaining a first state measurement by determining an average state of the qubits that results from the first symmetry; obtaining a second state measurement by determining an average state of the qubits that results from the second symmetry; The first state measurement is fitted into a first curve, the first curve is in the form of The second state measurement is fitted into a second curve, the second curve is in the form of where n is the error rate, A and γ are fitting parameters; and extrapolating an average state of the qubit at a second error rate using the first fitting curve and the second fitting curve; The second error rate is lower than the first error rate.

2. A method for suppressing errors in quantum computing according to any one of the preceding claims, wherein: The first basic operation and the second basic operation are selected from a set of basic operations, and the set of basic operations includes Pauli basic operations.

3. A method for suppressing errors in quantum computing according to any one of the preceding claims, wherein: The first symmetry result is pass, and the second symmetry result is fail.

4. The method for suppressing errors in quantum computing according to claim 1, wherein: The qubit is a first qubit, and the method further comprises: performing the operation a plurality of times on a state of a second qubit in the set of qubits; obtaining a third state measurement by determining an average state of the second qubit as a result of the first symmetry; obtaining a fourth state measurement by determining an average state of the second qubit that results from the second symmetry; fitting the third state measurement to a third curve and fitting the fourth state measurement to a fourth curve; and The average state of the second qubit at the second error rate is extrapolated using the third and fourth fitting curves.

5. A device for performing a quantum computing operation, comprising: A selection module is configured to: Selecting a first basic operation from the set of basic operations with a first probability; as well as selecting a second basic operation from the set of basic operations with a second probability; wherein the first basic operation and the second basic operation are different; A quantum processor configured to perform an operation on a state of a qubit in a set of qubits a plurality of times, wherein the operation has a first error rate, wherein each performance of the operation comprises: Perform gating, symmetry, and selected basic operations; a quantum measurement device configured to measure a state of the qubit; a symmetry measurement device configured to measure a symmetry of the set of qubits using the symmetry operation after each performance of the operation, wherein the set of qubits comprises a plurality of qubits; wherein the symmetry measure is a first symmetry result if the number of errors is an even number, or a second symmetry result if the number of errors is an odd number; and A classic processor, the classic processor being configured to: obtaining a first state measurement by determining an average state of the qubits for the first symmetry outcome, and obtaining a second state measurement by determining an average state of the qubits for the second symmetry outcome; The first state measurement is fitted into a first curve, the first curve is in the form of The second state measurement is fitted into a second curve, the second curve is in the form of where n is the error rate, A and γ are fitting parameters; and The average state of the qubit at a second error rate is extrapolated using the first and second fit curves, wherein the second error rate is lower than the first error rate.

6. A method for suppressing errors in quantum computing, wherein: The method comprises: performing a first operation on a state of the qubit, wherein the first operation has a first error rate; obtaining a first measurement of the state of the qubit; performing a second operation on the state of the qubit, wherein the second operation has the first error rate; obtaining a second measurement of the state of the qubit; calculating a first average value of the state of the qubit at the first error rate by averaging the first measurement and the second measurement; performing a third operation on the state of the qubit, wherein the third operation has a second error rate lower than the first error rate, wherein the third operation includes the first operation and a first base operation; obtaining a third measurement of the state of the qubit; performing a fourth operation on the state of the qubit, wherein the fourth operation has the second error rate, wherein the fourth operation includes the first operation and a second elementary operation; wherein the first basic operation and the second basic operation are different basic operations selected from a basic operation set; obtaining a fourth measurement of the state of the qubit; calculating a second average value of the state of the qubit at the second error rate by averaging the third measurement and the fourth measurement; fitting a first average value of the states of the qubits and a second average value of the states of the qubits into a curve; and The fitted curve is used to extrapolate an average state of the qubit at a third error rate, wherein the third error rate is lower than the first error rate and the second error rate.

7. The method for suppressing errors in quantum computing according to claim 6, wherein: The probability of selecting the first basic operation is a first probability, and the probability of selecting the second basic operation is a second probability.

8. The method for suppressing errors in quantum computing according to claim 6 or 7, wherein: The basic operation set includes Pauli basic operations.

9. The method for suppressing errors in quantum computing according to claim 6, wherein: The second operation is the same as the first operation.

10. The method for suppressing errors in quantum computing according to claim 6, wherein: The qubit is one of a plurality of qubits in a group of qubits.

11. The method for suppressing errors in quantum computing according to claim 6, wherein: The curve is an exponential decay curve.

12. The method for suppressing errors in quantum computing according to claim 11, wherein: The exponential decay curve is of the form A multi-exponential decay curve, where E is the average state of the qubit, n is the error rate, and A k and γ k are fitting parameters.

13. A device for performing a quantum computing operation, comprising: a selection module configured to select a basic operation from a basic operation set including a first basic operation and a second basic operation, wherein the first basic operation and the second basic operation are different; A quantum processor configured to: performing a first operation on a state of the qubit, wherein the first operation has a first error rate; performing a second operation on the state of the qubit, wherein the second operation has the first error rate; performing a third operation on the state of the qubit, wherein the third operation has a second error rate lower than the first error rate, wherein the third operation includes the first operation and the first elementary operation; and performing a fourth operation on the state of the qubit, wherein the fourth operation has the second error rate, wherein the fourth operation includes the first operation and the second elementary operation; a quantum measurement device configured to obtain a first measurement, a second measurement, a third measurement, and a fourth measurement after performing the first operation, the second operation, the third operation, and the fourth operation, respectively; and A classic processor, the classic processor being configured to: calculating a first average value of the state of the qubit at the first error rate by averaging the first measurement and the second measurement; calculating a second average value of the state of the qubit at the second error rate by averaging the third measurement and the fourth measurement; fitting a first average value of the states of the qubits and a second average value of the states of the qubits into a curve; and The fitted curve is used to extrapolate an average state of the qubit at a third error rate, wherein the third error rate is lower than the first error rate and the second error rate.

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