Iterative bias field hierarchy QAOA solving method and device based on quantum processor and medium

Abstract

The invention relates to the technical field of quantum computing and combinatorial optimization, and discloses an iterative bias field hierarchy QAOA solving method and device based on a quantum processor and a medium. In order to solve the problem that a parameterized quantum circuit is difficult to directly solve due to the fact that the graph scale is far larger than the number of available quantum bits, the method comprises the steps that S1, a core block set, a halo extension set and node affiliation mapping are obtained, and bias field parameters are initialized; s2, executing an inner layer quantum step, and calculating a first statistical magnitude and a second statistical magnitude by executing a quantum circuit on the QPU; s3, executing an outer layer interaction step, constructing an outer layer block diagram based on a cross-block edge, and obtaining outer layer soft variable estimation and outer layer soft orientation; s4, executing bias field recharge updating, calculating a next round of inner layer bias field candidate value, and updating the next round of inner layer bias field candidate value; and S5, judging a termination condition, and carrying out loop iteration or outputting a discrete solution. Through hierarchical iteration and bias field recharge, information loss caused by blocking is effectively reduced, and the solution stability on limited quantum hardware is improved.

Description

Technical Field

[0002] This invention relates to the fields of quantum computing and quantum-classical hybrid optimization technology, specifically to an iterative bias field hierarchical QAOA solution method, apparatus, and medium based on a quantum processor. Background Technology

[0003] Combinatorial optimization problems are widely found in engineering scenarios such as communication network design, resource scheduling, graph partitioning, and machine learning. Among them, problems represented by the two-body Ising model or the Quadratic Unconstrained Binary Optimization (QUBO) model are particularly common. Related research shows that many typical NP-hard problems can be mapped to the Ising / QUBO form at the polynomial scale, thus unifying them into a problem of minimizing (or equivalently maximizing) an energy function of discrete binary variables.

[0004] In recent years, variational quantum algorithms have provided new approaches for solving Ising / QUBO combinatorial optimizations. Among them, the Quantum Approximate Optimization Algorithm (QAOA) constructs parameterized quantum circuits by alternately applying cost Hamiltonian evolution and hybrid Hamiltonian evolution related to the objective function, and updates the circuit parameters under the drive of a classical optimizer, aiming to obtain a near-optimal discrete solution. However, applications for near-intermediate-scale quantum (NISQ) hardware are often constrained by factors such as the number of physical qubits, gate fidelity, decoherence time, and readout noise, resulting in limitations on the size and depth of reliably executable circuits, making it difficult to directly handle combinatorial optimization instances with a large number of variables.

[0005] Meanwhile, the objective function evaluation and gradient / update of variational quantum algorithms often rely on statistical estimation of the quantum circuit output distribution. Taking quantum processors as an example, the same quantum circuit is usually executed repeatedly in a "one shot at a time" manner, and the results of multiple measurements are used to form the expected value or other statistical estimates. Under conditions of noise and a finite number of measurements, statistical errors and readout errors will further affect the estimation accuracy and optimization stability. Therefore, it is necessary to engineer the management of measurement resources and error mitigation.

[0006] To accommodate the upper limit constraint on the number of physical qubits available in quantum hardware, existing technologies employ a hybrid decomposition approach: decomposing large-scale QUBO / Ising problems into multiple smaller subproblems for separate solving, and then using classical strategies to stitch or coordinate these subproblems together. For example, decomposition solvers for large-scale QUBOs can split the original problem into several sub-QUBOs and iteratively solve and combine them using classical or quantum solution resources, thus enabling the handling of larger-scale instances even with hardware limitations. In parallel computing fields such as graph partitioning / domain decomposition, minimizing the weight sum of cross-partition edges (edge-cuts) is often used to reduce the cost of cross-subdomain communication, and halo / boundary exchange mechanisms are used to update subdomain boundary information during iteration.

[0007] However, the aforementioned decomposition and splicing methods still have shortcomings when used for Ising / QUBO combinatorial optimization (especially graph cut objectives): On the one hand, the partitioning of subproblems inevitably introduces cross-block coupling terms. If each subproblem is solved independently and then directly spliced, cross-block interactions are often ignored or coarsely handled, making the optimization quality of the global objective sensitive to the partitioning scheme. On the other hand, under the execution conditions of quantum processors, the finite number of physical qubits and noise measurements make it more difficult to perform stable statistical estimation of subproblem outputs and cross-block information transmission, thus affecting the overall solution performance and repeatability.

[0008] Therefore, given the limited number of available physical qubits in a quantum processor and the constraints of noise and a finite number of measurements, there is an urgent need for a combinatorial optimization solution that can be implemented by a quantum-classical hybrid computing system. This solution should be able to: reduce cross-block information loss and partitioning sensitivity caused by block partitioning, while ensuring that the size of each subproblem mapped to the quantum processor for execution does not exceed the number of qubits it can handle; more effectively characterize short-range cross-block interactions and long-range cross-block effects within the measurable range; and manage the number of hardware measurements (number of circuit repetitions) to suppress statistical uncertainty and readout noise, thereby improving the executability and solution stability of large-scale problems on constrained quantum hardware. Summary of the Invention

[0009] In view of this, this application discloses an iterative bias field hierarchical QAOA solution method, apparatus, and medium based on a quantum processor to solve the aforementioned problems. This method decomposes a large-scale problem into multiple sub-problems adapted to hardware scale, and achieves global optimization through closed-loop iteration of inner-layer quantum sampling and outer-layer classical / quantum interaction.

[0010] The main technical solutions of this invention are as follows:

[0011] S1. Obtain the core block set, halo extension set and node affiliation mapping, and initialize the inner bias field parameters and outer soft variables;

[0012] S2. Perform inner-layer quantum steps: Execute parameterized quantum circuits and measure them on each expansion block of the QPU, and calculate the first statistic. With the second statistic ;

[0013] S3. Execute the outer layer interaction step: Construct an effective outer layer coupling based on cross-block edges and statistics. Solving for the outer soft variables And generate soft orientation ;

[0014] S4. Perform bias field recharge update: Calculate candidate values ​​for the inner bias field using outer layer information and perform damping update;

[0015] S5. Determine the termination condition, iterate through the loop, or output the final discrete solution.

[0016] This application includes at least the following beneficial effects:

[0017] (1) Meets the executable scale of quantum hardware and supports large-scale problem solving: by constraining the expansion set of each halo The size does not exceed This ensures that each subtask mapped to the QPU can be executed within the physical qubit limit, thus enabling processing under constrained quantum hardware conditions. The large-scale Ising / QUBO problem.

[0018] (2) Reduce cross-block information loss introduced by block partitioning: Through the design of extended sub-problems of Core+Halo, the two endpoints of some cross-block edges are included in the same executable sub-task, and second-order statistics are formed from the measurement samples and injected into the outer coupling; for cross-block edges that cannot be jointly measured, first-order statistics product degradation processing is adopted, so as to preserve cross-block short-range correlation as much as possible within the executable resources and reduce the performance degradation caused by simple splicing.

[0019] (3) Outer-inner closed-loop backfeeding improves global consistency: By iteratively updating the outer block graph and the inner subgraph and backfeeding the bias field, the long-range influence across blocks is gradually absorbed during the iteration process, which is conducive to improving the final solution's ability to approximate the global objective function and reducing the sensitivity to the block scheme.

[0020] (4) Smoothing and progressive hardening enhance iterative stability and repeatability: smoothing updates the outer soft variables to reduce jitter caused by finite measurements and noise, and progressive hardening enables the outer decision to gradually converge, reducing iterative oscillations and improving the consistency of the final discretized output.

[0021] (5) Reducing statistical uncertainty and improving resource utilization efficiency by scheduling the number of repeated measurements of inner and outer layers based on statistical uncertainty index: This reduces invalid measurements while ensuring the reliability of statistical estimation, thereby improving the utilization efficiency of QPU measurement resources and suppressing the impact of noise. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of the complete process of the method provided in the embodiments of the present invention.

[0023] Figure 2 The diagram shows the structure of the quantum-classical hybrid computing system described in this invention, including a quantum processing unit (QPU), a classical controller, and a data communication interface between them. The classical controller includes a circuit compilation and mapping module, a parameter optimization module, a measurement scheduling and statistics module, an outer layer graphing module, a soft variable processing module, a bias field refeedback and update module, and a termination criterion module. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0025] First, let's define the terms and symbols used in this invention:

[0026] (1) Graph and Optimization Model: Let the graph corresponding to the combinatorial optimization problem be . ,in The edge or coupling coefficient is This invention is applicable to objective functions of two-body Ising or QUBO form; this paper uses spin variables. (Value) The expression is as follows: When using bit variables (with values ​​of 0 / 1), they can be converted between the two through a regular mapping.

[0027] (2) Hardware constraints: The number of usable physical qubits in the quantum processing unit (QPU) shall not exceed The number of physical qubits used in a single subtask executed on the QPU does not exceed [a certain limit]. .

[0028] (3) Block input: Core block set Halo Extended Set and node affiliation mapping ,satisfy And for any have The aforementioned segmented data is provided as input. The method of this invention itself does not contain a segmentation generation algorithm, nor does it fine-tune the set of nodes contained in each subgraph during execution.

[0029] (4) Set of cross-block edges:

[0030]

[0031] (5) Number of measurements: The “number of measurements / number of times the circuit is repeatedly executed for measurement (shots)” mentioned in this paper refers to the number of times the same parameterized quantum circuit is repeatedly executed and projected on the QPU. Each execution produces a set of classical bit string outputs, which are repeated multiple times to form a statistical estimate.

[0032] (6) Statistic: The first statistic obtained from the measured sample. With the second statistic These are the sample mean values ​​of the joint spin of the node spin and the edge spin, respectively.

[0033] (7) Outer soft variables: Outer block variables in the first... The soft variable estimate of the wheel is The smoothed soft variables are The outer soft orientation used for recharge is .

[0034] like Figure 1 As shown, this embodiment of the invention provides an iterative bias field hierarchical QAOA solution method based on a quantum processor. This method, in the context of... Figure 2 The system operates on a hybrid system consisting of a classic controller and a QPU, specifically:

[0035] The QPU includes a physical qubit array, quantum gate control circuitry, and projection measurement readout circuitry. It supports quantum gate manipulation according to quantum circuit instructions issued by a classical controller and outputs measurement results; the number of usable physical qubits does not exceed [number missing]. .

[0036] Classic controllers include, but are not limited to, the following functional modules:

[0037] (1) Block data input and verification module: receiving and verify ;

[0038] (2) Circuit construction, compilation and physical mapping module: Maps logical variables to physical qubits and generates executable circuits based on chip coupling topology and gate set constraints;

[0039] (3) Parameter optimization module: Iteratively updates the parameters of the parameterized quantum circuit (hot start can be used);

[0040] (4) Measurement scheduling and statistics module: controls the number of measurements. Cache samples and calculate the first and second statistics, as well as the statistical uncertainty index;

[0041] (5) Outer block diagram construction module: based on , calculate ;

[0042] (6) Soft variable processing module: for Smoothing and progressive hardening are then performed to obtain... ;

[0043] (7) Offset field recharge update module: calculation and damping update ;

[0044] (8) Termination Criterion Module: Determines the termination condition of the iteration and outputs the final discrete solution.

[0045] Figure 1 The entire process shown strictly includes the following five core steps:

[0046] S1. Obtain the core block set, halo extension set, and node affiliation mapping; initialize the inner bias field parameters and outer soft variables.

[0047] First, for the given combinatorial optimization problem graph The classical controller executes the graph decomposition algorithm. This is to accommodate the hardware limitations of the QPU (maximum number of qubits). ), to set the nodes Divided into Each of the non-overlapping "core blocks" , making Define node affiliation mapping. If ,but .

[0048] Subsequently, in order to capture interactions across block boundaries, for each core block Construct the "Halo Extended Set" . Include All nodes in the original graph, and those in the original graph. All external neighbor nodes directly connected to a node. The decomposed constraint is: for any Expand the size of the set This ensures that each subproblem can be fully mapped to the QPU.

[0049] The classic controller performs initialization before the iteration begins, specifically including:

[0050] (1) For all nodes Initialize inner bias field (For example, setting it to zero or to a preset constant / random small perturbation);

[0051] (2) For all blocks Initialize outer soft variables (For example, setting it to zero);

[0052] (3) Set the initial and upper limit of the number of inner layer measurements. Initial and upper limit of the number of outer layer measurements , And statistical precision threshold; set damping coefficient Smoothing coefficient With progressive hardening scheduling sequence (For example (Grows in non-descending order with each iteration round).

[0053] S2, Perform inner quantum step: Calculate the first statistic and the second statistic.

[0054] In the In each round of iteration, for each block Perform the following sub-steps:

[0055] S2.1 Mapping and Compilation: For each block (Can be parallelized), classic controller in expansion block The inner layer cost Hamiltonian is constructed above. The local Hamiltonian includes the coupling terms within the block and the current bias field term:

[0056]

[0057] in For the inner bias field (initial value can be taken as follows) ).

[0058] S2.2, QPU Execution: The QPU receives line commands, executes the standard QAOA evolution (including the hybrid layer and the problem layer), and repeats the execution. (secondary projection measurement) to obtain Bit string samples ,in .

[0059] S2.3 Statistical Calculation and Disambiguation:

[0060] Map the measurement bits to spin samples:

[0061]

[0062] in, and Representing samples respectively The first in Each bit and its corresponding spin value. The spin sample mapped from the next measurement sample is calculated and output:

[0063] (1) First statistic (corresponding node first-order statistic) Compute node exist The average spin value in this measurement. If the node In the Halo region (the area where multiple extension blocks overlap), the "core block priority" principle is adopted: only the block to which it belongs is used. The generated measurement data as The value of .

[0064]

[0065] (2) Second statistic (corresponding node pair second-order statistic) : Calculate edges The average of the spin products at both endpoints. The disambiguation rule is also applied: if the edge... Completely contained in the core block Inside, use blocks The data; if the edge is at the boundary, the core block data that can contain both ends of the edge should be used first.

[0066]

[0067] S3. Perform outer layer interaction step: construct outer layer block diagram and obtain outer layer soft orientation.

[0068] This step aims to update the global overview using the high-precision local information from the inner layers.

[0069] S3.1 Constructing effective coupling in the outer layer :

[0070] Classic controllers recognize all cross-block edges For any two blocks and The effective coupling strength between them It is composed of the sum of contributions from all the original edges connecting the two blocks.

[0071] Define second-order terms for outer layer construction. :

[0072]

[0073] It satisfies the rule of "use if it can be measured, degrade if it cannot be measured":

[0074] (1) If it spans a block edge The two ends Able to fall into a certain expansion block at the same time (That is, by covering this edge using a Halo structure), we have the exact quantum correlation statistics for that edge, let .

[0075] (2) If it spans the block edge If the span is too large and not fully covered by any single extended block, it degenerates into a mean-field approximation, let .

[0076] Based on this, for any two blocks Define the effective coupling of the outer layer:

[0077]

[0078] S3.2 Outer Layer Solution and Soft Variable Generation:

[0079] Classic controllers in outer block diagrams (scale: The outer parameterized quantum circuit is constructed and compiled on the QPU, and then repeatedly executed. Each measurement is performed sequentially, yielding a measurement result for one outer block variable each time. Therefore, the outer soft estimate is calculated:

[0080]

[0081] Then a smooth update is performed:

[0082]

[0083] in The step size is updated by adjusting the weight ratio of historical retained values ​​to current calculated values, introducing inertia to suppress iterative oscillations caused by statistical noise in quantum measurements, thereby ensuring the stability of algorithm convergence.

[0084] And generate an outer layer soft orientation for re-irrigation according to the progressive hardening schedule:

[0085]

[0086] in, It is a non-descending sequence that increases with the number of iterations. It is used to gradually transition the outer layer soft orientation from "soft" to "hard" in order to improve the stability of the outer layer decision and suppress oscillations.

[0087] when At this time, the outer block diagram can be obtained by the classic controller using a batch mapping / decomposition execution method. (For example, selecting several blocks of variables in batches while keeping the remaining blocks of variables fixed or boundary-limited on the classical side) to ensure that the number of physical qubits occupied by each QPU task does not exceed .

[0088] S4. Perform bias field backfill update: Calculate and update the candidate values ​​of the inner layer bias field for the next round.

[0089] Classic controllers are based on outer soft orientation Compared with the first statistic Calculate the candidate values ​​for the next round of inner layer bias fields. For any block... core node Define candidate recharge items (which must include at least cross-block contributions):

[0090]

[0091] in This indicates that the neighboring node is not explicitly covered by the halo extension of this block, and its influence is injected in the form of an "outer field" through the backfill bias field.

[0092] To improve iterative stability, the classic controller performs damped updates on the bias field:

[0093]

[0094] in This involves updating the step size. This means the new bias field retains some historical information, smoothing out the parameter variation trajectory. After completing the above refeeding, proceed to the next round. Repeat the closed-loop iteration of "inner quantum step - outer mapping - outer quantum step - refeed update".

[0095] S5. Determine if the termination condition is met; if not, return to step S2; if met, output the discrete solution.

[0096] The iteration stops when at least one of the following termination conditions is met:

[0097] (1) ;

[0098] (2) ;

[0099] (3)

[0100] (4) .

[0101] in, , , For the preset threshold, The gain is the target energy or cut value. and These represent the current iteration round and the maximum number of iterations, respectively.

[0102] If the termination condition is met, final hardening is performed on the inner and outer soft variables, outputting the global discrete solution. For any node... The final spin output is given as follows:

[0103]

[0104] When overlapping nodes exist, the core block can be selected according to the "core block priority" rule. Alternatively, a weighted average can be used before determining the sign.

[0105] Finally, Substitution Calculate the cut value as the solution result and performance evaluation index.

Claims

1. A combinatorial optimization solving method based on a quantum-classical hybrid computing system, the quantum-classical hybrid computing system comprising a quantum processing unit (QPU) and a classical controller, characterized in that, Comprising: S1. Obtain the core block set, halo extension set, and node affiliation mapping: The classic controller will have a scale of... The picture Decomposed into One core block And based on the core block, construct a halo extension set containing first-order neighbors. and node affiliation mapping Ensure that the size of each extended set does not exceed the number of available qubits in the QPU. ; Initialization of inner bias field parameters with outer soft variables ; S2, Execute the inner quantum step: In the first... In each round of iteration, for each block , and its corresponding extended set Map to the QPU and compile to generate the first parameterized quantum circuit, then execute. The sample is obtained from the projection measurement; the first statistic of the node is calculated based on the sample. The second statistic of the edge ; S3, performing outer interaction step: based on the cross-block edge set and the second statistics obtained in step S2, constructing effective coupling of the outer block graph ; solving the outer target defined by , obtaining the outer soft variable estimation , smoothing updating to obtain , and generating the outer soft orientation for back-filling by ;​ S4, execute bias field recharge update: the classical controller is based on with the first statistical amount Calculate the next round of core node inner bias field candidate value , and to Damping update gets ; S5, judging whether a termination condition is satisfied; if not, returning to step S2 for next round iteration; if yes, performing final hardening on inner and outer layer soft variables, and outputting discrete solution .

2. The method of claim 1, wherein, In the calculation of the statistics in step S2, the core block priority principle is adopted to eliminate ambiguity: for the first statistics of node , only the measurement results corresponding to the core block to which the node belongs are adopted; for the second statistics of edge , if the edge is covered by multiple extension sets simultaneously, the measurement results corresponding to the core block that can cover both endpoints of the edge are adopted.​​ 3. The method of claim 1, wherein, constructing a first statistic in step S2 a second statistic for the edges comprises specifically: Node The first statistical quantity of the node is defined as: Any of the above The edges Define its second statistic as: wherein, is the sample bit by mapping the spin variable, represents the measured sample bit in the th position.

4. The method of claim 1, wherein, Constructing the effective couplings of the outer block graph in step S3 Specifically comprising: S3.1, define second order statistics term : for cross-block edges , if node falls into some extended set simultaneously and obtains the second statistics, then let ; otherwise, use mean field approximation to let ; S3.2, calculating the inter-outer-block coupling strength When a node The first statistical quantity Take The corresponding halo extension set The calculated; when an edge The second statistical quantity Take The corresponding or by default weighted average fusion.

5. The method of claim 1, wherein, In step S3, the smooth update satisfies: wherein is an update step. The progressive hardening schedule satisfies: wherein is a non-decreasing sequence.

6. The method of claim 1, wherein, In step S4, the damping update satisfies: wherein .

7. The method of claim 1, wherein, In step S2, the "mapping to the QPU and compiling to generate a parameterized quantum circuit" includes: quantum bit placement, two-bit gate routing and gate sequence optimization according to the physical coupling topology of the quantum chip and the gate set constraint, so that the number of physical quantum bits occupied by each execution does not exceed (when the outer block diagram adopts batch mapping / decomposition execution to obtain outer layer soft variable estimation), and the preparation and measurement required for one iteration within the gate depth allowed by the quantum coherence time are completed.

8. The method of claim 1, wherein, In step S5, the termination condition comprises at least one of: , , or . wherein, , , is a preset threshold value, 9. A quantum-classical hybrid computing device, comprising: Comprising: a quantum processing unit QPU, a classical controller, and a data interface between the two; wherein the QPU has no more than n available physical qubits and has quantum gate control lines and projection measurement lines; the classical controller is configured to execute instructions stored in its memory to implement the method of any one of claims 1 to 8.

10. A computer-readable storage medium, characterized in that, A computer program is stored thereon, the computer program is executed by a processor to implement the method of any one of claims 1 to 8.

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