Quantum heuristic algorithm and system for limited combinatorial optimization
By employing superposition state encoding and projection feedback mechanisms based on quantum heuristic algorithms, the exponential complexity and local optimum traps in constrained combinatorial optimization problems are solved, enabling fast and efficient solutions on traditional circuit systems and adapting to the complex requirements of industrial scenarios.
Patent Information
- Application Number
- CN202511573584.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-30
- Publication Date
- 2026-01-13
AI Technical Summary
When solving constrained combinatorial optimization problems, existing technologies suffer from problems such as exponential complexity, local optimum traps, and parameter sensitivity in classical algorithms, while quantum computing faces hardware barriers and lacks constraint handling, making it difficult to apply effectively in industrial scenarios.
A quantum-inspired algorithm is adopted, which combines the Ising model and gradient descent method with superposition state encoding and projection feedback mechanism to construct a time-dependent Hamiltonian. By using voltage-encoded superposition states, discrete solutions that meet the constraints are generated, and the search direction is optimized by roulette wheel strategy, which is suitable for closed-loop control of classical systems.
It improves global search capability, avoids local optimum traps, enhances parameter robustness, and achieves fast and efficient optimization solutions on traditional circuit systems. The number of iterations is linearly related to the problem size, which is significantly better than traditional algorithms, and no complex parameter tuning is required.
Smart Images
Figure CN121328756A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of constrained combinatorial optimization, in particular to a quantum heuristic algorithm and system for constrained combinatorial optimization. BACKGROUND
[0002] Constrained combinatorial optimization problems (such as the traveling salesman problem, the knapsack problem, etc.) exist widely in logistics scheduling, chip design, artificial intelligence, etc. The core challenge is to find the optimal configuration that meets the constraint conditions in the discrete solution space. With the surge of real-time decision-making needs in industrial scenarios, traditional solving methods face the following technical bottlenecks:
[0003] 1. Inherent defects of classical algorithms:
[0004] Exponential complexity: heuristic algorithms such as simulated annealing and ant colony optimization need to traverse a large number of candidate solutions. When the problem size n increases, the computational complexity increases exponentially.
[0005] Local optimal trap: constraint conditions lead to rugged energy landscape, and algorithms are prone to fall into local optimum.
[0006] Parameter sensitivity: algorithm performance is highly dependent on parameter adjustment, and industrial deployment adaptability is poor
[0007] 2. Application limitations of quantum computing:
[0008] Hardware barrier: quantum annealing has theoretical advantages, but is limited by decoherence time and sparse topology mapping of Hamiltonian.
[0009] Environmental constraints: requires extremely low temperature environment, difficult to scale deployment.
[0010] 3. Lack of constraint handling in quantum heuristic algorithms:
[0011] Existing quantum heuristic schemes (such as quantum local annealing, quantum heuristic parallel annealing, quantum bifurcation algorithm, etc.) lack effective constraint handling mechanisms, leading to infeasible solutions or degraded optimization quality.
[0012] There is an urgent need for an optimization scheme that combines physical scalability, constraint handling capability, and compatibility with classical environments to break through the "efficiency-precision-cost" dilemma. SUMMARY
[0013] The purpose of this invention is to provide a quantum-inspired algorithm and system for constrained combinatorial optimization. By encoding superposition states under quantum inspiration, the global search capability can be improved. Combined with a projection feedback mechanism, it avoids local optimum traps, replaces traditional random search, and improves computational performance. By simulating quantum state superposition through voltage superposition, it is adapted to the closed-loop control of classical systems and has high hardware compatibility. When the Hamiltonian relative strength coefficient γ, gradient descent step size η, and reward coefficient ζ in the algorithm architecture are selected within a certain range, this system can iteratively converge to a similar solution quality. It can cope with the complexity of industrial scenarios without complex manual parameter tuning, improves parameter robustness, and solves the problems mentioned in the background art.
[0014] To achieve the above objectives, the present invention provides the following technical solution:
[0015] Quantum heuristic algorithms for constrained combinatorial optimization include:
[0016] Step 1: Model the problem by transforming the constrained combinatorial optimization problem into the Ising model and constructing the time-dependent Hamiltonian. Constrained binary combinatorial problems;
[0017] Step 2: Model the system state, encode it using quantum superposition, and define the cost function. ;
[0018] Step 3: Update the variables using gradient descent in the data processor. Complete the time-dependent Hamiltonian The search optimization of the ground state uses the input voltage to encode the superposition state and the resistor network to encode the combined optimization problem information;
[0019] Step 4: Based on the constraints of the constrained combinatorial optimization problem, using variables... As weights, a roulette wheel strategy is used to generate discrete solutions that satisfy the constraints. Calculate the corresponding solution quality and update the historical best solution. Based on the historical best solution As an adjustment variable for reward items This enhances the search for high-quality solution neighborhoods.
[0020] Furthermore, in step 1, the constrained combinatorial optimization problem is transformed into the Ising model, including:
[0021] In computer modeling, the problem consists of three core elements:
[0022] Binary optimization variables Objective function and constraints ;
[0023] in, Indicated as the sequence number of the constraint condition; The number of constraints is represented; the optimization task is described as follows:
[0024] Under a series of constraints Under the premise of optimizing variables Make the objective function Take the minimum value;
[0025] The Hamiltonian of the constructed Ising model Its expression is:
[0026] (1)
[0027] in, Represented as spin orientation in the Ising model; It is expressed as the coupling coefficient between spins; It is expressed as the external field intensity.
[0028] Furthermore, in step 1, a time-dependent Hamiltonian and a constrained binary combinatorial problem are constructed, including:
[0029] In quantum heuristic algorithms for constrained combinatorial optimization, a time-dependent Hamiltonian is constructed by simulating the ground-state search path in the quantum adiabatic evolution process. :
[0030] (2)
[0031] in,
[0032] (3)
[0033] (4)
[0034] in, and These are represented by the Pauli z-matrix and Pauli x-matrix of the Ising model spin, respectively; Represented as the relative intensity coefficient of the Hamiltonian; at t=0, the time-dependent Hamiltonian. Represents the initial state; at time t=1, the time-dependent Hamiltonian. Let be the Hamiltonian of the objective Ising model for solving the ground state. .
[0035] Furthermore, in step 2, the system state is modeled, including:
[0036] Model the system state by determining the orientation of the i-th spin in the Ising model. Mapping to continuous variables Construct superposition state vector Its expression is:
[0037] (5)
[0038] in, Represented as a spin-up state; Represented as a spin-down state;
[0039] The overall state of the system can be represented in vector product form as follows:
[0040] (6).
[0041] Further, in step 2, the quantum superposition state is encoded, and a cost function is defined, including:
[0042] To make the system state Approaching the time-dependent Hamiltonian The ground state, the closer the system state is to the ground state, the more likely it is to be the ground state. When the ground state is reached, the cost function should be as small as possible;
[0043] Cost function Defined as a time-dependent Hamiltonian In vector The quadratic form under the following conditions is expressed as:
[0044]
[0045]
[0046] (7)
[0047] in, , .
[0048] Furthermore, in step 3, the cost function Regarding variables The gradient is expressed as:
[0049] (8)
[0050] Perform gradient descent to update the variables. Its expression is:
[0051] (9).
[0052] Furthermore, in step 4, based on the constraints of the constrained combinatorial optimization problem, variables are used... As weights, a roulette wheel strategy is used to generate discrete solutions that satisfy the constraints. Calculate the corresponding solution quality and update the historical best solution. ,include:
[0053] The set of feasible spins that meet the current constraints is progressively filtered, using the corresponding variables... As a probability selection weight, a spin is selected from the feasible set that meets the constraints in the form of roulette wheel.
[0054] Update the feasible set for the next round of roulette wheel sampling until a discrete solution that strictly satisfies all constraints is projected. ;
[0055] Based on the historical best solution As an adjustment variable for reward items Its expression is:
[0056] (10)
[0057] in, Represented as the reward coefficient, after completing the feedback, the time parameter t←t+τ is updated, and steps 3-4 are repeated until t=1, then output. As the final solution.
[0058] A quantum heuristic system for constrained combinatorial optimization, comprising: a matrix multiplication module and an adder amplifier module;
[0059] The matrix multiplication module is configured to include n input nodes ( ) and n output nodes ( ), used to implement the coupling coefficient matrix With spin coefficient vector Matrix multiplication; the core components of the matrix multiplication module include:
[0060] A resistor network, configured such that input node k and output node l are connected by a resistor. Connection, Configuration Realizing the spin coupling coefficient of the Ising model The physical code, where R0 represents a fixed resistance value;
[0061] The input voltage interface is configured to receive external power signals. ,in Encoding spin superposition states;
[0062] The operational amplifier is configured based on the virtual short and virtual open characteristics of the operational amplifier, and the output node voltage corresponds to the coupling coefficient matrix. With spin coefficient vector Matrix multiplication result:
[0063] (11)
[0064] in, This is expressed as the output voltage.
[0065] The adder amplifier module is configured to include n parallel processing units, each unit corresponding to an output node l, which is used to perform a weighted summation operation of the gradient of the cost function at time t.
[0066] Furthermore, it also includes: a data processor, the data processor comprising:
[0067] The analog-to-digital conversion acquisition unit is configured for real-time acquisition. Gradient voltage sequence;
[0068] The control logic unit is configured to perform three core operations, including:
[0069] Gradient descent, configured to update variables according to equation (9) ;
[0070] Constrained projection, configured to generate feasible solutions based on roulette wheel betting strategy. Update the historical best solution ;
[0071] Feedback adjustment, configured to optimize the search direction according to formula (10);
[0072] The parameter modulation interface is configured to send to the adjustable resistor. , and Configuration commands are sent to the voltage source. , and Setting value.
[0073] Furthermore, the core components of the adder amplifier module include:
[0074] Adjustable resistor group: configuration , and Achieve time-varying coefficient modulation;
[0075] Multiple voltage inputs: Encoding the local field terms of the Ising model, Input superposition state information;
[0076] Operational amplifier circuit: Output node voltage satisfies:
[0077] (12)
[0078] The output precisely matches the gradient in equation (8). The output of the adder amplifier module Connect to the analog-to-digital conversion acquisition unit.
[0079] Compared with the prior art, the beneficial effects of the present invention are:
[0080] 1. This invention improves global search capability through quantum-inspired superposition state encoding, avoids local optima traps by combining a projection feedback mechanism, and replaces traditional random search. Furthermore, given that the number of iterations required to find an approximate solution is linearly related to the problem size, the optimization time for a 100-city TSP on a dedicated integrated circuit chip is expected to be on the order of 10ms, which is 2-3 orders of magnitude faster than traditional algorithms such as simulated annealing. In 20 benchmark tests on TSPLIB, the average percentage error (PEav) after 5000 iterations is ≤3%, significantly outperforming simulated annealing and ant colony algorithms with the same number of iterations, and maintaining stable convergence in 100-node problems.
[0081] 2. This invention, based on a traditional circuit system, simulates quantum state superposition through voltage superposition, adapting to closed-loop control of classical systems; it avoids the technical requirements of decoherence and ultra-low temperature in quantum hardware, and can be implemented by a traditional circuit system; at the same time, it has a high tolerance for resistance accuracy. Simulation shows that the circuit system can converge to a similar solution quality under the condition of resistance accuracy of 0% to 5%.
[0082] 3. In this invention, when the Hamiltonian relative strength coefficient γ, gradient descent step size η, and reward coefficient ζ in the algorithm architecture are selected within a certain range, the system can iteratively converge to a similar solution quality, and can cope with the complexity of industrial scenarios without complicated manual parameter tuning. Attached Figure Description
[0083] Figure 1 This is a flowchart illustrating the workflow of the quantum-inspired fast algorithm of this invention.
[0084] Figure 2 This is a schematic diagram of the classic circuit system of the present invention;
[0085] Figure 3 This invention presents a geographic distribution and optimal route map of 20 global cities based on the WGS-84 ellipsoidal Earth model mapping.
[0086] Figure 4 This is a hardware layout diagram of the printed circuit board of the present invention;
[0087] Figure 5 This is a graph showing the data change curves of the quantum-inspired fast algorithm of the present invention in an embodiment. Detailed Implementation
[0088] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0089] To address the inherent flaws in existing classical algorithms, the application limitations of quantum computing, and the lack of constraint handling in quantum-inspired algorithms, please refer to [link to relevant documentation]. Figures 1-5 This embodiment provides the following technical solution:
[0090] Quantum heuristic algorithms for constrained combinatorial optimization include:
[0091] Step 1: Model the problem by transforming the constrained combinatorial optimization problem into the Ising model and constructing the time-dependent Hamiltonian. The constrained binary combinatorial problem includes the following steps:
[0092] In computer modeling, the problem consists of three core elements: binary optimization variables. Objective function and constraints ;in, Indicated as the sequence number of the constraint condition; The number of constraints is represented; the optimization task is described as follows:
[0093] Under a series of constraints Under the premise of optimizing variables Make the objective function To find the minimum value; for example, in the Traveling Salesman Problem, the constraints are that each city is visited once and only one loop is formed. The objective function is the total path length of the loop that passes through all cities. Through variable substitution, the combinatorial optimization problem can be transformed into solving the ground state problem of the Ising model. The Hamiltonian of the Ising model... It has the following general form:
[0094] (1)
[0095] in, Represented as spin orientation in the Ising model; It is expressed as the coupling coefficient between spins; It is expressed as the external field intensity.
[0096] According to the quantum adiabatic theorem, under the condition that the system slowly evolves from the initial Hamiltonian to the target Hamiltonian, the system state will slowly evolve from the ground state of the initial Hamiltonian to the ground state of the target Hamiltonian under the description of the Schrödinger equation. In the quantum heuristic algorithm for constrained combinatorial optimization, the ground state search path in the quantum adiabatic evolution process is simulated to construct the time-dependent Hamiltonian. :
[0097] (2)
[0098] in,
[0099] (3)
[0100] (4)
[0101] in, and These are represented by the Pauli z-matrix and Pauli x-matrix of the Ising model spin, respectively; Represented as the relative intensity coefficient of the Hamiltonian; at t=0, the time-dependent Hamiltonian. Represents the initial state; at time t=1, the time-dependent Hamiltonian. Let be the Hamiltonian of the objective Ising model for solving the ground state. .
[0102] Step 2: Model the system state, encode it using quantum superposition, and define the cost function. Specifically, it includes the following steps:
[0103] To simulate the quantum adiabatic evolution process, a time-dependent Hamiltonian is searched progressively as the time parameter t is updated. Ground state; modeling the system state by aligning the i-th spin in the Ising model. Mapping to continuous variables Construct superposition state vector Its expression is:
[0104] (5)
[0105] in, Represented as a spin-up state; Represented as a spin-down state;
[0106] The overall state of the system can be represented in vector product form as follows:
[0107] (6).
[0108] To make the system state Approaching the time-dependent Hamiltonian The ground state, the closer the system state is to the ground state, the more likely it is to be the ground state. When the ground state is reached, the cost function should be as small as possible;
[0109] Cost function Defined as a time-dependent Hamiltonian In vector The quadratic form under the following conditions is expressed as:
[0110]
[0111]
[0112] (7)
[0113] in, , .
[0114] Step 3: Update the variables using gradient descent in the data processor. Complete the time-dependent Hamiltonian The search optimization of the ground state encodes the superposition state with the input voltage, and the resistor network encodes the combined optimization problem information; among them, the cost function... Regarding variables The gradient is expressed as:
[0115] (8)
[0116] Perform gradient descent to update the variables. Its expression is:
[0117] (9).
[0118] Step 4: Based on the constraints of the constrained combinatorial optimization problem, using variables... As weights, a roulette wheel strategy is used to generate discrete solutions that satisfy the constraints. Calculate the corresponding solution quality and update the historical best solution. Based on the historical best solution As an adjustment variable for reward items This enhances the search for high-quality solution neighborhoods; specifically, it includes the following steps:
[0119] The set of feasible spins that meet the current constraints is progressively filtered, using the corresponding variables... As a probability selection weight, a spin is selected from the feasible set that meets the constraints in the form of roulette wheel.
[0120] Update the feasible set for the next round of roulette wheel sampling until a discrete solution that strictly satisfies all constraints is projected. ;
[0121] Based on the historical best solution As an adjustment variable for reward items Its expression is:
[0122] (10)
[0123] in, Represented as the reward coefficient, after completing the feedback, the time parameter t←t+τ is updated, and steps 3-4 are repeated until t=1, then output. As the final solution.
[0124] In one embodiment, taking the Traveling Salesman Problem as an example, 20 instances on the open-source dataset TSPLIB are used as benchmark test cases. The solutions of simulated annealing, ant colony optimization, local quantum annealing, and quantum-inspired fast algorithms are compared under 5000 iterations in 100 repeated calculations, and their average percentage error compared to the optimal solution is shown in Table 1 below. The first column Ins is the name of the instance, and the second column opt is the optimal solution loop length of the corresponding TSP problem. From the results of each algorithm listed in the table, it can be seen that the solution of QIFA is significantly better than the other comparison objects.
[0125]
[0126] Table 1. Experimental Data Table
[0127] Please see Figures 3-5 Using 20 major global cities as examples for a traveling salesman task, find the shortest loop that traverses all cities; the specific names and locations of the cities and the shortest loop path are as follows: Figure 3 As shown, the corresponding circuit experiments are implemented using a manufactured printed circuit board. The structure of the printed circuit board is as follows: Figure 4 As shown; in Figure 5 The figure shows the curves of squareness and experimental path length of the quantum-inspired fast algorithm on the 20-city global traveling salesman problem as a function of the number of iterations. The dark line represents the average result of 10 trials, and the dashed line represents the simulation result. Based on this, it can be seen that the experiment and simulation form a relatively consistent correspondence.
[0128] The beneficial effects achieved by the above are as follows: Superposition state encoding under quantum inspiration improves global search capability; combined with projection feedback mechanism, it avoids local optimum traps and replaces traditional random search; and considering that the number of iterations required to find an approximate solution is linearly related to the problem size, the optimization time for a 100-city TSP on a dedicated integrated circuit chip is expected to be on the order of 10ms, which is 2-3 orders of magnitude faster than traditional algorithms such as simulated annealing. In 20 benchmark tests on TSPLIB, the average percentage error (PEav) after 5000 iterations is ≤3%, significantly outperforming simulated annealing and ant colony algorithms with the same number of iterations, maintaining stable convergence in the 100-node problem.
[0129] A quantum heuristic system for constrained combinatorial optimization, comprising: a matrix multiplication module, an adder amplifier module, and a data processor.
[0130] The matrix multiplication module is configured to include n input nodes ( ) and n output nodes ( ), used to implement the coupling coefficient matrix With spin coefficient vector Matrix multiplication; its core components include:
[0131] A resistor network, configured such that input node k and output node l are connected by a resistor. Connection, Configuration Realizing the spin coupling coefficient of the Ising model The physical encoding.
[0132] The input voltage interface is configured to receive external power signals. ,in Encodes spin superposition states.
[0133] The operational amplifier is configured based on the virtual short and virtual open characteristics of the operational amplifier, and the output node voltage corresponds to the coupling coefficient matrix. With spin coefficient vector Matrix multiplication result:
[0134] (11)
[0135] Where R0 represents a fixed resistance value, which is set to 1kΩ in the experiment. This circuit module is used to implement matrix-vector multiplication operations. The output voltage is represented as the output voltage of the matrix multiplication module. The input terminal of the adder amplifier module is directly connected via copper foil traces.
[0136] The adder amplifier module is configured to include n parallel processing units, each corresponding to an output node l, used to perform a weighted summation of the gradients of the cost function at time t. Its core components include:
[0137] Adjustable resistor group: configuration , and Achieve time-varying coefficient modulation;
[0138] Multiple voltage inputs: Encoding the local field terms of the Ising model, Input superposition state information;
[0139] Operational amplifier circuit: Output node voltage satisfies:
[0140] (12)
[0141] The output precisely matches the gradient in equation (8). The output of the adder amplifier module Connect to the analog-to-digital conversion acquisition unit.
[0142] The data processor includes: an analog-to-digital conversion acquisition unit, a control logic unit, and a parameter modulation interface.
[0143] The analog-to-digital conversion acquisition unit is configured for real-time acquisition. Gradient voltage sequence;
[0144] The control logic unit is configured to perform three core operations, including:
[0145] Gradient descent, configured to update variables according to equation (9) ;
[0146] Constrained projection, configured to generate feasible solutions based on roulette wheel betting strategy. Update the historical best solution ;
[0147] Feedback adjustment, configured to optimize the search direction according to formula (10);
[0148] The parameter modulation interface is configured to send to the adjustable resistor. , and Configuration commands are sent to the voltage source. , and Setting value.
[0149] The beneficial effects achieved by the above are as follows: By simulating quantum state superposition through voltage superposition based on a traditional circuit system, it is adapted to the closed-loop control of classical systems; it avoids the technical requirements of decoherence and ultra-low temperature in quantum hardware, and can be implemented by a traditional circuit system; at the same time, it has a high tolerance for resistance accuracy. Simulation shows that the circuit system can converge to a similar solution quality under the condition of resistance accuracy from 0% to 5%; and by selecting the Hamiltonian relative strength coefficient γ, gradient descent step size η, and reward coefficient ζ within a certain range in the algorithm architecture, the system can iteratively converge to a similar solution quality, and can cope with the complexity of industrial scenarios without complicated manual parameter tuning.
[0150] Working principle: via parameters The proposed superposition state is encoded, and a time-dependent cost function is constructed based on the Ising Hamiltonian. Subsequently, the variables are iteratively updated using gradient descent. Trial solutions are generated under constrained projection, and the search direction is further optimized by adjusting the feedback. This iterative cycle continues until the time parameter reaches t=1, and finally the historical best solution is obtained. As the output.
[0151] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.
[0152] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.
Claims
1. A quantum heuristic algorithm for constrained combinatorial optimization, characterized in that, include: Step 1: Model the problem by transforming the constrained combinatorial optimization problem into the Ising model and constructing the time-dependent Hamiltonian. Constrained binary combinatorial problems; Step 2: Model the system state, encode it using quantum superposition, and define the cost function. ; Step 3: Update the variables using gradient descent in the data processor. Complete the time-dependent Hamiltonian The search optimization of the ground state uses the input voltage to encode the superposition state and the resistor network to encode the combined optimization problem information; Step 4: Based on the constraints of the constrained combinatorial optimization problem, using variables... As weights, a roulette wheel strategy is used to generate discrete solutions that satisfy the constraints. Calculate the corresponding solution quality and update the historical best solution. ; using the historical best solution As an adjustment variable for reward items This enhances the search for high-quality solution neighborhoods.
2. The quantum heuristic algorithm for constrained combinatorial optimization according to claim 1, characterized in that, In step 1, the constrained combinatorial optimization problem is transformed into the Ising model, including: In computer modeling, the problem consists of three core elements: Binary optimization variables Objective function and constraints ; in, Indicated as the sequence number of the constraint condition; The number of constraints is represented; the optimization task is described as follows: Under a series of constraints Under the premise of optimizing variables Make the objective function Take the minimum value; The Hamiltonian of the constructed Ising model Its expression is: （1）； in, Represented as spin orientation in the Ising model; It is expressed as the coupling coefficient between spins; It is expressed as the external field intensity.
3. The quantum heuristic algorithm for constrained combinatorial optimization according to claim 2, characterized in that, In step 1, the time-dependent Hamiltonian and constrained binary combinatorial problem are constructed, including: In quantum heuristic algorithms for constrained combinatorial optimization, a time-dependent Hamiltonian is constructed by simulating the ground-state search path in the quantum adiabatic evolution process. : （2）； in, （3）； （4）； in, and These are represented by the Pauli z-matrix and Pauli x-matrix of the Ising model spin, respectively; Represented as the relative intensity coefficient of the Hamiltonian; at t=0, the time-dependent Hamiltonian. Represents the initial state; at time t=1, the time-dependent Hamiltonian. Let be the Hamiltonian of the objective Ising model for solving the ground state. .
4. The quantum heuristic algorithm for constrained combinatorial optimization according to claim 3, characterized in that, Step 2 involves modeling the system state, including: Model the system state by determining the orientation of the i-th spin in the Ising model. Mapping to continuous variables Construct superposition state vector Its expression is: （5）； in, Represented as a spin-up state; Represented as a spin-down state; The overall state of the system can be represented in vector product form as follows: （6）。 5. The quantum heuristic algorithm for constrained combinatorial optimization according to claim 4, characterized in that, In step 2, quantum superposition state encoding is performed, and a cost function is defined, including: To make the system state Approaching the time-dependent Hamiltonian The ground state, the closer the system state is to the ground state, the more likely it is to be the ground state. When the ground state is reached, the cost function should be as small as possible; Cost function Defined as a time-dependent Hamiltonian In vector The quadratic form under the following conditions is expressed as: ； ； （7）； in, , .
6. The quantum heuristic algorithm for constrained combinatorial optimization according to claim 5, characterized in that, In step 3, the cost function Regarding variables The gradient is expressed as: （8）； Perform gradient descent to update the variables. Its expression is: （9）。 7. The quantum heuristic algorithm for constrained combinatorial optimization according to claim 6, characterized in that, In step 4, based on the constraints of the constrained combinatorial optimization problem, variables are used... As weights, a roulette wheel strategy is used to generate discrete solutions that satisfy the constraints. Calculate the corresponding solution quality and update the historical best solution. ,include: The set of feasible spins that meet the current constraints is progressively filtered, using the corresponding variables... As a probability selection weight, a spin is selected from the feasible set that meets the constraints in the form of roulette wheel. Update the feasible set for the next round of roulette wheel sampling until a discrete solution that strictly satisfies all constraints is projected. ; Based on the historical best solution As an adjustment variable for reward items Its expression is: （10）； in, Represented as the reward coefficient, after completing the feedback, the time parameter t←t+τ is updated, and steps 3-4 are repeated until t=1, then output. As the final solution.
8. A quantum heuristic system for constrained combinatorial optimization, applied in the quantum heuristic algorithm for constrained combinatorial optimization as described in any one of claims 1-7, characterized in that, include: Matrix multiplication module and adder amplifier module; The matrix multiplication module is configured to include n input nodes ( ) and n output nodes ( ), used to implement the coupling coefficient matrix With spin coefficient vector Matrix multiplication; The core components of the matrix multiplication module include: A resistor network, configured such that input node k and output node l are connected by a resistor. Connection, Configuration Realizing the spin coupling coefficient of the Ising model The physical code, where R0 represents a fixed resistance value; The input voltage interface is configured to receive external power signals. ,in Encoding spin superposition states; The operational amplifier is configured based on the virtual short and virtual open characteristics of the operational amplifier, and the output node voltage corresponds to the coupling coefficient matrix. With spin coefficient vector Matrix multiplication result: （11）； in, Represented as output voltage; The adder amplifier module is configured to include n parallel processing units, each unit corresponding to an output node l, which is used to perform a weighted summation operation of the gradient of the cost function at time t.
9. The quantum heuristic system for constrained combinatorial optimization according to claim 8, characterized in that, Also includes: Data processor, the data processor comprising: The analog-to-digital conversion acquisition unit is configured for real-time acquisition. Gradient voltage sequence; The control logic unit is configured to perform three core operations, including: Gradient descent, configured to update variables according to equation (9) ; Constrained projection, configured to generate feasible solutions based on roulette wheel betting strategy. Update the historical best solution ; Feedback adjustment, configured to optimize the search direction according to formula (10); The parameter modulation interface is configured to send to the adjustable resistor. , and Configuration commands are sent to the voltage source. , and Setting value.
10. The quantum heuristic system for constrained combinatorial optimization according to claim 8, characterized in that, The core components of the adder amplifier module include: Adjustable resistor group: configuration , and Achieve time-varying coefficient modulation; Multiple voltage inputs: Encoding the local field terms of the Ising model, Input superposition state information; Operational amplifier circuit: Output node voltage satisfies: （12）； The output precisely matches the gradient in equation (8). The output of the adder amplifier module Connect to the analog-to-digital conversion acquisition unit.