Quantum joint measurement method, system and electronic device based on check matrix

Abstract

The application discloses a quantum joint measurement method and system based on a check matrix and electronic equipment, and the quantum joint measurement method based on the check matrix comprises the following steps: obtaining and preprocessing generators of a Pauli term set to obtain complete generators corresponding to the Pauli term set; generating an initial check matrix according to the complete generators; transforming the initial check matrix into a target check matrix and recording quantum gates used in the transformation process and the order of the quantum gates; generating a joint measurement quantum circuit composed in sequence according to the quantum gates and the order of the quantum gates; obtaining a measurement result corresponding to the generators under a Z basis according to the joint measurement quantum circuit, a joint measurement frequency and a quantum state to be measured; generating and updating a first check matrix corresponding to the Pauli term set to obtain a second check matrix, and calculating an expected value of a Pauli term in the Pauli term set. The application can obtain a quantum circuit for joint measurement through simple transformation based on a matrix, without complex operation on the entire quantum state, and the calculation efficiency is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of quantum technology, and in particular to a quantum joint measurement method based on a check matrix, a quantum joint measurement system based on a check matrix and an electronic device. BACKGROUND

[0002] In quantum mechanics, the Hamiltonian is a core operator that describes the energy of a system, and measuring the expectation value of the Hamiltonian is an important step in solving problems such as quantum simulation, quantum chemistry, and quantum optimization. For example, in the field of quantum chemistry, the ground state energy of a molecular system is obtained by solving the minimum expectation value of the Hamiltonian. The Hamiltonian of a real physical system can usually be decomposed into a linear combination of multiple Pauli terms, i.e., the direct product of Pauli operators {I, X, Y, Z}. The expectation value of the Hamiltonian in the conventional technique is obtained by calculating the weighted sum of the expectation values of all Pauli terms, which requires measuring the expectation value of each Pauli term separately. Since quantum information cannot be directly and completely observed, the preparation and measurement of quantum states must be repeated M times, and the probability distribution of the measurement data must be statistically analyzed, in order to indirectly and approximately estimate the expectation value of the measured Pauli term. If there are N Pauli terms in total, then approximately NM measurements are required to obtain the expectation value of the Hamiltonian. Obviously, when the number of Pauli terms N in the Hamiltonian is large, the conventional technique will consume a large amount of time and resources, and the efficiency is extremely low.

[0003] In order to improve the efficiency, the joint measurement method in the related art divides all Pauli terms into k (k is less than N) sets according to the commutation relation, and extracts the generators of each set, and the Pauli terms in the set can be composed of the generators. The target is simplified to measure the expectation value of the generator, and then the expectation values of all Pauli terms are obtained through a classical post-processing method, and the total number of measurements is directly reduced to about kM times. However, the joint measurement method in the related art has the following problems: 1. The variational quantum-classical hybrid algorithm is applied in the related art, and the joint measurement quantum circuit contains parameters to be trained, which needs to be trained and optimized based on a complete quantum state with the help of a classical simulator, resulting in a complex calculation process and a large amount of calculation. 2. Due to the training and optimization characteristics of the variational algorithm, only the basis vector transformation of the generator can be approximately realized, which enlarges the error between the actual measurement result and the theoretical value. SUMMARY

[0004] The present application is proposed to solve at least one of the above problems. According to a first aspect of the present application, a quantum joint measurement method based on a check matrix is provided, which comprises: obtaining and preprocessing generators of a Pauli term set to obtain complete generators corresponding to the Pauli term set; generating an initial check matrix according to the complete generators; transforming the initial check matrix into a target check matrix and recording quantum gates used in the transformation process and the order thereof; generating a joint measurement quantum circuit composed in sequence according to the quantum gates and the order thereof; obtaining measurement results of the generators corresponding to the Pauli term set in the Z basis according to the joint measurement quantum circuit, a joint measurement number and a quantum state to be measured; generating a first check matrix corresponding to the Pauli term set, updating the first check matrix using the joint measurement quantum circuit to obtain a second check matrix, and calculating expected values of Pauli terms in the Pauli term set according to the measurement results and the second check matrix; wherein the initial check matrix is composed of phase exponents, an X matrix and a Z matrix, and the feature of the target check matrix is that the X matrix is a zero matrix, the Z matrix is a unit matrix, and the phase exponents are all zero.

[0005] In an embodiment of the present application, the step of transforming the initial check matrix into a target check matrix and recording quantum gates used in the transformation process and the order thereof comprises:

[0006] The initial check matrix is updated using an H gate to maximize the rank of the X matrix, to obtain a first target check matrix and record the H gates used in sequence.

[0007] The first target check matrix is updated using a SWAP gate and / or a CX gate to transform the X matrix into a lower triangular matrix, to obtain a second target check matrix and record the SWAP gate and / or the CX gate used in sequence.

[0008] The second target check matrix is updated using a CX gate to transform the X matrix into a unit matrix, to obtain a third target check matrix and record the CX gate used in sequence.

[0009] The third target check matrix is updated using an S gate to transform the Z matrix into a zero matrix, to obtain a fourth target check matrix and record the S gate used in sequence.

[0010] The fourth target check matrix is updated using an H gate to transform the X matrix into a zero matrix and the Z matrix into a unit matrix, to obtain a fifth target check matrix and record the H gate used in sequence.

[0011] The fifth target check matrix is updated using an X gate to make the phase exponents all zero, to obtain the target check matrix and record the X gate used in sequence.

[0012] In one embodiment of the present invention, the step of updating the initial parity-check matrix using H gates to maximize the rank of the X matrix, obtaining the first target parity-check matrix, and recording the H gates used in sequence includes:

[0013] Use in sequence The gate updates the initial parity-check matrix. During the update process, if... If the gate increases the rank of the X matrix, the updated parity check matrix is ​​retained; otherwise, the updated parity check matrix is ​​not retained, thus obtaining the first target parity check matrix.

[0014] Recording in order increases the rank of the X matrix. Door.

[0015] in, The gate represents the H gate on the a-th qubit. , This represents the total number of qubits.

[0016] In one embodiment of the present invention, the condition for updating the first target parity check matrix using the SWAP gate is: sequentially traversing the transpose of the X matrix. The main diagonal, during the traversal, if the a-th element of the main diagonal is not 1 and the element in the b-th row and a-th column is 1, then use... The gate updates the first target verification matrix.

[0017] The condition for updating the first target parity check matrix using the CX gate is: the transpose of the X matrix... Performing PLU decomposition yields matrices P, L, and U, where... If the inverse matrix of matrix L is If the element in row a, column b is 1, then use The gate updates the first target verification matrix.

[0018] The condition for updating the fifth target parity check matrix using the X-gate is: sequentially traversing the phase index of the a-th row of the fifth target parity check matrix. ,like Then use The gate updates the fifth target verification matrix.

[0019] in, , The gate represents the SWAP gate on the a-th and b-th qubits. The gate represents the CX gate on the b-th and a-th qubits, where b points to the control bit and a points to the target bit. The gate represents the X gate on the a-th qubit.

[0020] In one embodiment of the present invention, using The step of updating the initial parity check matrix by the gate comprises: updating the phase index of the i-th row in the initial parity check matrix in sequence by the following formula:

[0021]

[0022] Swap the a-th column of the X matrix with the a-th column of the Z matrix.

[0023] Using The step of updating the first target parity check matrix by the gate comprises:

[0024] Swap the a-th column and the b-th column of the X matrix.

[0025] Swap the a-th column and the b-th column of the Z matrix.

[0026] Using The step of updating the first target parity check matrix by the gate comprises:

[0027] Update the phase index of the i-th row in the first target parity check matrix in sequence by the following formula:

[0028]

[0029] Column-wise XOR the a-th column of the X matrix to the b-th column.

[0030] Column-wise XOR the b-th column of the Z matrix to the a-th column.

[0031] The step of updating the second target parity check matrix by the CX gate comprises:

[0032] Traverse the X matrix from right to left by column, and in the traversal process, if the element of the m-th column and the k-th row is 1, then update the second target parity check matrix by the gate.

[0033] The step of updating the third target parity check matrix by the S gate comprises:

[0034] Update the phase index of the i-th row in the third target parity check matrix in sequence by the following formula:

[0035]

[0036] Column-wise XOR the a-th column of the X matrix to the a-th column of the Z matrix.

[0037] Using The step of updating the fifth target parity check matrix by the gate comprises.

[0038] Update the phase index of the i-th row in the fifth target parity check matrix in sequence by the following formula:

[0039]

[0040] wherein, , denotes XOR operation, denotes the element in the i-th row and a-th column of the X matrix, denotes the element in the i-th row and a-th column of the Z matrix, denotes the CX gate on the k-th and m-th qubits, k points to the control bit and m points to the target bit, k > m, , .

[0041] In an embodiment of the present application, the step of pre-processing the generating element of the set of Pauli terms comprises:

[0042] determining whether the number of the generating element is equal to the number of bits of the Pauli term in the set of Pauli terms.

[0043] if yes, taking the generating element as the complete generating element.

[0044] if no, padding the generating element to obtain the complete generating element.

[0045] In an embodiment of the present application, the step of obtaining the measurement result corresponding to the generating element in the Z basis according to the joint measurement quantum circuit, the number of joint measurements and the quantum state to be measured comprises:

[0046] obtaining the quantum state to be measured and the number of joint measurements, denoting the number of joint measurements as M.

[0047] making the quantum state to be measured execute the joint measurement quantum circuit to obtain a new quantum state.

[0048] performing a Z basis measurement on the new quantum state to obtain a measurement data.

[0049] repeating the above steps M times to obtain M measurement data.

[0050] summarizing the probabilities corresponding to different measurement data to obtain the measurement result corresponding to the generating element.

[0051] In an embodiment of the present application, the step of calculating the expected value of the Pauli term in the set of Pauli terms according to the measurement result and the second check matrix comprises:

[0052] traversing the Z matrix in the second check matrix by row, and extracting the column sequence number of the column with element 1 in the current row of the Z matrix.

[0053] after extracting the column sequence number of the current row, traversing the measurement data, and recording the number of elements with value 1 in the column sequence number in the traversed measurement data as t.

[0054] The expected value of the Pauli term is calculated by the following formula:

[0055]

[0056] wherein p represents a probability corresponding to the measurement data, .

[0057] According to the second aspect of the present application, there is provided a quantum joint measurement system based on a check matrix, the quantum joint measurement system based on the check matrix comprising:

[0058] A preprocessing module is configured to obtain and preprocess generators of a Pauli term set to obtain complete generators corresponding to the Pauli term set.

[0059] A check matrix initialization module is configured to generate an initial check matrix according to the complete generators.

[0060] A check matrix transformation module is configured to transform the initial check matrix into a target check matrix and record quantum gates used in the transformation process and an order thereof.

[0061] A quantum circuit generation module is configured to generate a joint measurement quantum circuit composed in sequence according to the quantum gates and the order thereof.

[0062] A joint measurement module is configured to obtain measurement results corresponding to the generators in the Z basis according to the joint measurement quantum circuit, a joint measurement number and a quantum state to be measured.

[0063] A classical post-processing module is configured to generate a first check matrix corresponding to the Pauli term set, update the first check matrix using the joint measurement quantum circuit to obtain a second check matrix, and calculate expected values of Pauli terms in the Pauli term set according to the measurement results and the second check matrix.

[0064] The initial check matrix is composed of phase indexes, an X matrix and a Z matrix, and the target check matrix is characterized in that the X matrix is a full zero matrix, the Z matrix is a unit matrix, and the phase indexes are all zero.

[0065] According to the third aspect of the present application, there is provided an electronic device comprising a memory, a processor and a computer program stored in the memory, wherein the computer program is executed by the processor to implement any of the quantum joint measurement methods based on a check matrix.

[0066] According to the quantum joint measurement method based on the check matrix, the quantum joint measurement system based on the check matrix and the electronic device provided by the embodiments of the present application, when solving the expected value measurement of the Hamiltonian, the generation element in the Pauli item set can be transformed into the base vector of the z base in parallel through joint measurement, the number of quantum state preparation and measurement is reduced, and thus the quantum computing resources are saved. Meanwhile, the quantum circuit used for joint measurement can be obtained through simple transformation based on the matrix, without complex operation and simulation on the whole quantum state, and thus the computing efficiency is improved. Moreover, the accurate base vector transformation can be realized without loss, and thus the computing accuracy is improved. BRIEF DESCRIPTION OF DRAWINGS

[0067] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed to be used in the embodiment description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and for those skilled in the art, other drawings can be obtained without creative labor.

[0068] Figure 1 The flowchart of the quantum joint measurement method based on the check matrix provided by an embodiment of the present application is shown in the figure.

[0069] Figure 2 The circuit diagram of the joint measurement quantum circuit provided by an embodiment of the present application is shown in the figure.

[0070] Figure 3 The structure diagram of the quantum joint measurement system based on the check matrix provided by an embodiment of the present application is shown in the figure.

[0071] Figure 4 The hardware structure block diagram of the computer terminal of the quantum joint measurement method based on the check matrix provided by an embodiment of the present application is shown in the figure. DETAILED DESCRIPTION

[0072] In order to make the objects, technical solutions and advantages of the present application more obvious, the following will describe the example embodiments according to the present application with reference to the drawings. Obviously, the described embodiments are only some of the embodiments of the present application, not all the embodiments of the present application, and it should be understood that the present application is not limited to the example embodiments described herein. Based on the embodiments of the present application described in the present application, all other embodiments obtained by those skilled in the art without creative labor should fall within the protection scope of the present application.

[0073] In the following description, numerous specific details are set forth to provide a more thorough understanding of the present application. However, it will be apparent to one of skill in the art that the present application can be practiced without one or more of these specific details. In other instances, well-known features have not been described in order to avoid obscuring the present application.

[0074] It should be understood that the present application can be practiced with the

[0075] For a thorough understanding of the present application, reference should be made to the following detailed description taken in conjunction with the accompanying drawings, in which:

[0076] Some embodiments of the present application will now be described in detail with reference to the accompanying drawings. The following embodiments and features can be combined with each other, if not in conflict.

[0077] For the expectation value measurement of a Hamiltonian, the expectation value of each Pauli term can be measured separately. Due to the characteristics of quantum measurement, for each Pauli term, the quantum state preparation and measurement must be repeated M times to obtain the probability statistics of the measurement results, so as to approximately estimate the expectation value of the Pauli term. Therefore, if there are N Pauli terms, the quantum state preparation and measurement need to be repeated NM times. The related technology divides all Pauli terms into k (k is much smaller than N) sets, each set has a set of generators, and the expectation value of the set of generators is measured, so that the expectation value of each Pauli term in the set can be calculated, and the expectation value of the Hamiltonian can be calculated by measuring the expectation value of the k sets of generators. A set of generators can be jointly measured, that is, the expectation value of a set of generators can be known by preparing and measuring the quantum state M times. Therefore, only kM times of quantum state preparation and measurement are needed, and the number of times is less. However, the related technology has some defects and problems: first, the variational quantum classical hybrid algorithm is applied, the joint measurement quantum circuit contains parameters to be trained, and the classical simulator needs to be used for training and optimization based on the complete quantum state, the calculation process is complex, and the calculation amount is large. Second, due to the training and optimization characteristics of the variational algorithm, only the basis vector transformation of the generator can be approximately realized, which enlarges the error between the actual measurement result and the theoretical value, and the measurement result may be inaccurate.

[0078] In order to improve the calculation efficiency and the accuracy of the calculation result, the first aspect of the present application provides a quantum joint measurement method based on a check matrix, as shown in Figure 1 The quantum joint measurement method based on the check matrix comprises:

[0079] S1, obtain and preprocess the generators of the Pauli term set to obtain the complete generators corresponding to the Pauli term set.

[0080] S2, generate an initial check matrix according to the complete generators.

[0081] It should be noted that the check matrix is an algebraic representation of the stabilizer generators. For a quantum state on n qubits , if there exists a Pauli term , such that , then is stable under , and is a stabilizer of . If has stabilizers, then is a stabilizer state, and there are n generators that can uniquely determine . The standard form of the check matrix is as follows:

[0082]

[0083] where n rows represent n generators, represents the phase index of the i-th generator, and the corresponding phase is . If the phase of the i-th generator is +1, then ; if it is -1, then . If the j-th bit of the i-th generator is the Pauli operator X, then ; if the j-th bit of the i-th generator is the Pauli operator Z, then ; if the j-th bit of the i-th generator is the Pauli operator Y, then ; and the rest are all 0. The matrix composed of all is simply referred to as an X matrix, and the matrix composed of all is simply referred to as a Z matrix. The n columns of the X matrix and the Z matrix correspond to n qubits, respectively.

[0084] S3, transform the initial check matrix into a target check matrix, and record the quantum gates used in the transformation process and their order.

[0085] As an example, the quantum gates can include Clifford gates (including H gates, S gates, and CX gates) and their composite gates (including SWAP gates and X gates).

[0086] S4, generate a joint measurement quantum circuit composed in sequence according to the quantum gates and their order.

[0087] Exemplarily, the quantum gates recorded in step S3 are combined in a positive order into a joint measurement quantum circuit.

[0088] S5, obtaining a measurement result corresponding to the generator in the Z basis according to the joint measurement quantum circuit, the joint measurement times and the quantum state to be measured.

[0089] It should be noted that the measurement result includes measurement data and its probability.

[0090] As an example, first, a quantum state to be measured is prepared; then, the quantum state to be measured is caused to execute the joint measurement quantum circuit; then, a Z basis measurement is performed on the obtained result to obtain a measurement data; the above steps are repeated for the joint measurement times; finally, the probabilities corresponding to different measurement data are summarized to obtain the measurement result.

[0091] S6, generating a first check matrix corresponding to the set of Pauli terms, updating the first check matrix using the joint measurement quantum circuit to obtain a second check matrix, and calculating the expected value of the Pauli term in the set of Pauli terms according to the measurement result and the second check matrix.

[0092] The initial check matrix is composed of a phase index, an X matrix and a Z matrix, and the feature of the target check matrix is that the X matrix is a zero matrix, the Z matrix is a unit matrix, and the phase index is zero.

[0093] Specifically, for calculating the expected value of a Hamiltonian, the Hamiltonian can be decomposed into multiple Pauli terms, and then the multiple Pauli terms are divided into k Pauli term sets. Through the above steps, the expected value of each Pauli term in each Pauli term set is obtained, that is, the expected value of the Hamiltonian is obtained.

[0094] The quantum joint measurement method based on the check matrix in the embodiment of the application can complete the basis vector transformation of the generator in the Pauli term set to the Z basis in parallel through joint measurement when measuring the expected value of the Hamiltonian, reduces the number of quantum state preparation and measurement, thereby saving quantum computing resources. At the same time, the application can obtain a quantum circuit for joint measurement through simple transformation based on the matrix, without complex operation and simulation on the entire quantum state, thereby improving the calculation efficiency. Moreover, the application can realize accurate basis vector transformation without loss, thereby improving the calculation accuracy.

[0095] In some embodiments, the step of transforming the initial check matrix into the target check matrix and recording the quantum gates used in the transformation process and the order thereof includes:

[0096] S31, updating the initial check matrix using an H gate to maximize the rank of the X matrix to obtain a first target check matrix and record the H gate used in order.

[0097] S32, updating the first target check matrix using SWAP gates and / or CX gates, so that the X matrix is transformed into a lower triangular matrix, obtaining a second target check matrix and recording the used SWAP gates and / or CX gates in sequence.

[0098] As an example, when the SWAP gates and the CX gates are needed to update the first target check matrix, the first target check matrix can be updated by the SWAP gates first, and then the first target check matrix updated by the SWAP gates is updated by the CX gates, obtaining the second target check matrix.

[0099] S33, updating the second target check matrix using CX gates, so that the X matrix is transformed into an identity matrix, obtaining a third target check matrix and recording the used CX gates in sequence.

[0100] S34, updating the third target check matrix using S gates, so that the Z matrix is transformed into an all-zero matrix, obtaining a fourth target check matrix and recording the used S gates in sequence.

[0101] S35, updating the fourth target check matrix using H gates, so that the X matrix is transformed into an all-zero matrix and the Z matrix is transformed into an identity matrix, obtaining a fifth target check matrix and recording the used H gates in sequence.

[0102] S36, updating the fifth target check matrix using X gates, so that the phase index is all zero, obtaining a target check matrix and recording the used X gates in sequence.

[0103] In this embodiment, by step-by-step transformation, each step uses a specific quantum gate to convert the initial check matrix into the target check matrix, which reduces the complexity of the transformation logic, eliminates the need for complex operations and simulations on the entire quantum state, and improves the calculation efficiency.

[0104] In some embodiments, the step of updating the initial check matrix using H gates to maximize the rank of the X matrix, obtaining a first target check matrix and recording the used H gates in sequence, includes:

[0105] S311, sequentially updating the initial check matrix using gates, and in the updating process, if the gate makes the rank of the X matrix larger, the updated check matrix is retained, otherwise the updated check matrix is not retained, obtaining a first target check matrix.

[0106] S312, recording the gate that makes the rank of the X matrix larger in sequence.

[0107] wherein, H a represents an H gate on the a-th quantum bit, , represents the total number of quantum bits.

[0108] Specifically, using The steps for updating the initial parity-check matrix include:

[0109] S3111, the phase index of the i-th row in the initial parity check matrix is ​​updated sequentially using the following formula:

[0110]

[0111] S3112, swap the a-th column of matrix X with the a-th column of matrix Z.

[0112] It should be noted that the product operation has higher precedence than the XOR operation.

[0113] In this embodiment, by retaining the H gate that increases the rank of the X matrix, the integrity of the generator information is guaranteed, and an optimal starting point is provided for subsequent transformations.

[0114] In some embodiments, the condition for updating the first target parity check matrix using the SWAP gate is: sequentially traversing the transpose of the X matrix. The main diagonal, during the traversal, if the a-th element of the main diagonal is not 1 and the element in the b-th row and a-th column is 1, then use... The gate updates the first target verification matrix.

[0115] The condition for updating the first target parity check matrix using the CX gate is: the transpose of the X matrix. Performing PLU decomposition yields matrices P, L, and U, where... If the inverse matrix of matrix L is If the element in row a, column b is 1, then use The gate updates the first target verification matrix.

[0116] It should be noted that the inverse matrix Follow modulo-2 operations.

[0117] The condition for updating the fifth target parity check matrix using the X-gate is: sequentially traversing the phase index of the a-th row in the fifth target parity check matrix. ,like Then use The gate updates the fifth target verification matrix.

[0118] in, , The gate represents the SWAP gate on the a-th and b-th qubits. The gate represents the CX gate on the b-th and a-th qubits, where b points to the control bit and a points to the target bit. The gate represents the X gate on the a-th qubit.

[0119] In this embodiment, by stipulating the use conditions of SWAP gate, CX gate and X gate, it is ensured that there is no logical loophole in the transformation process. At the same time, only when the use conditions are met, the quantum gate is used, avoiding invalid operation, reducing the depth and complexity of the quantum circuit.

[0120] In some embodiments, the first target syndrome matrix is updated by using the following quantum gates: The step of updating the first target syndrome matrix by using the following quantum gates comprises: swapping the a-th column and the b-th column of the X matrix; and swapping the a-th column and the b-th column of the Z matrix.

[0121] The step of updating the first target syndrome matrix by using the following quantum gates comprises: The step of updating the first target syndrome matrix by using the following quantum gates comprises:

[0122] The phase index of the i-th row in the first target syndrome matrix is updated in sequence by the following formula:

[0123]

[0124] The a-th column of the X matrix is column XORed to the b-th column; and the b-th column of the Z matrix is column XORed to the a-th column.

[0125] The step of updating the second target syndrome matrix by using the following quantum gates comprises:

[0126] The X matrix is traversed column by column from right to left, and in the traversal process, if the element of the m-th column and the k-th row is 1, the following quantum gate is used to update the second target syndrome matrix:

[0127] The step of updating the third target syndrome matrix by using the following quantum gates comprises:

[0128] The phase index of the i-th row in the third target syndrome matrix is updated in sequence by the following formula:

[0129]

[0130] The a-th column of the X matrix is column XORed to the a-th column of the Z matrix.

[0131] The step of updating the fifth target syndrome matrix by using the following quantum gates comprises: The phase index of the i-th row in the fifth target syndrome matrix is updated in sequence by the following formula:

[0132]

[0133]

[0134] wherein, , represents XOR operation, represents the element of the i-th row and the a-th column in the X matrix, represents the element of the i-th row and the a-th column in the Z matrix, ​​The gate represents a CX gate on the kth and mth qubits, k points to the control bit, and m points to the target bit, k > m, , .

[0135] In this embodiment, the accuracy of the transformation process from the initial check matrix to the target check matrix is improved by updating the check matrix in sequence using various quantum gates.

[0136] In some embodiments, the step of preprocessing the generators of the Pauli term set comprises:

[0137] S11, determining whether the number of generators is equal to the number of bits of the Pauli term in the Pauli term set.

[0138] S12, if equal, the generator is taken as a complete generator.

[0139] S13, if not equal, the generator is padded to obtain a complete generator.

[0140] As an example, if the number of bits of the Pauli term in the Pauli term set is n, and the number of generators is less than n, the generator can be padded to n by the generator padding technique.

[0141] For example, the number of Pauli terms in the Pauli term set {XYZ, XZY, YZX, YYZ} is 4, and the number of bits is 3. Check if the number of generators is equal to the number of bits. If the number of generators is 2, pad the generators to 3 by the generator padding technique.

[0142] In this embodiment, by padding the generators, the preprocessed generators can form a standard check matrix form, which provides a guarantee for subsequent joint measurement.

[0143] In some embodiments, the step of obtaining the measurement result corresponding to the generator in the Z basis according to the joint measurement quantum circuit, the number of joint measurements and the quantum state to be measured comprises:

[0144] S51, obtaining the quantum state to be measured and the number of joint measurements, denoted as M.

[0145] S52, make the quantum state to be measured execute the joint measurement quantum circuit to obtain a new quantum state.

[0146] S53, perform a Z basis measurement on the new quantum state to obtain a measurement data.

[0147] S54, repeat step S53 M times to obtain M measurement data.

[0148] S55, summarize the probabilities corresponding to different measurement data to obtain the measurement result corresponding to the generator.

[0149] In this embodiment, the statistical result is obtained through multiple measurements, thereby improving the accuracy and reliability of the measurement of the to-be-measured quantum state. Meanwhile, the above steps can realize accurate basis vector transformation without loss, thereby improving the calculation accuracy.

[0150] In some embodiments, the step of calculating the expected value of the Pauli term in the Pauli term set according to the measurement result and the second check matrix comprises:

[0151] S61, traversing the Z matrix in the second check matrix by row, and extracting the column sequence number of the element 1 in the current row of the Z matrix.

[0152] It should be noted that each row in the target check matrix corresponds to a Pauli term.

[0153] S62, after extracting the column sequence number of the current row, traversing the measurement data, and recording the number of elements 1 in the column sequence number of the traversed measurement data as t.

[0154] S63, calculating the expected value of the Pauli term by the following formula:

[0155]

[0156] Wherein, p represents the probability corresponding to the measurement data, .

[0157] It is worth mentioning that after traversing all the rows, the expected value of each Pauli term in the Pauli term set can be obtained.

[0158] In this embodiment, the expected value of the Pauli term is accurately calculated by combining the Z matrix in the target check matrix, which not only simplifies the calculation by using the structured information of the target check matrix, but also ensures the accuracy of the result by probability statistics.

[0159] Next, taking a set of five Pauli terms {XZYI, YZXI, IXZY, IYZX, YIXZ} (wherein, the generating element of the Pauli term set is {XZYI, YZXI, IXZY, IYZX}, and the Pauli term YIXZ can be composed by sequentially multiplying the generating elements YZXI, IXZY and IYZX bit by bit, i.e. YIXZ = YZXI·IXZY·IYZX) as an example, the specific process of the joint measurement of the present application is described:

[0160] A1, obtaining the generating element {XZYI, YZXI, IXZY, IYZX} of the Pauli term set, the number of generating elements is equal to the bit number of the Pauli term, and the generating element {XZYI, YZXI, IXZY, IYZX} is directly used as a complete generating element without padding the generating element.

[0161] A2, generate the initial check matrix according to the complete generator:

[0162]

[0163] A3, update the initial check matrix using H gates to maximize the rank of the X matrix, and record the used H gates in order. Specifically, try to update the initial check matrix using , , , gates in turn, and only , gates make the rank of the X matrix larger during the update process. Record the used , gates, and obtain the first target check matrix:

[0164]

[0165] A4, update the first target check matrix using SWAP gates and / or CX gates to transform the X matrix into a lower triangular matrix. Specifically:

[0166] A41, traverse the main diagonal of the transpose matrix of the X matrix in turn, where is:

[0167]

[0168] During the traversal process, if the first element of the main diagonal is not 1 and the element in the second row and the first column is 1, update the first target check matrix using gates; if the third element of the main diagonal is not 1 and the element in the fourth row and the third column is 1, continue to update using gates, and obtain the matrix:

[0169]

[0170] A42, perform PLU decomposition on the transpose matrix of the X matrix in the matrix obtained in step A41, so that , and obtain matrices P, L, and U:

[0171]

[0172] The inverse matrix of matrix L (following modulo 2 operation) is:

[0173]

[0174] The element in the fourth row and the first column of the inverse matrix of matrix L is 1, and gates are used.The matrix obtained in the door updating step A41 is obtained as a second target check matrix:

[0175]

[0176] A43, record the used SWAP door and CX door in order.

[0177] A5, update the second target check matrix using the CX door, so that the X matrix is transformed into a unit matrix. Specifically, traverse the X matrix column by column from right to left, and in the traversal process, the elements of the 3rd column 4th row, the 1st column 2nd row, and the 1st column 4th row are 1, and the CX door is used in turn 、 、 update the second target check matrix, record the used CX door, and obtain a third target check matrix:

[0178]

[0179] A6, update the third target check matrix using the S door, so that the Z matrix is transformed into a full zero matrix. Specifically, update the third target check matrix using the S door in turn 、 、 、 , record the used S door, and obtain a fourth target check matrix:

[0180]

[0181] A7, update the fourth target check matrix using the H door, so that the X matrix is transformed into a full zero matrix and the Z matrix is transformed into a unit matrix. Specifically, update the fourth target check matrix using the H door in turn 、 、 、 , record the used H door, and obtain a fifth target check matrix:

[0182]

[0183] A8, update the fifth target check matrix using the X door, so that the phase index is zero. Specifically, traverse the phase index of each row of the fifth target check matrix in turn, and the phase index of the 1st and 3rd rows is 1, and the X door is used in turn 、 update the fifth target check matrix, record the used X door, and obtain a target check matrix:

[0184]

[0185] A9, combine the quantum doors used in steps A3 to A8 in order to form a complete joint measurement quantum circuit, see Figure 2.

[0186] It should be noted that, Figure 2 Each horizontal line in the above represents a qubit, and the symbols in the box on the horizontal line represent the quantum gate acting on the corresponding qubit. From left to right, the execution order of the quantum gate is represented. Among them, two × connected represent a SWAP gate, a solid black dot connected with a ⊕ symbol represents a CX gate, and the solid black dot points to the control bit and the ⊕ symbol points to the target bit.

[0187] A10, prepare the quantum state to be measured and set the joint measurement number M = 10000.

[0188] A11, make the quantum state to be measured execute the joint measurement quantum circuit, obtain a new quantum state, and perform a Z basis measurement on the new quantum state to obtain a measurement data; repeat 10000 times to obtain 10000 measurement data.

[0189] A12, aggregate the probabilities corresponding to different measurement data to obtain the measurement result, assuming that the measurement result is {0000: 0.1572, 0001: 0.0498, 0010: 0.1908, 0011: 0.0372, 0100: 0.1484, 0101: 0.0524, 0110: 0.0871, 0111: 0.1313, 1000: 0.0321, 1001: 0.0041, 1010: 0.0269, 1011: 0.0051, 1100: 0.0435, 1101: 0.0132, 1110: 0.0132, 1111: 0.0077}. Among them, the measurement data before the colon corresponds to the probability after the colon.

[0190] A13, generate the first check matrix corresponding to the Pauli term set {XZYI, YZXI, IXZY, IYZX, YIXZ}:

[0191]

[0192] A14, update the first check matrix using the joint measurement quantum circuit to obtain the second check matrix:

[0193]

[0194] A15, traverse the Z matrix in the second check matrix by row, taking the last row as an example, the 1st column and the last column of the Z matrix are 1, and then traverse the probability statistics in the measurement result. The number of elements 1 in the 1st position and the last position in the current traversal result is recorded as t. For example, the 1st position and the last position of 0000 are not 1, The weighted probability is ;0001's first bit is not 1, and the last bit is 1, with a weighted probability of ; in this way, finally, the expectation value of the Pauli term IYZX is the sum of the weighted probabilities of all the measurement data:

[0195]

[0196] In addition, the application also provides a quantum joint measurement system based on a check matrix, as shown in Figure 3 The quantum joint measurement system based on the check matrix comprises:

[0197] The preprocessing module 10 is used to acquire and pre-process the generators of the Pauli term set to obtain complete generators corresponding to the Pauli term set.

[0198] The check matrix initialization module 20 is used to generate an initial check matrix according to the complete generators.

[0199] The check matrix transformation module 30 is used to transform the initial check matrix into a target check matrix and record quantum gates used in the transformation process and the order thereof.

[0200] The quantum circuit generation module 40 is used to generate a joint measurement quantum circuit composed in sequence according to the quantum gates and the order thereof.

[0201] The joint measurement module 50 is used to obtain measurement results corresponding to the generators in the Z basis according to the joint measurement quantum circuit, the number of joint measurements and a quantum state to be measured.

[0202] The classical post-processing module 60 is used to generate a first check matrix corresponding to the Pauli term set, update the first check matrix using the joint measurement quantum circuit to obtain a second check matrix, and calculate expectation values of the Pauli terms in the Pauli term set according to the measurement results and the second check matrix.

[0203] The initial check matrix is composed of phase indexes, an X matrix and a Z matrix, and the feature of the target check matrix is that the X matrix is a full zero matrix, the Z matrix is a unit matrix, and all the phase indexes are zero.

[0204] Other specific embodiments of the quantum joint measurement system based on the check matrix of the embodiments of the application can refer to the specific embodiments of the quantum joint measurement method based on the check matrix of the embodiments of the application described above.

[0205] The quantum joint measurement system based on a check matrix in this invention, when solving the expectation value measurement of the Hamiltonian, can perform the basis vector transformation from generators in the Pauli term set to z-basis in parallel through joint measurement, reducing the number of quantum state preparations and measurements, thereby saving quantum computing resources. Furthermore, this invention obtains the quantum circuit for joint measurement based only on simple matrix transformations, without requiring complex calculations and simulations across the entire quantum state, thus improving computational efficiency. Moreover, this invention can achieve accurate basis vector transformations without loss, improving computational accuracy.

[0206] The following detailed explanation uses a computer terminal as an example. Figure 4 This is a hardware structure block diagram of a computer terminal for a quantum joint measurement method based on a check matrix, provided as an embodiment of the present invention. Figure 4 As shown, a computer terminal may include one or more ( Figure 4 Only one is shown in the diagram. A processor 401 (processor 401 may include, but is not limited to, a microprocessor MCU or a programmable logic device FPGA, etc.) and a memory 402 for storing data are also shown. Optionally, the computer terminal may further include a transmission device 403 for communication functions and an input / output device 404. Those skilled in the art will understand that... Figure 4 The structure shown is for illustrative purposes only and does not limit the structure of the computer terminal described above. For example, the computer terminal may also include components that are more complex than those described above. Figure 4 The more or fewer components shown, or having the same Figure 4 The different configurations shown.

[0207] The memory 402 can be used to store software programs and modules for application software, such as the program instructions / modules corresponding to the quantum joint measurement method based on the check matrix in this embodiment. The processor 401 executes various functional applications and data processing by running the software programs and modules stored in the memory 402, thereby implementing the above-described method. The memory 402 may include high-speed random access memory, and may also include non-volatile memory, such as one or more magnetic storage devices, flash memory, or other non-volatile solid-state memory. In some instances, the memory 402 may further include memory remotely located relative to the processor 401, and these remote memories can be connected to a computer terminal via a network. Examples of such networks include, but are not limited to, the Internet, corporate intranets, local area networks, mobile communication networks, and combinations thereof.

[0208] The transmission device 403 is configured to receive or send data via a network. The network can include a wireless network provided by a communication provider of a computer terminal. In an example, the transmission device 403 includes a network interface controller (NIC) which can be connected to other network devices through a base station to communicate with the Internet. In an example, the transmission device 403 can be a radio frequency (RF) module configured to communicate with the Internet in a wireless manner. Embodiments of the present application also provide a computer readable storage medium storing a computer program for electronic data exchange, which causes a computer to perform some or all of the steps of any of the methods described in the above method embodiments. The computer includes an electronic device.

[0209] Embodiments of the present application also provide a computer program product including a non-transitory computer readable storage medium storing a computer program operable to cause a computer to perform some or all of the steps of any of the methods described in the above method embodiments. The computer program product can be a software installation package, and the computer includes an electronic device.

[0210] Although the example embodiments have been described with reference to the accompanying drawings, it is to be understood that the example embodiments are only exemplary and are not intended to limit the scope of the present application. Those of ordinary skill in the art can make various changes and modifications without departing from the scope and spirit of the present application. All such changes and modifications are intended to be included within the scope of the present application as claimed in the appended claims.

[0211] Those of ordinary skill in the art can realize that the units and algorithm steps of each example described in connection with the embodiments disclosed herein can be realized by electronic hardware, or a combination of computer software and electronic hardware. Whether the functions are performed by hardware or software depends on the specific application and design constraints of the technical solution. Those of ordinary skill in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present application.

[0212] In several embodiments provided in the present application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative, for example, the division of the units is only a logical function division, and actual implementation can have another division manner, for example, a plurality of units or components can be combined or integrated into another device, or some features can be omitted or not executed.

[0213] In the description provided herein, numerous specific details are set forth. However, it is understood that embodiments of the application can be practiced without these specific details. In some instances, well-known methods, structures and techniques have not been shown in detail in order not to obscure an understanding of this description.

[0214] Similarly, it is to be understood that the various features of the application can sometimes be used to advantage together, while at other times they can not be used to advantage together. It is therefore contemplated that the application can be practiced or carried out in other ways than is explicitly shown and described herein.

[0215] One skilled in the art will appreciate that, aside from specific features being mutually exclusive, all of the features disclosed in this specification (including the claims, abstract, and drawings) and all of the processes or steps (alone or in combination with other features) of any method or apparatus so disclosed can be combined in any combination, except to the extent that such features or steps are mutually exclusive. Each of the features disclosed in this specification (including the claims, abstract, and drawings) can be replaced by alternative features serving the same, equivalent, or similar purpose, unless expressly stated otherwise.

[0216] Furthermore, those skilled in the art will recognize that references in the specification to "one embodiment", "an embodiment", "an example embodiment", etc., mean that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the application. The appearances of such phrases in various places in the specification are not necessarily all referring to the same embodiment. Further, the particular features, structures, or characteristics can be combined in any suitable manner in one or more embodiments without necessarily being included in all embodiments in order to produce the anticipated embodiments of the application.

[0217] Various component embodiments of the application can be implemented in hardware, or as software modules running in one or more processors, or in combinations thereof. Skilled persons will appreciate that a microprocessor or digital signal processor (DSP) can be used in practice to implement some or all of the functionality of some of the modules according to embodiments of the application. The application can also be implemented as a program for executing part or all of the methods described herein on a computer program (e.g., a computer program and a computer program product). Such program implementing the application can be stored on a computer readable medium, or can be in the form of one or more signals. Such signals can be downloaded from an Internet website, or provided on a carrier medium, or in any other form.

[0218] It should be noted that the above-mentioned embodiments illustrate rather than limit the application, and that one skilled in the art will be able to design many alternative embodiments without departing from the scope of the appended claims. In the claims, any reference signs placed between parentheses shall not be construed as limiting the claim. The word "comprising" does not exclude the presence of elements or steps other than those listed in a claim. The word "a" or "an" preceding an element does not exclude the presence of a plurality of such elements. The application can be implemented by means of both hardware and software, and any combination thereof. In a unitary claim, several devices or sub-claims can be joined by means of the expression "and / or". The use of the term "at least" followed by a list of one or more items should be interpreted as including at least one of the items but it does not exclude the presence of others not listed. The use of the term "one" followed by a list of one or more items should be interpreted as including at least one of the items but it does not exclude the presence of others not listed. It is emphasized that the terms "comprises / comprising" when used in this specification are taken to specify the presence of stated features, integers, steps or components but do not preclude the presence or addition of one or more other features, integers, steps, components or groups thereof.

[0219] The above description is only specific embodiments of the present application or specific explanations of specific embodiments, and the protection scope of the present application is not limited thereto. Any person skilled in the art can easily think of changes or replacements within the technical range disclosed in the present application, and all of them should be covered in the protection scope of the present application. The protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method of quantum joint measurement based on a check matrix, characterized by, The method comprises: obtaining and preprocessing generators of a Pauli term set to obtain complete generators corresponding to the Pauli term set; generating an initial check matrix according to the complete generators; transforming the initial check matrix into a target check matrix and recording quantum gates used in the transformation process and the order thereof; generating a joint measurement quantum circuit composed in sequence according to the quantum gates and the order thereof; obtaining measurement results of the generators corresponding to the Pauli term set in the Z basis according to the joint measurement quantum circuit, joint measurement times and a quantum state to be measured; generating a first check matrix corresponding to the Pauli term set, updating the first check matrix using the joint measurement quantum circuit to obtain a second check matrix, and calculating expected values of Pauli terms in the Pauli term set according to the measurement results and the second check matrix. The initial check matrix is composed of phase indexes, an X matrix and a Z matrix, and the feature of the target check matrix is that the X matrix is a full zero matrix, the Z matrix is a unit matrix and the phase indexes are all zero.

2. The method of claim 1, wherein, The step of transforming the initial check matrix into the target check matrix and recording the quantum gates used in the transformation process and the order thereof comprises: updating the initial check matrix using H gates to maximize the rank of the X matrix to obtain a first target check matrix and record the H gates used in sequence; updating the first target check matrix using SWAP gates and / or CX gates to transform the X matrix into a lower triangular matrix to obtain a second target check matrix and record the SWAP gates and / or CX gates used in sequence; updating the second target check matrix using CX gates to transform the X matrix into a unit matrix to obtain a third target check matrix and record the CX gates used in sequence; updating the third target check matrix using S gates to transform the Z matrix into a full zero matrix to obtain a fourth target check matrix and record the S gates used in sequence; updating the fourth target check matrix using H gates to transform the X matrix into a full zero matrix and the Z matrix into a unit matrix to obtain a fifth target check matrix and record the H gates used in sequence; updating the fifth target check matrix using X gates to make the phase indexes all zero to obtain the target check matrix and record the X gates used in sequence.

3. The method of claim 2, wherein, The step of updating the initial check matrix using H gates to maximize the rank of the X matrix to obtain a first target check matrix and record the H gates used in sequence comprises: sequentially using The door updates the initial check matrix, and in the updating process, if The door makes the rank of the X matrix larger, retains the updated check matrix, otherwise does not retain the updated check matrix, and obtains the first target check matrix. Sequential recording causes the rank of the X matrix to increase Door; wherein, denotes an H gate on the a-th qubit, , denotes the total number of qubits.

4. The method of claim 3, wherein, The condition for updating the first target check matrix using the SWAP gate is that the main diagonal of the transposed matrix of the X matrix is traversed in turn, and during the traversal, if the a-th element of the main diagonal is not 1 and the element in the b-th row and the a-th column is 1, the first target check matrix is updated using the SWAP gate. gate.​ The condition for updating the first target check matrix using the CX gate is that the element in the ath row and the bth column of the transpose of the X matrix performing PLU decomposition to obtain a matrix P, a matrix L and a matrix U, wherein, ; if the inverse matrix of the matrix L is 1, the first target check matrix is updated using the gate. The condition for updating the fifth target check matrix using X gate is: traversing the phase index of the ath row in the fifth target check matrix in turn , if , then updating the fifth target check matrix using gate wherein , The gate represents a SWAP gate on the a-th and b-th qubit, The gate represents a CX gate on the b-th and a-th qubit, b points to the control bit and a points to the target bit, The gate represents an X gate on the a-th qubit.

5. The method of claim 3 or 4, wherein, Using The step of updating the initial parity check matrix by the door includes: updating the phase index of the i-th row in the initial check matrix in sequence by the following formula: ; swapping the a-th column of the X matrix with the a-th column of the Z matrix; Using The step of updating the first target check matrix by the door includes: swapping the a-th column and the b-th column of the X matrix; swapping the a-th column and the b-th column of the Z matrix; Using The step of updating the first target check matrix by the door includes: updating the phase index of the i-th row in the first target check matrix in sequence by the following formula: ; performing column-wise XOR of the a-th column of the X matrix to the b-th column; performing column-wise XOR of the b-th column of the Z matrix to the a-th column; The step of updating the second target check matrix using CX gates comprises: The X matrix is traversed column by column from right to left, and during the traversal, if the element in the mth column and the kth row is 1, the second target check matrix is updated using the gate The step of updating the third target check matrix using S gates comprises: updating the phase index of the i-th row in the third target check matrix in sequence by the following formula: ; performing column-wise XOR of the a-th column of the X matrix to the a-th column of the Z matrix; Using The step of updating the fifth target check matrix by the door includes: The phase index of the i-th row in the fifth target check matrix is updated in sequence by the following formula: ; wherein , denotes an XOR operation, denotes the element in the i-th row and a-th column of the X matrix, denotes the element in the i-th row and a-th column of the Z matrix, denotes a CX gate on the k-th and m-th qubit, k pointing to the control bit and m pointing to the target bit, k>m, , .

6. The method of claim 1, wherein, The step of preprocessing the generator of the Pauli term set comprises: determining whether the number of the generator is equal to the number of bits of the Pauli term in the Pauli term set; if yes, taking the generator as the complete generator; if no, padding the generator to obtain the complete generator.

7. The method of claim 1, wherein, The step of obtaining the measurement result corresponding to the generator in the Z basis according to the joint measurement quantum circuit, the joint measurement times and the quantum state to be measured comprises: obtaining the quantum state to be measured and the joint measurement times, denoting the joint measurement times as M; making the quantum state to be measured execute the joint measurement quantum circuit to obtain a new quantum state; performing a Z basis measurement on the new quantum state to obtain a measurement data; repeating the above steps M times to obtain M measurement data; summarizing the probabilities corresponding to different measurement data to obtain the measurement result corresponding to the generator.

8. The method of claim 7, wherein, The step of calculating the expected value of the Pauli term in the Pauli term set according to the measurement result and the second check matrix comprises: traversing the Z matrix in the second check matrix by row, and extracting the column sequence number of the element 1 in the current row of the Z matrix; after extracting the column sequence number of the current row, traversing the measurement data, and denoting the number of elements 1 in the column sequence number in the traversed measurement data as t; calculating the expected value of the Pauli term by the following formula: ; wherein p represents a probability corresponding to the measurement data, .

9. A quantum joint measurement system based on a check matrix, characterized by, The system comprises: a preprocessing module configured to obtain and preprocess the generator of the Pauli term set to obtain the complete generator corresponding to the Pauli term set; a check matrix initialization module configured to generate an initial check matrix according to the complete generator; a check matrix transformation module configured to transform the initial check matrix into a target check matrix and record the quantum gates used in the transformation process and the order thereof; a quantum circuit generation module configured to generate a joint measurement quantum circuit composed in sequence according to the quantum gates and the order thereof; a joint measurement module configured to obtain the measurement result corresponding to the generator in the Z basis according to the joint measurement quantum circuit, the joint measurement times and the quantum state to be measured; a classical post-processing module configured to generate a first check matrix corresponding to the Pauli term set, update the first check matrix using the joint measurement quantum circuit to obtain a second check matrix, and calculate the expected value of the Pauli term in the Pauli term set according to the measurement result and the second check matrix. When the computer program is executed by the processor, the quantum joint measurement method based on the check matrix according to any one of claims 1-8 is implemented.

10. An electronic device comprising a memory, a processor, and a computer program stored on the memory, characterized in that, When the computer program is executed by the processor, the quantum joint measurement method based on the check matrix according to any one of claims 1-8 is implemented.

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