Fast quantum read error calibration software and hardware cooperation method based on Hamming sparsity

Abstract

The invention discloses a fast quantum read error calibration software and hardware cooperation method based on Hamming sparsity, and belongs to the technical field of quantum computing, and the method comprises the following steps: determining a structured sparse mode of a calibration matrix based on a Hamming distance, and providing higher sparsity and higher fidelity; a Hamming distance row matrix sparse format is designed according to a structured sparse mode to store non-zero values in a corresponding calibration matrix, and a high compression ratio is achieved; proposing a calculation flow of sparse matrix vector multiplication according to a Hamming distance row matrix sparse format and a calibration matrix; a hardware architecture for executing the compute stream is designed based on the compute stream to accelerate quantum read error calibration.

Description

Technical Field

[0001] The present invention belongs to the technical field of quantum computing, and in particular relates to a software-hardware collaborative method for fast quantum read error calibration based on Hamming sparsity. Background Art

[0002] Compared with classical computers, quantum computers have the potential to significantly speed up the solution of specific problems such as large number factorization and machine learning. However, we are currently in the era of noisy medium-scale quantum computing. When executing quantum programs, available quantum computers will inevitably encounter various noise sources, such as gate noise, read noise, crosstalk between quantum bits, and so on. Among these noise sources, read noise is the most serious, that is, the noise generated by reading the output from the quantum device and converting it into classical data. For most physical quantum implementations, this error reaches 1%-10% in each quantum bit operation, which seriously hinders the practical application of quantum computing.

[0003] In order to alleviate the impact of read noise, quantum error mitigation technology has been proposed, including machine learning, statistical analysis methods, etc. Among these technologies, matrix-based read error mitigation is a well-known method that has been experimentally proven to be effective in superconducting, ion trap, and optical quantum hardware, and is therefore widely used in commercial quantum cloud platforms such as IBMQ and Rigetti. The essence of matrix-based read error mitigation is to map the probability distribution containing noise to a calibrated probability distribution based on matrix-vector multiplication (MVM). The calibrated probability distribution is closer to the probability distribution in the ideal case.

[0004] Although the matrix-based calibration method can be easily deployed on the software stack, it faces a trade-off between scalability and calibration accuracy. In order to maximize the accuracy of the calibration process, that is, to accurately characterize the noise matrix, a large number of benchmark circuits need to be executed exhaustively to cover all possible measurement outputs, and their number grows exponentially with the number of qubits. For example, a 20qubits noise matrix requires 8TB of storage space, which far exceeds the available memory capacity of current classical computers. In addition to the characterization of the noise matrix, the MVM process is also computationally overwhelmed. This is because the size of the matrix grows exponentially with the number of qubits. In addition, the statistical analysis method Q-BEEP (from the article Quantum Bayesian Error Mitigation Employing Poisson Modeling over the Hamming Spectrum, Quantum Bayesian Error Suppression of Poisson Modeling over the Hamming Spectrum) requires continuous iterations to ensure the effectiveness of error calibration, but this takes a lot of time. For example, Q-BEEP takes more than an hour to calibrate the results of the GHZ algorithm circuit of 16qubits. Therefore, this method is severely limited by time and space in the error calibration of large-scale quantum circuits.

[0005] In order to speed up the calibration process, some methods such as Mthree (from the article Scalable mitigation of measurement errors on quantum computers) propose to decompose the original calibration matrix into a tensor product of a series of element matrices (single-bit 2×2 matrices), thereby greatly reducing the time complexity of generating the calibration matrix. However, these methods ignore the crosstalk effect between quantum bits, which seriously reduces the effectiveness of calibration. For example, when calibrating the output of a quantum circuit with more than 81 quantum bits, this inaccuracy becomes intolerable. In addition, they are mainly applicable to GHZ and BV algorithms because their output consists of fewer bit strings, which limits their versatility.

[0006] Another possible way to reduce memory requirements and speed up the calibration process is to exploit the sparsity in the calibration matrix. This is because the calibration matrix itself contains a large number of quantum states that are very close to zero. These near-zero values ​​contribute little to the accuracy of the calibration and can be pruned. However, traditional threshold-based pruning methods do not work well on the calibration matrix. For example, when the threshold is set to 1x10 -6 When , a 16-qubit calibration matrix can achieve 98.6% sparsity, but it will cause more than 20 times of fidelity loss. Summary of the invention

[0007] In view of the above, the object of the present invention is to provide a fast quantum read error calibration software and hardware collaborative method based on Hamming sparsity, comprising the following steps: Determine the structured sparse pattern of the calibration matrix based on the Hamming distance; Design a sparse format of Hamming distance row matrix according to the structured sparse pattern, and construct a sparse calibration matrix; The computational flow of sparse matrix-vector multiplication is proposed based on the Hamming distance row matrix sparse format and calibration matrix; Design a hardware architecture for executing computational flows based on computational flows to accelerate quantum readout error calibration.

[0008] Preferably, determining a structured sparse pattern of a calibration matrix based on the Hamming distance and constructing a sparse calibration matrix comprises: The Hamming distance is an indicator for quantifying the difference between quantum states. It refers to the number of bits of binary code that differ between the measured quantum state and the ideal quantum state. Its value reflects the number of quantum bits flipped. The larger the Hamming distance, the greater the difference between the two quantum states. The element values ​​in the calibration matrix decrease exponentially with the increase of the Hamming distance threshold. Given an ideal quantum state, the Hamming distance threshold HD determines the number of non-zero elements in the calibration matrix. , calculated as: ; Among them, serial number indicates that no qubits in the calibration matrix are flipped, n is the total number of elements in the calibration matrix.

[0009] Preferably, the Hamming distance row matrix sparse format is designed according to the structured sparse pattern, including: Design the Hamming distance row matrix sparse format according to the structured sparse pattern and construct a sparse calibration matrix, including: The Hamming distance row matrix sparse format contains the number of quantum bits n, the Hamming distance threshold HD, and a one-dimensional array val for storing the non-zero element values ​​in the calibration matrix. Based on the Hamming distance threshold HD, the row index and column index of each non-zero element in the calibration matrix can be calculated. For the first k non-zero elements, the row index and column index are calculated as follows: ; ; ; in, It represents the number of non-zero elements in each row calculated based on the Hamming distance threshold HD. Indicates rounding down. represents the row indices of non-zero elements in the sparse calibration matrix, symbol Indicates the remainder. represents the remainder, represents the flip function, Represents the column indices of non-zero elements in the sparse calibration matrix, where the row indices represent ideal quantum states and the column indices represent flipped quantum states.

[0010] Preferably, a calculation flow of sparse matrix-vector multiplication is proposed based on the Hamming distance row matrix sparse format and the calibration matrix, including the following process: (1) For each ideal quantum state, the number of non-zero elements in the calibration matrix corresponding to it is calculated based on the Hamming distance threshold HD ; (2) Initialize a flip array and find the non-zero elements from the noise matrix whose Hamming distance to the ideal quantum state is less than the preset Hamming distance threshold HD and store them; (3) Calculate the row index and column index of each non-zero element in the flip array to construct the calibration matrix; (4) Use the calibration matrix to calculate the measurement result matrix to obtain the calibration result.

[0011] Preferably, the calibration matrix is ​​used to calculate the measurement result matrix to be calibrated to obtain the calibration result, including: After arranging all column indexes in the calibration matrix in ascending order, the probability value of the corresponding position in the measurement result matrix to be calibrated is extracted based on the column index, and the probability value is multiplied by the element value in the calibration matrix and then accumulated to obtain the calibration result.

[0012] Preferably, a hardware architecture for executing the computational flow is designed based on the computational flow, including: The hardware architecture includes a conversion unit and a computing unit, wherein the conversion unit is used to execute processes (1)-(3) in the computing flow; and the computing unit is used to execute process (4) in the computing flow.

[0013] Preferably, in the conversion unit, each element in the flipped array is XORed with the row index to obtain the column index of each non-zero element, and the column index is arranged in ascending order through a comparator, while the quantum state with a probability of 0 in the measurement result matrix to be calibrated can also be detected.

[0014] Preferably, in the computing unit, calibration calculation is performed through a reconfigurable addition tree, specifically for a quantum state with a probability value of 0 read through a comparator, and an addition number and a multiplication array are configured for this purpose, and the calculation is implemented specifically through a series of AND gates and OR gates.

[0015] Compared with the prior art, the present invention has the following beneficial effects: The present invention determines the structured sparse pattern of the calibration matrix based on the Hamming distance, providing higher sparsity and higher fidelity; Based on the Hamming distance, the present invention proposes a method for compressing the calibration matrix at the software level, and designs a Hamming Distance Sparse Row (HDSR) sparse format to store the non-zero values ​​in the corresponding calibration matrix, achieving a higher compression ratio; The present invention also proposes a computational flow for sparse matrix-vector multiplication, and designs a proprietary hardware architecture based on the computational flow. The hardware architecture uses an XOR array and a reconfigurable addition tree to cooperate with the HDSR sparse format to accelerate read error calibration. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0017] Figure 1 is a flow chart of a software-hardware collaborative method for fast quantum read error calibration based on Hamming sparsity provided in an embodiment; Figure 2 is an example of a matrix-based read error calibration process provided by an embodiment; Figure 3 is an example of a process based on Hamming distance compression calibration matrix provided by an embodiment; Figure 4 is an example of the HDSR sparse format provided in the embodiment; Figure 5 It is a hardware design diagram of the SpREM sparse matrix-vector multiplication provided in the embodiment. DETAILED DESCRIPTION

[0018] To make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific implementation methods described herein are only used to explain the present invention and do not limit the scope of protection of the present invention.

[0019] The inventive concept of the present invention is: the threshold pruning method of the matrix cannot be well extended to the technical problem of the quantum read error calibration matrix, and due to the specific mechanism of interaction between quantum bits, the sparse format of the calibration matrix follows the structured characteristics. Even if the threshold pruning of the matrix is ​​amplified and extended to the quantum read error calibration matrix, although a higher sparsity can be achieved, it will lead to a significant decrease in fidelity. To this end, the embodiment of the present invention provides a fast quantum read error calibration software and hardware collaborative method based on Hamming sparsity.

[0020] Figure 2 What is shown is an example of a matrix-based read error calibration process. When preparing the quantum state, after measurement, it is found that there is noise to obtain a noise matrix. The noise matrix indicates that there is an error in the quantum state reading and calibration is required. Specifically, a calibration matrix needs to be constructed to calibrate the measurement results with calibration to obtain the calibration results.

[0021] like Figure 1 As shown, the embodiment provides a fast quantum read error calibration software and hardware collaborative method based on Hamming sparsity, comprising the following steps: S110 , determining a structured sparse pattern of the calibration matrix based on the Hamming distance.

[0022] In quantum computing, the Hamming distance can be used as an indicator to quantify the difference between quantum states. It refers to the number of bits of binary code that differ between the measured quantum state and the ideal quantum state. Its value reflects the number of quantum bits that have been flipped. The larger the Hamming distance, the greater the difference between the two quantum states. However, the larger the Hamming distance, the lower the corresponding probability value, which means that the probability of such a quantum state appearing in actual calculations is low.

[0023] In quantum computing, a bit flip in the output quantum state is considered an error. Therefore, the Hamming distance threshold HD can be used to quantify the probability of a flip error. Figure 3 Two examples in a 4-qubit system are shown, where HD=1 means no flip or only one qubit is flipped, and HD=2 means no flip or only one or two qubits are flipped. Therefore, for the quantum state '0001', if no flip or only one bit is flipped, 5 quantum states will be obtained, namely '0000', '0001', '0011', '0101' and '1001'. Similarly, when HD=2, 0, 1, and 2 qubits need to be flipped to obtain the corresponding quantum states, namely '0000', '0001', '0010', '0011', …, '1011' and '1101'. Given an ideal quantum state, the Hamming distance threshold HD determines the number of non-zero elements in the calibration matrix. , calculated as: ; Among them, serial number indicates that no qubits in the calibration matrix are flipped, n is the total number of elements in the calibration matrix.

[0024] The compression method of the correction matrix based on a given Hamming distance threshold HD is to retain the flipped bits mentioned above and prune all other quantum states. That is, for each row in the calibration matrix, only The column index of the non-zero elements in each row can be calculated by flipping the binary format of the quantum state.

[0025] like Figure 2 As shown, the quantum state '0001' has five flipped quantum states '0000', '0001', '0011', '0101' and '1001'. Convert its binary to the corresponding decimal, that is, 0, 1, 3, 5, 9, which are the column indices of these flipped quantum states. Similarly, when the Hamming distance threshold HD=2, each row of the calibration matrix will retain more elements, that is, a larger Hamming distance threshold, which means a lower sparsity. Generally speaking, for a specific read error, its probability decreases exponentially with the number of quantum bit flips. This means that during the calculation process, the probability of encountering multiple flips is very low. For example, the probability of 4 quantum bit flips is less than 10 -5 Therefore, redundant values ​​can be easily pruned by setting the Hamming distance threshold HD, achieving a good balance between calibration time and calibration accuracy.

[0026] S120, designing a sparse format of a Hamming distance row matrix according to the structured sparse pattern, and constructing a sparse calibration matrix.

[0027] The Hamming distance row matrix sparse format (abbreviated as HDSR sparse format) includes the number of quantum bits n, the Hamming distance threshold HD, and a one-dimensional array val for storing the non-zero element values ​​in the calibration matrix (the value is a probability value of 0-1). Compared with the traditional COO and CSR sparse formats, the HDSR sparse format of the present invention only needs to store the non-zero element values, without storing the row index and column index of each element. The present invention can use the Hamming distance threshold HD to calculate the row index and column index of each non-zero element in the calibration matrix. Such a feature brings about a very large memory space saving.

[0028] Specifically, for the first k non-zero elements, the row index and column index are calculated as follows: ; ; ; in, It represents the number of non-zero elements in each row calculated based on the Hamming distance threshold HD. Indicates rounding down. represents the row indices of non-zero elements in the sparse calibration matrix, symbol Indicates the remainder. represents the remainder, represents the flip function, Represents the column indices of non-zero elements in the sparse calibration matrix, where the row indices represent ideal quantum states and the column indices represent flipped quantum states.

[0029] Figure 4 Two examples of HDSR sparse format are shown. The first one uses the Hamming distance threshold HD=1 to prune the calibration matrix of 3 qubits, and the second one uses the Hamming distance threshold HD=2 to prune the calibration matrix of 4 qubits, resulting in a sparse calibration matrix. For the calibration matrix of 3 qubits, the number of non-zero elements in each row can be calculated to be 4. For the first element of the first row, the value is 1.1. Its position in the val array (5) is divided by 4 and rounded down to get its row index, which is 1 (001). At this time, the remainder is 1, which means that 1.1 is the first element of the first row in the calibration matrix. The next step is to calculate the corresponding column index based on, which is 1 (001). For the calibration matrix of 4 qubits, the number of non-zero elements in each row is 11, and the 28th element is marked with a red star. Similarly, 28 is divided by 11 and rounded down to get the corresponding row index 2 (0010). The remainder is 6, which means it is the 6th element in the 2nd row. Based on , we can get its corresponding column index, which is 7 (0111).

[0030] Compared with directly pruning the calibration matrix based on thresholds, the method of the present invention takes into account the interaction between quantum bits and utilizes the characteristics of the Hamming distance. Therefore, the method of the present invention exhibits two types of advantages: 1) Higher sparsity and higher accuracy Fundamentally, the calibration matrix of a real quantum computer is obtained based on a large number of measurement operations to describe the characteristics of each quantum bit. Furthermore, the calibration matrix will contain some values ​​that cannot perfectly simulate the quantum state transfer. On the other hand, the method of the present invention chooses to theoretically locate the non-zero element values ​​of each row in the calibration matrix, and uses different Hamming distance thresholds to quantize the interaction between quantum bits. Therefore, the method of the present invention can achieve higher sparsity and accuracy.

[0031] 2) Structured sparsity and higher compression rate.

[0032] The method of the present invention prunes the calibration matrix based on the Hamming distance threshold, so the number of values ​​retained in each row of the calibration matrix is ​​equal. This feature ensures that parallel computing can support load balancing. In addition, the HDSR sparse format only needs to store two constants and a one-dimensional array, which reduces storage pressure compared to traditional sparse formats.

[0033] S130, a calculation flow of sparse matrix-vector multiplication is proposed according to the sparse format of the Hamming distance row matrix and the calibration matrix.

[0034] In the embodiment, a computation flow of sparse matrix-vector multiplication is proposed based on the sparse format of the Hamming distance row matrix and the calibration matrix, which includes 4 inputs and one output. The input specifically includes the number of quantum bits n, the Hamming distance threshold HD, an array val for storing the non-zero element values ​​of the calibration matrix (this value is 0-1), and an array meas (i.e., the measurement result matrix to be calibrated) storing the measured and to-be-calibrated probability vectors, and the output is an array miti storing the calibrated probability vectors. The entire computation flow includes the following processes: (1) For each ideal quantum state, the number of non-zero elements in the calibration matrix corresponding to it is calculated based on the Hamming distance threshold HD , that is, the number of non-zero elements that can be retained in each row of the calibration matrix based on the Hamming distance threshold pruning; (2) Initialize a flip array , and select non-zero elements (that is, binary strings) from the original calibration matrix whose Hamming distance to the ideal quantum state is less than the preset Hamming distance threshold HD and store them. For example, for the original calibration matrix of 4 qubits, the Hamming distance threshold HD = 1 for: ; (3) Calculate the flip array The sparse calibration matrix is ​​constructed by calculating the row index and column index of each non-zero element in . Specifically, the row index of each non-zero element is calculated first, and then the ideal quantum state corresponding to the row index is compared with The XOR array is executed between them, that is, the above flip function is implemented by executing the XOR array to obtain the column index of each non-zero element. For example, for the ideal quantum state 0001, HD=1, reasonable flips and their column indices for: ; in, Represents the exclusive OR operation; (4) Use the calibration matrix to calculate the measurement result matrix to be calibrated to obtain the calibration result. Specifically, after all column indexes in the calibration matrix are arranged in ascending order, the probability value of the corresponding position in the measurement result matrix to be calibrated is extracted based on the column index, and the probability value is multiplied by the element value in the calibration matrix and then accumulated to obtain the calibration result and saved in the array. middle.

[0035] S140, designing a hardware architecture for executing computational flows based on computational flows to accelerate quantum read error calibration.

[0036] In the embodiment, for the above data flow, a hardware architecture for executing a computing flow is designed to accelerate the operation, and the hardware architecture includes a conversion unit and a computing unit, wherein the conversion unit is used to execute processes (1)-(3) in the computing flow; and the computing unit is used to execute process (4) in the computing flow.

[0037] Although the calibration matrix is ​​device-dependent, it is different at different time points and under different qubit usage conditions. Therefore, the present invention stores the calibration matrix stored in HDSR format in an off-chip memory at the beginning. That is, all outputs of the method of the present invention are initially stored off-chip. Since sparse matrix-vector multiplication is a communication-intensive operator, the method of the present invention uses a double buffer to overlap the communication time and the computation time.

[0038] Figure 5 The main components of the hardware design of the present invention are shown, namely, generating the column index of each non-zero element and performing sparse matrix-vector multiplication. In order to obtain the column index of each row of non-zero elements, the method of the present invention introduces an XOR array to parallelize the loop. Specifically, in the conversion unit, by flipping the array Each element in is XORed with the row index to obtain the column index of each non-zero element, and the column index is sorted in ascending order through the comparator. Because the measurement operation will cause the final result to contain many quantum states with a probability value of 0, the comparator not only sorts the column index, but also detects the quantum state with a probability of 0 in the measurement result matrix to be calibrated. For example, in Figure 5 In the example, we use the flip array for row index 5. An XOR operation is performed to obtain the corresponding column indexes 5, 4, ..., 15, 9. Next, these column indexes are arranged in ascending order, and the corresponding read probabilities are captured and then input into the calculation unit.

[0039] In the computing unit, the present invention performs calibration calculations through a reconfigurable addition tree, specifically for a quantum state with a probability value of 0 read by a comparator, and configures an addition number and a multiplication array for this purpose, specifically implementing the calculation through a series of AND gates and OR gates. Figure 5An example of the entire configuration process is also shown. The read probability is compared with the value of 0, and finally 1, 0,1, 1, 1, 0, 1, 1 is obtained. Then, the corresponding multipliers are activated according to these values, except that the first and fifth are not activated. Finally, these results are ANDed in pairs to obtain 0, 1, 0, 1. Therefore, the sum adder of the first layer is deactivated. The adders of the remaining layers are configured in the same way. The above units are pipelined in the hardware architecture design to reduce latency.

[0040] Compared with the threshold-based pruning method, the method of the present invention shows 98.9% sparsity and 27.3 times reduction in fidelity loss on a real quantum computer. The computational flow of sparse matrix-vector multiplication is implemented on the Xilinx AlveoU50 platform, showing an acceleration ratio of 11.2 to 36.4 times compared with the Xilinx Vitis SPARSE library and the NVIDIA A100 GPU.

[0041] The specific implementation methods described above provide a detailed description of the technical solutions and beneficial effects of the present invention. It should be understood that the above is only the most preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, supplements and equivalent substitutions made within the scope of the principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A fast quantum readout error calibration software-hardware collaborative method based on Hamming sparsity, characterized in that: The following steps are involved: Determine the structured sparse pattern of the calibration matrix based on the Hamming distance; Design a sparse format of Hamming distance row matrix according to the structured sparse pattern, and construct a sparse calibration matrix; The computational flow of sparse matrix-vector multiplication is proposed based on the Hamming distance row matrix sparse format and calibration matrix; Design a hardware architecture for executing computational flows based on computational flows to accelerate quantum readout error calibration.

2. The fast quantum read error calibration software-hardware collaborative method based on Hamming sparsity according to claim 1 is characterized in that: Determine the structured sparse pattern of the calibration matrix based on the Hamming distance, including: The Hamming distance is an indicator for quantifying the difference between quantum states. It refers to the number of bits of binary code that differ between the measured quantum state and the ideal quantum state. Its value reflects the number of quantum bits flipped. The larger the Hamming distance, the greater the difference between the two quantum states. The element values ​​in the calibration matrix decrease exponentially with the increase of the Hamming distance threshold. Given an ideal quantum state, the Hamming distance threshold HD determines the number of non-zero elements in the calibration matrix. , calculated as: ； Among them, serial number indicates that no qubits in the calibration matrix are flipped, n is the total number of elements in the calibration matrix.

3. The fast quantum readout error calibration software-hardware collaborative method based on Hamming sparsity according to claim 2 is characterized in that: Design the Hamming distance row matrix sparse format according to the structured sparse pattern and construct a sparse calibration matrix, including: The Hamming distance row matrix sparse format contains the number of quantum bits n, the Hamming distance threshold HD, and a one-dimensional array val for storing the non-zero element values ​​in the calibration matrix. Based on the Hamming distance threshold HD, the row index and column index of each non-zero element in the calibration matrix can be calculated. For the first k non-zero elements, the row index and column index are calculated as follows: ； ； ； in, It represents the number of non-zero elements in each row calculated based on the Hamming distance threshold HD. Indicates rounding down. represents the row indices of non-zero elements in the sparse calibration matrix, symbol Indicates the remainder. represents the remainder, represents the flip function, Represents the column indices of non-zero elements in the sparse calibration matrix, where the row indices represent ideal quantum states and the column indices represent flipped quantum states.

4. The fast quantum readout error calibration software-hardware collaborative method based on Hamming sparsity according to claim 3 is characterized in that: According to the Hamming distance row matrix sparse format and calibration matrix, the calculation flow of sparse matrix vector multiplication is proposed, including the following process: (1) For each ideal quantum state, the number of non-zero elements in the calibration matrix is ​​calculated based on the Hamming distance threshold HD: ; (2) Initialize a flip array and find and store the non-zero elements whose Hamming distance to the ideal quantum state is less than the preset Hamming distance threshold HD from the original calibration matrix; (3) Calculate the row and column indices of each non-zero element in the flip array to construct a sparse calibration matrix; (4) Use the calibration matrix to calculate the measurement result matrix to obtain the calibration result.

5. The fast quantum readout error calibration software-hardware collaborative method based on Hamming sparsity according to claim 4 is characterized in that: The calibration matrix is ​​used to calculate the measurement result matrix to be calibrated to obtain the calibration result, including: After arranging all column indexes in the calibration matrix in ascending order, the probability value of the corresponding position in the measurement result matrix to be calibrated is extracted based on the column index, and the probability value is multiplied by the element value in the calibration matrix and then accumulated to obtain the calibration result.

6. The fast quantum readout error calibration software-hardware collaborative method based on Hamming sparsity according to claim 5, characterized in that: The hardware architecture for executing computational flows is designed based on computational flows, including: The hardware architecture includes a conversion unit and a computing unit, wherein the conversion unit is used to execute processes (1)-(3) in the computing flow; and the computing unit is used to execute process (4) in the computing flow.

7. The fast quantum readout error calibration software-hardware collaborative method based on Hamming sparsity according to claim 6 is characterized in that: In the conversion unit, each element in the flip array is XORed with the row index to obtain the column index of each non-zero element, and the column index is arranged in ascending order through a comparator. At the same time, the quantum state with a probability of 0 in the measurement result matrix to be calibrated can be detected.

8. The fast quantum readout error calibration software-hardware collaborative method based on Hamming sparsity according to claim 6, characterized in that: In the calculation unit, calibration calculation is performed through a reconfigurable addition tree, specifically for a quantum state with a probability value of 0 read by a comparator, and an addition number and a multiplication array are configured for this purpose, and the calculation is implemented specifically through a series of AND gates and OR gates.

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