Quantum computer error correction method based on quantum circuit

Abstract

The invention relates to the technical field of quantum computing, in particular to a quantum computer error correction method based on a quantum circuit, and the method comprises the following steps: 1, building an error model according to a quantum code of quantum computer noise; 2, a data result is obtained according to error model measurement or from real quantum computer hardware, error correction is carried out on the data result, and the data result is correspondingly composed of multiple syndromes and logic operators; 3, performing learning training by using the data result to obtain a decoding quantum circuit; 4, the decoding quantum circuit is operated for decoding, and when the quantum computer generates noise or a new error, the syndrome serves as input, the decoding quantum circuit can directly output a corresponding error correction logic operator, and decoding and error correction are conducted in real time. According to the invention, the decoding quantum circuit after learning training is directly deployed on the quantum computer, the logic operator required for correcting the error of the quantum computer can be directly identified, and real-time decoding and error correction are realized.

Description

Technical Field

[0001] The present application relates to the field of quantum computing technology, and in particular to a quantum computer error correction method based on quantum circuits. Background Art

[0002] Quantum computers need to perform error correction to achieve universal quantum computing. However, the decoding of quantum error correction codes currently relies on classical computing. In superconducting quantum bits, classical computing is slower than quantum operations. This difference makes the practical application of real-time quantum error correction challenging.

[0003] Ideal quantum computers have the potential to achieve exponential speedups over classical computing in tasks such as prime factorization. However, quantum computers are susceptible to noise at the physical level, which must be corrected to ensure the accuracy of the computational results. Quantum error-correcting codes address this challenge by integrating multiple physical qubits into a smaller number of logical qubits and encoding logical information through redundant measurements of auxiliary qubits. When an error occurs, non-trivial measurement results are triggered and used to infer how the logical information changes, allowing appropriate corrections to be made. This inference process is called decoding and is considered a classic statistical inference problem. A variety of decoding algorithms have been proposed to address this problem, including minimum weight perfect matching (MWPM), union lookup, belief propagation with ordered statistical decoding (BPOSD), tensor network methods, and neural network decoders.

[0004] Despite the availability of numerous decoders and their acceleration using modern computing power such as GPUs and FPGAs, accurately correcting actual quantum codes at speeds matching the operating speed of superconducting qubit quantum devices remains challenging in the presence of practical circuit-level noise, making real-time decoding difficult. Summary of the Invention

[0005] This application provides a quantum computer error correction method based on quantum circuits, which uses quantum circuits instead of classical computing devices to solve the decoding problem, so that the decoding speed matches the operating speed of the quantum circuit to be corrected.

[0006] To achieve the above-mentioned objectives, the present application provides a quantum computer error correction method based on a quantum circuit, comprising the following steps: Step 1: establishing an error model based on the quantum code of the quantum computer noise; Step 2: measuring or obtaining data results from real quantum computer hardware according to the error model, and correcting the errors thereof, wherein the data results are composed of multiple syndromes and logical operators; Step 3: using the data results for learning and training to obtain a decoding quantum circuit; Step 4: running the decoding quantum circuit for decoding. When the quantum computer generates noise or a new error, the syndrome is used as input, and the decoding quantum circuit directly outputs the corresponding error correction logical operator to perform decoding and error correction in real time.

[0007] Furthermore, in step 1, the quantum code is represented by a Tanner graph.

[0008] Furthermore, in step 2: error model measurement is constructed by measuring the auxiliary quantum bit; the syndrome represents the parity check error in a specific set of error models; and error correction of the data result means inferring the logical operator caused by the error when the syndrome is known and correcting it.

[0009] Furthermore, in step 3, the decoding quantum circuit involves a parameterized single-qubit gate and a non-parameterized two-qubit gate, that is, the decoding quantum circuit consists of multiple qubits and multiple groups of unitary operation blocks.

[0010] Furthermore, each group of unitary operation blocks includes a plurality of X rotation gates, a plurality of Y rotation gates, and a plurality of controlled Z gates.

[0011] Furthermore, the parameters of the revolving door can be optimized through learning and training, which is performed using tensor network methods or quantum computer hardware sampling.

[0012] Furthermore, the learning and training process includes forward propagation and backpropagation, and the parameters of the revolving door are iteratively adjusted to make the conditional distribution close to the training data distribution.

[0013] Furthermore, in step 4, decoding the quantum circuit is a pure quantum operation and does not require the participation of classical operations.

[0014] This application provides a quantum computer error correction method based on quantum circuits, which has the following beneficial effects:

[0015] This application deploys the learned and trained decoding quantum circuit directly onto a quantum computer, which can directly identify the logical operators required to correct quantum computer errors, thereby achieving real-time decoding and error correction. The decoding quantum circuit is used to directly output the logical operators, which has a fast decoding speed and significantly reduces the operation time of decoding and error correction. In addition, quantum sampling is fast and simple, and the logical operators are directly sampled using quantum circuits, without the need to calculate conditional probabilities like classical sampling. At the same time, the parameters of single-qubit gates can be iteratively updated, greatly reducing the recognition error rate. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] The drawings that constitute part of this application are used to provide a further understanding of this application and make other features, objects and advantages of this application more apparent. The illustrative embodiment drawings of this application and their descriptions are used to explain this application and do not constitute an improper limitation of this application. In the drawings:

[0017] Figure 1 is a Tanner diagram of a quantum code provided according to an embodiment of the present application;

[0018] Figure 2 This is a schematic diagram of the change in the logical error rate of a surface code with a code distance of 3 during the learning and training process of the decoding quantum circuit provided in an embodiment of the present application;

[0019] Figure 3 This is a schematic diagram of the change in the logical error rate of a surface code with a code distance of 5 during the learning and training process of the decoding quantum circuit provided in an embodiment of the present application;

[0020] Figure 4 This is a schematic diagram of the change in the logical error rate of a surface code with a code distance of 7 during the learning and training process of the decoding quantum circuit provided in an embodiment of the present application;

[0021] Figure 5 Schematic diagram of a self-correcting repeating code quantum memory with a code distance of 3 provided according to an embodiment of the present application. DETAILED DESCRIPTION

[0022] In order to enable those skilled in the art to better understand the present invention, the following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of this application.

[0023] It should be noted that the terms "first", "second", etc. in the specification and claims of the present application and the above-mentioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequential order. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present application described here. In addition, the terms "including" and "having" and any of their variations are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0024] In this application, terms such as "upper," "lower," "left," "right," "front," "back," "top," "bottom," "inner," "outer," "center," "vertical," "horizontal," "transverse," and "longitudinal" indicate positions or locations based on the positions or locations shown in the accompanying drawings. These terms are primarily intended to better describe this application and its embodiments and are not intended to limit the devices, elements, or components indicated to having a specific orientation, or to being constructed or operated in a specific orientation.

[0025] Furthermore, some of the above terms may be used to express other meanings besides indicating a position or location. For example, the term "on" may also be used to indicate a dependency or connection in certain circumstances. Those skilled in the art will understand the specific meanings of these terms in this application based on the specific circumstances.

[0026] Additionally, the term "plurality" shall mean two or more.

[0027] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0028] A quantum computer is a physical device that follows the properties and laws of quantum mechanics to perform high-speed mathematical and logical operations, store, and process quantum information. When a device processes and calculates quantum information and runs quantum algorithms, it is considered a quantum computer. With the rapid development of quantum computer technology, its powerful computing power and high speed have led to an increasingly broad range of applications. Currently, the quantum computing era is in its second phase, involving dozens of noisy quantum bits. A complete quantum error correction scheme has yet to be implemented, primarily because decoding quantum error correction codes requires classical computers, which operate slower than superconducting quantum hardware.

[0029] The quantum computer error correction method based on quantum circuits provided in the embodiments of the present application utilizes a decoding scheme for the quantum circuit's own operation. Specifically, given a noisy quantum circuit A, the obtained syndrome measurement is used to train a decoding quantum circuit B to identify the logical operators required to correct errors in quantum circuit A. The trained decoding quantum circuit B is deployed on a quantum device such as a quantum computer to perform real-time decoding and error correction. The method specifically includes the following steps:

[0030] Step 1: Build an error model based on the quantum code of quantum computer noise;

[0031] Specifically, such as Figure 1 As shown, the quantum code is represented by a Tanner graph, wherein the upper left panel represents the rotating surface code under quantum bit noise, and the upper right panel represents the repetitive code with a code distance of 3 under circuit-level noise, R represents reset, M represents measurement, and I represents idle; then their corresponding Tanner graphs are displayed in the top middle panel, and the error mechanism corresponds to the circle in the middle upper panel. The measurement results in the Tanner graph produce a syndrome, which is then used to decode the logical sector and perform correction. In the embodiment of the present application, only three syndrome measurements are depicted in different colors.

[0032] Step 2: Measure the data results according to the error model or obtain them from real quantum computer hardware and correct the errors. The data results are composed of multiple syndromes and logical operators.

[0033] Specifically, the error model measurement is constructed by measuring the auxiliary qubits; the syndrome indicates whether an odd number of errors occurs in a specific set of error models. If no errors occur, the syndrome will be trivial (all zeros); if an odd number of errors occurs, some measurements will be triggered and report non-trivial syndromes, that is, for m measurements, there are 2 m possible syndromes γ = {γ1, γ2, ..., γ m}∈{0,1} m ; In the case of known syndromes, the logical operators caused by errors are inferred and corrected to achieve error correction of data results.

[0034] Step 3: Use the data results for learning and training to obtain the decoding quantum circuit;

[0035] Specifically, the decoding quantum circuit involves parameterized single-qubit gates and non-parameterized two-qubit gates, and ultimately indicates the logical sector through a single measurement. In the embodiment of the present application, error symptoms (syndromes) are encoded as parameters of the single-qubit gate. Figure 1 Below, we take the decoding quantum circuit consisting of 3 qubits and 2 unitary operation blocks as an example: each unitary operation block consists of a set of rotating X gates Followed by a set of revolving Y doors where q∈{1, 2, 3} represents the qubit index in the decoding circuit, b∈{1, 2} represents the block index, and i is the error symptom index. The parameters of the rotation gate are determined by the product of the learnable parameter θ and the error symptom γ. The matrix form of the X rotation gate is:

[0036]

[0037] The matrix form of the Y revolving door is:

[0038]

[0039] Here, θ and φ are learnable parameters. The parameters of the rotation gate can be optimized through learning and training, either using a tensor network approach or sampling from quantum computer hardware. The training process consists of forward propagation and backpropagation, in which the parameters of the rotation gate are iteratively adjusted to bring the conditional distribution closer to the training data distribution. During the forward propagation, a single-qubit gate is constructed using the training syndrome γ and the parameters θ and φ. A tensor network is then used to simulate the quantum circuit to obtain the final state, and the conditional probability p(β|γ) is calculated as the output. A cross-entropy loss function is then formulated based on this output and the corresponding label γ in the training data. During the backpropagation process, the gradient of the loss function with respect to the parameters is calculated using the backpropagation algorithm, and these gradients are then used by the optimizer to update the parameters.

[0040] More specifically, in order to verify whether the proposed decoding quantum circuit can effectively suppress the error in the actual quantum code, numerical experiments were conducted on the Z-based surface code quantum memory under depolarized circuit-level noise. Surface codes with code distances of 3, 5, and 7 were tested, as shown in Figure 2. Figure 2-4The figure shows the evolution of the logical error rate of the decoding quantum circuit over the training steps, compared with the minimum weight perfect matching (MWPM) algorithm. The vertical axis represents the logical error rate, and the horizontal axis represents the number of training epochs. In the experiment, the physical error rate was fixed at 0.001 to simulate the error level of current superconducting quantum devices. The decoding circuit for each code consists of 3 qubits and 10 operation blocks, and the decoding circuit is assumed to be noise-free. All decoding quantum circuits were trained with 200,000 syndromes randomly generated from the error model, and 100,000 test syndromes were randomly generated with different random seeds. The figure shows that the logical error rates of both training and test syndromes initially decrease from higher values ​​to lower values ​​with increasing training epochs. For a surface code with a code length of 3 and four measurement epochs, the test logical error rate after 10,000 training epochs outperforms the MWPM algorithm and remains below the break-even point of 0.999, which is attributed to the shorter code length of the code. For the code distances of 5 and 7, it can be clearly seen that at 10 4 After training rounds, the test logic error rate exceeds the break-even point.

[0041] Furthermore, once the parameters are correctly learned, the resulting decoding quantum circuit can be deployed on a quantum computer or other quantum device to perform decoding, that is, after applying single-qubit gates and two-qubit gates to the initial state, the final state is prepared and then measured under the computational basis. This process effectively derives the value corresponding to the final state in the computational basis |ψ(β1, β2, …, β Q )| 2 The probability distribution under which the bit string {β1, β2, ..., β Q}, denoted as q(β|γ). When Q>k, that is, when the number of qubits Q in the decoding circuit exceeds the number of logical qubits k, a subset of the decoding qubits can be measured or selected. For example, in the quantum memory example characterized by k=1, only one qubit in the decoding quantum circuit needs to be measured to obtain the conditional probability of q(β|γ1,γ2,…,γ m ) to obtain a sample of logical sectors; alternatively, repeat the process several times to estimate the conditional probability of the logical sectors given the error symptoms, and then select the logical sector that maximizes the conditional probability.

[0042] Step 4: Run the decoding quantum circuit for decoding. When the quantum computer generates noise or new errors, the decoding quantum circuit will directly output the corresponding error correction logic operator with the syndrome as input, and perform decoding and error correction in real time.

[0043] Specifically, the decoding speed of the decoding quantum circuit matches the operating speed of the quantum computer's error-corrected quantum circuit. Using the quantum circuit-based quantum computer error correction method provided by the embodiment of the present application, it is no longer necessary to measure the auxiliary quantum bits to obtain the classical syndrome for error detection and correction. Instead, the state of the auxiliary quantum bits can directly control the parameters of the decoding circuit (through a controlled single quantum bit gate with learning parameters) to perform decoding; in addition, the results of the decoding circuit can be directly fed back to the operating circuit using a controlled gate to perform logical operations, forming a self-correcting circuit. Figure 5 As shown, the blue-shaded portion of the circuit represents the storage portion, which consists of three data qubits and two ancillary qubits. In this round, measurements are taken on the ancillary qubits, which are directly used to control the learned single-qubit gates in the decoding section of the circuit (shown in green), which contains two decoding qubits. Finally, the second decoding qubit is used to manipulate the data qubit, introducing a controlled logic X gate to correct errors in the repeating memory.

[0044] More specifically, the quantum computer error correction method based on quantum circuits provided in the embodiments of the present application uses a variational quantum circuit to decode the quantum error correction code. The decoding quantum circuit is a purely quantum operation and does not require the participation of classical operations. The proposed method is based on learning and training and can be applied to various codes under different noise conditions. The decoding time is consistent with the operation time of the noisy quantum circuit, and logical errors in the noisy quantum circuit can be corrected in real time.

[0045] The foregoing description is merely a preferred embodiment of the present application and is not intended to limit the present application. Persons skilled in the art will readily appreciate that various modifications and variations are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present application shall be included within the scope of protection of the present application.

Claims

1. A quantum computer error correction method based on quantum circuits, characterized in that: The steps include: Step 1: Build an error model based on the quantum code of quantum computer noise; Step 2: Measure the data results according to the error model or obtain them from real quantum computer hardware and correct the errors. The data results are composed of multiple syndromes and logical operators. Step 3: Use the data results for learning and training to obtain the decoding quantum circuit; Step 4: Run the decoding quantum circuit for decoding. When the quantum computer generates noise or new errors, the decoding quantum circuit will directly output the corresponding error correction logic operator with the syndrome as input, and perform decoding and error correction in real time.

2. The quantum computer error correction method based on quantum circuit according to claim 1, characterized in that: In step 1, the quantum code is represented by a Tanner graph.

3. The quantum computer error correction method based on quantum circuit according to claim 2, characterized in that: In step 2: The error model measurement is constructed by measuring the auxiliary qubit; The syndrome represents the parity of errors in a particular set of error models; Error correction of data results means inferring logical operators caused by errors and correcting them when the syndrome is known.

4. The quantum computer error correction method based on quantum circuit according to claim 3, characterized in that: In step 3, the decoding quantum circuit involves a parameterized single-qubit gate and a non-parameterized two-qubit gate, that is, the decoding quantum circuit consists of multiple qubits and multiple groups of unitary operation blocks.

5. The quantum computer error correction method based on quantum circuit according to claim 4, characterized in that: Each group of the unitary operation blocks includes a plurality of X rotation gates, a plurality of Y rotation gates, and a plurality of controlled Z gates.

6. The quantum computer error correction method based on quantum circuits according to claim 5, characterized in that: The parameters of the revolving door can be optimized through learning and training, which is performed using tensor network methods or quantum computer hardware sampling.

7. The quantum computer error correction method based on quantum circuit according to claim 6, characterized in that: The learning and training process includes forward propagation and back propagation, and the parameters of the revolving door are iteratively adjusted to make the conditional distribution close to the training data distribution.

8. The quantum computer error correction method based on quantum circuits according to claim 7, characterized in that: In step 4, decoding the quantum circuit is a purely quantum operation and does not require the participation of classical operations.

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