Optimizer Design Method, Device and Medium Utilizing Quantum Tunneling Effect

Abstract

The present invention discloses an optimizer design method, device and medium using the quantum tunneling effect, which relates to the fields of computer science and technology and quantum information technology. The method includes: converting an optimization problem into a quantum state through mathematical modeling; implementing iterative optimization of the quantum state through a parameterized quantum circuit and introducing a quantum tunneling effect mechanism to jump out of local optimal solutions; after each evolution of the quantum state, evaluating the quality of the current solution by observing the objective function value; introducing an adaptive multi-layer optimization strategy, and gradually converging to the global optimal quantity by adjusting the learning rate of parameters, so as to balance the capabilities of global search and local optimization; after the quantum circuit completes optimization, measuring and extracting the observed value, and determining the global optimal solution according to the observed value. The present invention introduces a quantum circuit and a tunneling mechanism in hardware design, and realizes a fast jump function through the tunneling phenomenon, which can improve the optimization performance and provide a more efficient solution for hardware acceleration.

Description

Technical Field

[0001] The present invention relates to the fields of computer science and technology and quantum information technology, and more specifically, to an optimizer design method, device, and medium using the quantum tunneling effect. Background Art

[0002] In the field of hardware acceleration of optimization algorithms, existing hardware devices are mostly based on classical computing architectures, and their design ideas mainly rely on means such as improving computing speed, optimizing algorithm execution paths, and using parallel computing to enhance optimization performance. However, for complex optimization problems, especially global optimization tasks in high-dimensional solution spaces, the performance of such devices is often limited by the local optimum problem, that is, it is easy to fall into local optimum solutions during the optimization process and difficult to jump to a better solution area.

[0003] Currently, the methods for solving the local optimum problem mainly focus on the improvement of software algorithms. For example, by introducing various heuristic algorithms (such as genetic algorithms, particle swarm algorithms, and simulated annealing algorithms) to balance global search and local search. However, these methods are still limited by the limitations of classical computing. Especially when dealing with complex nonlinear problems, their efficiency and effect are difficult to be satisfactory. In terms of hardware implementation, the design of existing optimization devices does not provide effective support for jumping out of the local optimum and lacks a dedicated mechanism for specific bottlenecks in the optimization process. For example, although the acceleration schemes of FPGA and GPU can improve the overall computing speed, their hardware designs do not provide a direct solution to how to get rid of the local optimum.

[0004] Some studies have tried to use random perturbation or high-temperature mechanisms to simulate the "jumping" in the search process, but these methods rely on a large number of iterations and computing resources, and the optimization efficiency is low. At the same time, the hardware design is still based on classical architectures and fails to make full use of physical mechanisms in quantum mechanics (such as the quantum tunneling effect) to construct a hardware solution that can more effectively jump out of the local optimum.

[0005] The quantum tunneling effect provides a new possibility for solving the local optimum problem. The tunneling effect is a typical quantum mechanical phenomenon, which is manifested as microscopic particles "tunneling" through the potential barrier to the other side through the expansion characteristics of the quantum wave function when the energy is not enough to cross the potential barrier. In optimization problems, this characteristic can be analogized to the jumping mechanism in the optimization process, enabling the solution to "cross" from one local optimum solution area to other areas in the global search space, thereby improving the ability to jump out of the local optimum.

[0006] Although existing research has explored how to use the quantum tunneling effect to solve the local optimum problem at the software level, the implementation of these studies relies on complex simulation algorithms with high computational overhead, making it difficult to meet the efficiency requirements in practical applications. At the hardware level, the architecture design of existing optimization devices does not consider the direct introduction of the quantum tunneling effect, resulting in the performance of existing devices in optimization algorithms being limited to the classical logic framework and unable to fully exploit the potential of quantum effects.

[0007] In summary, the existing optimization hardware devices have the following main deficiencies: First, the hardware design does not provide a dedicated solution mechanism for the local optimum problem, and the jumping ability is limited; Second, the device architecture lacks support for the quantum tunneling effect and cannot use this quantum mechanical property to improve the optimization performance. These deficiencies are rooted in the fact that existing technologies are mainly based on classical computing logic and lack exploration of the application of quantum properties. Summary of the Invention

[0008] To solve the above technical problems, the present invention provides an optimizer design method, device and medium using the quantum tunneling effect. By introducing quantum circuits and tunneling mechanisms in the hardware design, the fast jumping function is realized through the tunneling phenomenon, which can not only improve the optimization performance, but also make up for the deficiencies of the existing technology and provide a more efficient solution for hardware acceleration.

[0009] In a first aspect, the present invention provides an optimizer design method using the quantum tunneling effect, the method comprising:

[0010] Converting the optimization problem into a quantum state through mathematical modeling;

[0011] Realizing iterative optimization of the quantum state through a parameterized quantum circuit;

[0012] Introducing a quantum tunneling effect mechanism to jump out of the local optimum solution;

[0013] After each quantum state evolution, evaluating the quality of the current solution by observing the objective function value;

[0014] Introducing an adaptive multi-layer optimization strategy, and gradually converging to the global optimum by adjusting the learning rate of the parameters, so as to balance the global search and local optimization capabilities;

[0015] After the quantum circuit is optimized, measuring and extracting the observed value, and determining the global optimum solution according to the observed value.

[0016] Further, converting the optimization problem into a quantum state through mathematical modeling includes:

[0017] For the variable , where represents the real number space, n represents the dimension of the problem, and for the objective function of the variable Perform operations to introduce qubits to represent the states of each variable;

[0018] Through quantum amplitude encoding, each possible state of the variable x is mapped to a quantum state , where:

[0019] ;

[0020] Among them, represents the index of the qubit state, represents the component of the quantum state;

[0021] Map the optimization problem to the construction problem of the quantum state, and the weight represents the possibility of each solution;

[0022] When initializing the quantum circuit, apply the Hadamard gate to each qubit to generate the initial uniform superposition state through the following formula:

[0023] ;

[0024] Among them, represents the initial uniform superposition state.

[0025] Furthermore, realize the iterative optimization of the quantum state through a parameterized quantum circuit, including:

[0026] Through a series of parameterized rotation gates and controlled gates CX constitute a quantum variational circuit, expressed as:

[0027] ;

[0028] Among them, represents the composite operation composed of a series of parameterized quantum gates, represents the quantum gate that rotates along the y-axis, and the rotation angle is determined by the parameter decides, represents the index of the rotation gate in the quantum circuit, represents the number of parameterized quantum gates in the quantum circuit;

[0029] Use the parameterized circuit to update the quantum state and form a parameterized target state through the following formula:

[0030] ;

[0031] Among them, is a composite operation composed of rotation gates, controlled gates CX and CZ gates. The CZ gate is a control gate, Represents the quantum state after the optimization of the parameterized quantum circuit, and the parameterized quantum circuit is achieved by adjusting the parameters Implementation.

[0032] Furthermore, a quantum tunneling effect mechanism is introduced to jump out of the local optimal solution, including:

[0033] The basis of the quantum tunneling effect mechanism comes from the Schrödinger equation shown below:

[0034] ;

[0035] Among them, Represents the imaginary unit, Represents the reduced Planck constant, The wave function of the quantum system, representing the probability amplitude of the particle at a certain position and time, Represents the time variable, Represents the potential barrier function, Represents the mass of the particle;

[0036] The quantum tunneling effect mechanism is through non-linear operation of the controlled rotation gate And two-qubit entanglement:

[0037] ;

[0038] Among them, Represents the controlled rotation gate, Represents the phase rotation of the complex number, Represents the rotation angle or phase angle.

[0039] Furthermore, after each quantum state evolution, the quality of the current solution is evaluated by observing the objective function value, including:

[0040] Using a quantum observer to map the objective function value to the measurement result M , and the quality of the solution is given by the probability amplitude:

[0041] ;

[0042] Among them, Represents the probability that the quantum state is measured, Represents the quantum state 's probability amplitude, and argmax represents returning the index corresponding to the maximum probability in a probability distribution.

[0043] Furthermore, an adaptive multi-layer optimization strategy is introduced, and the learning rate of the parameters is adjusted through the following formula to gradually converge to the global optimal quantity:

[0044] ;

[0045] Among them, represents the updated optimization parameter at the (t + 1)-th iteration, represents the optimization parameter at the t-th iteration, represents the estimated value of the gradient of the objective function, represents the learning rate, represents that under the parameter the quantum state obtained through the quantum circuit.

[0046] Furthermore, after the quantum circuit is optimized, the observed value is measured and extracted through the following formula:

[0047] ;

[0048] Among them, represents the observed value; represents that under the optimal parameter the quantum state generated through the quantum circuit.

[0049] Furthermore, the method further includes:

[0050] Based on the set optimization requirements, verify whether the objective function value meets the optimization requirements. In the case where the optimization requirements are not met, adjust the circuit parameters through the feedback mechanism until the objective function value meets the optimization requirements.

[0051] In a second aspect, the present invention provides an optimizer design device using the quantum tunneling effect, and the device includes:

[0052] A quantum state conversion unit configured to convert the optimization problem into a quantum state through mathematical modeling;

[0053] An iterative optimization unit configured to implement iterative optimization of the quantum state through a parameterized quantum circuit;

[0054] A mechanism introduction unit configured to introduce the quantum tunneling effect mechanism to jump out of the local optimal solution;

[0055] A function evaluation unit configured to evaluate the quality of the current solution by observing the objective function value after each quantum state evolution;

[0056] A multi-layer optimization unit configured to introduce an adaptive multi-layer optimization strategy, and gradually converge to the global optimal quantity by adjusting the learning rate of the parameters, thereby balancing the global search and local optimization capabilities;

[0057] An optimal solution determination unit configured to measure and extract the observed value after the quantum circuit is optimized, and determine the global optimal solution according to the observed value.

[0058] In a third aspect, the present invention provides a readable storage medium storing one or more programs, which can be executed by one or more processors to implement the method as described above.

[0059] Based on the combination of QVAs and the quantum tunneling effect, it aims to solve the problems existing in traditional ABC in high-dimensional, non-linear, and multi-objective optimization problems, such as local optimal traps, low search efficiency, and difficulty in analyzing complex solution spaces. The beneficial effects of the technical solution disclosed in the present invention will be elaborated in detail below.

[0060] 1. Overcoming the limitations of traditional ABC: The quantum optimizer proposed in this application combines QVAs and the quantum tunneling effect to address the deficiencies of traditional ABC in high-dimensional, non-linear, and multi-objective optimization problems, especially when the objective function has multiple extreme points. The quantum tunneling effect, through the superposition property of quantum states and the non-locality of quantum entanglement, helps the optimizer cross the potential barriers in the solution space, avoiding local optimal traps and thus increasing the probability of finding the global optimal solution.

[0061] 2. Significantly improving the search efficiency in complex solution spaces: The quantum optimizer, through the exponential superposition ability of QVAs, enables the search space to grow exponentially with the increase in the number of qubits, allowing potential optimal solutions to be evaluated and screened in a shorter time, thus significantly enhancing the computational efficiency. The parallel nature of quantum computing enables the optimization process to achieve a more efficient search in multi-dimensional solution spaces, adapting to complex high-dimensional problems.

[0062] 3. Adaptability of the optimizer's scalability and diversity: The quantum circuit structure of the present invention is highly modular and parameterizable, capable of adapting to various types of optimization problems, including combinatorial optimization, continuous optimization, and multi-objective optimization problems. By modifying the encoding method of the objective function and adjusting the specific structure of the parameterized quantum circuit, the optimizer can flexibly adapt to different actual requirements. This highly flexible structure makes it possible to apply this technical solution in different fields, providing an extensible solution for solving diverse optimization problems.

[0063] 4. Structure improvement of the quantum circuit and tunneling mechanism: The quantum circuit designed in the present invention adopts a multi-layer parameterized structure, with each layer consisting of rotation gates and entanglement gates, which can enhance the global search ability for the solution space. The rotation gates provide the ability to locally adjust quantum states, while the entanglement gates enhance the global search ability of the solution space by introducing non-local correlations between qubits. In addition, a tunneling module is added to the quantum circuit, which changes the distribution of quantum states through non-linear phase adjustment, enhancing the global search ability and helping the system jump from a local optimal solution to a broader region of the solution space.

[0064] 5. Integrated Design of Quantum-Classical Feedback Mechanism: The present invention further improves the quantum-classical feedback mechanism by measuring the quantum state in real time and dynamically adjusting the parameterized structure and learning rate of the quantum circuit according to the measurement results. This mechanism deeply integrates quantum computing and classical computing, and can adjust the optimization strategy in real time according to the quantum measurement results during the optimization process to ensure that the optimization process always converges in the direction of decreasing the objective function value. This feedback mechanism effectively improves the efficiency of the optimization process and maintains the stability and convergence of the optimization process during continuous adjustment. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 A quantum circuit diagram depicting the quantum tunneling effect according to an embodiment of the present invention is shown;

[0066] Figure 2 A quantum circuit designed using Qiskit according to an embodiment of the present invention is shown;

[0067] Figure 3 A statistical histogram of quantum state candidate solutions according to an embodiment of the present invention is shown;

[0068] Figure 4 A framework diagram of an optimizer based on quantum tunneling according to an embodiment of the present invention is shown;

[0069] Figure 5 An overall flowchart of a method for designing an optimizer using the quantum tunneling effect according to an embodiment of the present invention is shown;

[0070] Figure 6 A quantum circuit diagram with quantum tunneling added according to an embodiment of the present invention is shown;

[0071] Figure 7 A structural diagram of a device for designing an optimizer using the quantum tunneling effect according to an embodiment of the present invention is shown. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0072] To enable those skilled in the art to better understand the technical solutions of the present invention, the present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments. The embodiments of the present invention will be further described in detail below in conjunction with the accompanying drawings and specific examples, but shall not be construed as a limitation to the present invention. For the various steps described herein, if there is no necessity for a sequential relationship between them, the order in which they are described as examples herein shall not be regarded as a limitation, and those skilled in the art should know that they can be adjusted in order as long as the logic between them is not destroyed and the entire process cannot be realized.

[0073] An optimizer design method using the quantum tunneling effect is provided in an embodiment of the present invention, aiming to solve the technical problems that traditional ABC is prone to falling into local optima, has insufficient global search ability, and a slow convergence speed in complex problems. Here, ABC is the abbreviation of "Artificial Bee Colony Algorithm", representing the artificial bee colony algorithm. For general dynamic constraint problems, the present invention introduces the quantum tunneling effect and realizes jumping out of the local optimal solution through the quantum jump mechanism to enhance the global search ability. At the same time, combined with the ABC optimization strategy, the accuracy and stability of the algorithm in complex scenarios are improved, so as to meet the requirements for efficient and stable optimization solutions in practical applications. This method can be widely applied to multi-objective optimization and dynamic constraint optimization scenarios, covering fields such as intelligent traffic scheduling, engineering design, and data mining, providing innovative solutions for complex problems.

[0074] Next, the key technologies required to implement the optimizer design method using the quantum tunneling effect are introduced:

[0075] One of the core technologies for implementing the optimizer design method using the quantum tunneling effect lies in the quantum tunneling effect, aiming to realize the function of jumping out of the local optimal solution in ABC through hardware. The quantum tunneling effect is an important physical phenomenon in quantum mechanics, which can explain how microscopic particles "pass through" the insurmountable potential barrier in classical mechanics. This characteristic provides a new idea for solving local optimal jumps in high-dimensional optimization problems.

[0076] The quantum tunneling effect means that even if the energy of a particle is lower than the height of the potential barrier, there is still a certain probability for the particle to pass through the potential barrier. This phenomenon violates the view of classical mechanics but widely exists in the microscopic world. Its origin lies in the superposition principle and probability interpretation of wave functions in quantum mechanics.

[0077] According to the time-independent Schrödinger equation:

[0078] ;

[0079] where is the reduced Planck constant, is the mass of the particle, is the wave function of the particle, is the potential energy function, is the total energy of the particle.

[0080] Assume that the particle encounters a rectangular potential barrier, , represents the height of the potential barrier, and the potential barrier region is within , and the potential energy is 0 in the remaining regions. If the total energy of the particle , its classical mechanics view holds that particles cannot pass through the potential barrier. However, according to the solution of quantum mechanics, the particle wave function shows exponential decay in the potential barrier region:

[0081] ;

[0082] where A and B represent constants of the wave function in the potential barrier region, represents the exponential decay rate of the wave function in the potential barrier region, represents the input parameter.

[0083] The transmission coefficient of the potential barrier, that is, the probability of a particle passing through the potential barrier, is:

[0084] ;

[0085] where, represents the transmission coefficient, represents the width of the potential barrier.

[0086] The penetration probability of the particle decreases rapidly as the potential barrier width and the potential barrier height increase.

[0087] When applied to optimization problems, the local optimal energy in the solution space is simulated as a potential barrier, and the state of the solution corresponds to the wave function of the particle. Through the tunneling effect, the local optimum can be skipped to find the global optimal solution. In the optimizer hardware, this process can be implemented through a quantum circuit. The superposition state of qubits and quantum gate operations can reflect the evolution of particles in the tunneling potential barrier. In a specific implementation, the transmission probability in the potential barrier region can be controlled by a parameterized rotation gate, and it is judged whether tunneling is completed through the result of quantum measurement.

[0088] As Figure 1 shown, it is a quantum circuit diagram for describing the quantum tunneling effect. Figure 1 In it, q represents qubits, H represents the Hadamard gate, represents the parameterized rotation gate, C represents classical bits, and "0" and "1" represent the results of finally measuring the qubits. This quantum circuit parameterizes the state transfer of qubits through the rotation gate ( gate) to represent the transmission probability of particles in the potential barrier region. Then, parameters can be designed to control the height of the potential barrier, expressed as being consistent with the exponential relationship of the actual transmission probability. The final measurement result of the qubits is 0 or 1, indicating whether the particle has completed tunneling.

[0089] Another core technology for implementing the optimizer design method utilizing the quantum tunneling effect is the Quantum Variational Algorithms (QVAs). Quantum variational algorithms are hybrid quantum-classical optimization algorithms that use classical optimizers to adjust the parameters of quantum circuits, thereby minimizing the expected value of the objective function. It is mainly applied in the fields of quantum chemistry, combinatorial optimization problems, and machine learning, etc.

[0090] The core of QVAs lies in the variational principle: by optimizing the expected value of the parameterized quantum state to make it close to the optimal solution of the problem. For the objective function to be optimized it is usually written as:

[0091] ;

[0092] where is the Hamiltonian related to the problem (such as the operator describing the energy of the system), is the parameterized quantum state, which depends on the parameters of the quantum circuit. Immediately afterwards, the quantum circuit evolves the initial state into the parameterized quantum state , expressed as:

[0093] ;

[0094] where is the single-particle and multi-particle operation composed of several parameterized quantum gates. After the parameterized quantum state, parameter optimization is carried out, and the goal is to minimize by optimizing the parameter :

[0095] ;

[0096] where represents the optimal parameter solution.

[0097] Finally, the quantum state is measured to obtain , and then the parameter is updated:

[0098] ;

[0099] where is the learning rate, is the gradient of the objective function, represents the parameter value updated in each iteration, represents the parameter in the current iteration.

[0100] Using Qiskit of International Business Machines Corporation (IBM), a quantum circuit as shown in Figure 2 can be designed. Figure 2 In 1 , q 2 and q 3 all represent qubits, and "0", "1", "2", and "3" represent the indices of the measurement results. , , represent parametric rotation gates.

[0101] This quantum circuit can transform the local search parameters of ABC into the input of the quantum circuit, then map these parameters to the rotation angles of the qubits, and process the input parameters through quantum operations. Initially, it receives the local search parameters of ABC (an array of real numbers), and then maps these parameters to the qubits through the parametric rotation gates and . The range of the parameters can be adjusted to a suitable angle range through normalization or other methods. Then, quantum state evolution is performed on the input parameters, and the CNOT gate is used to entangle the qubits to generate the corresponding quantum state and enhance its expressive ability. Finally, the constructed quantum circuit is output and measurement is provided.

[0102] As shown in Figure 3 , by plotting and outputting the corresponding histogram, it can be seen that the measurement result of the quantum circuit is a dictionary, and the result represents the number of occurrences of different quantum states during measurement. The states with higher frequencies in the distribution may be candidate solutions for the global solution. If the solutions corresponding to some measurement results have never been explored by classical algorithms, these results may prompt the algorithm to jump out of the local optimum.

[0103] This optimizer design method using the quantum tunneling effect designs a hardware optimizer specifically for enhancing the global search ability of ABC through the quantum tunneling effect. Traditional ABC often falls into local optimal solutions, resulting in the inability to find the global optimal solution. To solve this problem, the present invention introduces QVAs and the quantum tunneling effect, transforms the parameters of the optimization problem into the input of the quantum circuit through quantum hardware, and uses the quantum tunneling effect to jump out of the local optimal solution, thereby improving the global search ability and optimization accuracy. The framework of the optimizer based on quantum tunneling is as shown in Figure 4 , and its main steps are as follows: First, the optimization problem is formalized as the objective function , and the input parameters x are mapped to the superposition state of the qubits through quantum state encoding:

[0104] ;

[0105] where represents the discrete state of the parameter, and is its corresponding superposition coefficient. Then, design the parameterized quantum circuit , and realize the evolution of the quantum state through rotation gates and CNOT gates, forming:

[0106] ;

[0107] wherein, is the parameterized quantum state.

[0108] The parameters of this quantum circuit are dynamically updated by a classical optimization algorithm. During the search process, through the quantum tunneling effect, the quantum state overcomes the energy barrier during evolution and jumps out of the local optimal solution. Its mathematical description is the time evolution of the quantum state:

[0109] ;

[0110] where H is the Hamiltonian of the system, is the quantum state after evolving for time t, t is the time variable.

[0111] Finally, measure the expected value of the optimization objective function:

[0112] ;

[0113] wherein, is the objective function at the quantum state under the expected value, is the objective function after being transformed into a quantum operator and acting on the quantum state on the result.

[0114] Obtain the feedback information of the optimal solution and adjust the parameters of the quantum circuit, and iterate repeatedly until the global optimal solution is found, so as to realize the efficient solution of the optimization problem.

[0115] Specifically, as Figure 5 shown, it is the overall flowchart of an optimizer design method using the quantum tunneling effect provided by an embodiment of the present invention. The optimizer design method using the quantum tunneling effect includes the following steps S10 to S60.

[0116] S10: Convert the optimization problem into a quantum state through mathematical modeling.

[0117] In some embodiments, the optimization problem is first converted into a form suitable for quantum computing through mathematical modeling. For the variable , for its objective function Perform operations to introduce qubits to represent the states of each variable. Through quantum amplitude encoding, each possible state of the variable x is mapped to a quantum state , where:

[0118] ;

[0119] where, represents the index of the qubit state, represents the component of the quantum state.

[0120] This representation method maps the optimization problem to the construction problem of quantum states. The weight , represents the possibility of each solution. When initializing the quantum circuit, apply the Hadamard gate to each qubit to generate the initial uniform superposition state :

[0121] ;

[0122] By applying the Hadamard gate to each qubit, the construction of the above superposition state can be achieved, providing a basis for subsequent parametric evolution. As Figure 6 shown, it is the quantum circuit diagram with quantum tunneling added. Figure 6 In it, q 0 , q 1 , q 2 and q 3 respectively represent the four qubits in the quantum circuit, H represents the Hadamard gate, "0", "1", "2", "3" and "4" represent the indices of the measurement results, , , and respectively represent the rotation gates that rotate by an angle around a specific axis; , , and respectively represent the rotation gates that rotate by an angle around the Z axis.

[0123] S20: Implement iterative optimization of the quantum state through a parametric quantum circuit.

[0124] In some embodiments, iterative optimization of the quantum state is achieved through a parametric quantum circuit based on QVAs. The quantum variational circuit consists of a series of parametric rotation gates and controlled gates CX and is represented as:

[0125] ;

[0126] Among them, represents a composite operation composed of a series of parameterized quantum gates, represents a quantum gate that rotates along the y-axis, and the rotation angle is determined by the parameter determined, represents the index of the rotation gate in the quantum circuit, represents the number of parameterized quantum gates in the quantum circuit.

[0127] In actual operation, by adding a series of parameterized gate operations on the initial state . The core of this step is to update the quantum state using a parameterized circuit to form a parameterized target state:

[0128] ;

[0129] Among them, is a composite operation composed of rotation gates, controlled gates CX and CZ gates. The CZ gate is a control gate, represents the quantum state optimized by the parameterized quantum circuit, and the parameterized quantum circuit is realized by adjusting the parameter achieved.

[0130] The evolution of the quantum state is the search direction and step size in the optimization problem, ensuring that the solution gradually approaches the global optimum.

[0131] S30: Introduce the mechanism of quantum tunneling effect to jump out of the local optimal solution.

[0132] In some embodiments, to jump out of the local optimal solution, the mechanism of quantum tunneling effect is introduced. The mathematical basis of the quantum tunneling effect comes from the Schrödinger equation:

[0133] ;

[0134] Among them, represents the imaginary unit, represents the reduced Planck constant, the wave function of the quantum system, representing the probability amplitude of the particle at a certain position and time, represents the time variable, represents the potential barrier function, represents the mass of the particle.

[0135] In the quantum optimizer, this mechanism is quantified as the ability to jump in the solution space, and its realization depends on non-linear operations and quantum entanglement. The core of the tunneling effect is through the non-linear operation controlled rotation gate and two-qubit entanglement:

[0136] ;

[0137] Among them, represents a controlled revolving door, represents a complex phase rotation, represents a rotation angle or a phase angle.

[0138] The tunneling effect allows the system to jump out of the potential well where the local optimal solution is located, and then explore other regions in the solution space, thereby significantly improving the optimization ability.

[0139] S40: After each quantum state evolution, evaluate the quality of the current solution by observing the objective function value.

[0140] In some embodiments, after each quantum state evolution, it is necessary to evaluate the quality of the current solution by observing the objective function value. A quantum observer is used to map the objective function value to a measurement result M , and the superiority and inferiority of the solution are given by the probability amplitude:

[0141] ;

[0142] Among them, represents the probability that the quantum state is measured, represents the quantum state , and argmax represents returning the index corresponding to the maximum probability in a probability distribution.

[0143] The evaluation result of the objective function provides feedback for optimizing the next step.

[0144] S50: Introduce an adaptive multi-layer optimization strategy, and gradually converge to the global optimal quantity by adjusting the learning rate of the parameters, so as to balance the global search and local optimization capabilities.

[0145] In some embodiments, in order to balance the global search and local optimization capabilities, an adaptive multi-layer optimization strategy is introduced. By adjusting the learning rate of the parameter , gradually converge to the global optimal quantity:

[0146] ;

[0147] Among them, represents the updated optimization parameter at the (t + 1)-th iteration, represents the optimization parameter at the t-th iteration, represents the estimated value of the objective function gradient, represents the learning rate, represents the quantum state obtained through the quantum circuit under the parameter .

[0148] In the initial stage, a larger learning rate helps to quickly explore the solution space; in the later stage, a smaller learning rate improves the fineness of the solution.

[0149] S60: After the quantum circuit is optimized, measure and extract the observed value, and determine the global optimal solution according to the observed value.

[0150] In some embodiments, after the quantum circuit is optimized, the system extracts the final result through measurement and determines the global optimal solution according to the observed value. Among them, the calculation method of the observed value is:

[0151] ;

[0152] Among them, represents the observed value; represents the quantum state generated by the quantum circuit under the optimal parameter .

[0153] In some embodiments, based on steps S10 to S60, the classical computing part further checks whether the objective function value meets the optimization requirements. If the requirements are not met, the circuit parameters are adjusted through the classical feedback mechanism to verify whether the objective function value meets the optimization requirements. If the conditions are not met, the above steps S10 to S60 are iterated.

[0154] The embodiment of the present invention also provides an optimizer design device using the quantum tunneling effect, as Figure 7 shown, the device includes:

[0155] A quantum state conversion unit 701, configured to convert the optimization problem into a quantum state through mathematical modeling;

[0156] An iterative optimization unit 702, configured to implement iterative optimization of the quantum state through a parameterized quantum circuit;

[0157] A mechanism introduction unit 703, configured to introduce the quantum tunneling effect mechanism to jump out of the local optimal solution;

[0158] A function evaluation unit 704, configured to evaluate the quality of the current solution by observing the objective function value after each quantum state evolution;

[0159] A multi-layer optimization unit 705, configured to introduce an adaptive multi-layer optimization strategy, and gradually converge to the global optimal quantity by adjusting the learning rate of the parameters, so as to balance the global search and local optimization capabilities;

[0160] An optimal solution determination unit 706, configured to measure and extract the observed value after the quantum circuit is optimized, and determine the global optimal solution according to the observed value.

[0161] In some embodiments, the quantum state conversion unit is further configured to:

[0162] For a variable , where represents the real number space, n represents the dimension of the problem, operate on the objective function of the variable, and introduce qubits to represent the states of each variable;

[0163] Through quantum amplitude encoding, each possible state of the variable x is mapped to a quantum state , where:

[0164] ;

[0165] where represents the index of the qubit state, represents the component of the quantum state;

[0166] Map the optimization problem to the construction problem of the quantum state, and the weight represents the possibility of each solution;

[0167] When initializing the quantum circuit, apply the Hadamard gate to each qubit, and generate the initial uniform superposition state through the following formula:

[0168] ;

[0169] where represents the initial uniform superposition state.

[0170] In some embodiments, the iterative optimization unit is further configured to:

[0171] Form a quantum variational circuit through a series of parameterized rotation gates and controlled gates CX , which is expressed as:

[0172] ;

[0173] where represents a composite operation formed by a series of parameterized quantum gates, represents a quantum gate that rotates along the y-axis, and the rotation angle is determined by the parameter , represents the index of the rotation gate in the quantum circuit, represents the number of parameterized quantum gates in the quantum circuit;

[0174] Update the quantum state using the parameterized circuit, and form a parameterized target state through the following formula:

[0175] ;

[0176] Among them, is a composite operation composed of a rotating gate, a controlled gate CX and a CZ gate. The CZ gate is a control gate, represents the quantum state after optimization by a parameterized quantum circuit. The parameterized quantum circuit is achieved by adjusting parameters .

[0177] In some embodiments, the mechanism introduction unit is further configured to:

[0178] The basis of the quantum tunneling effect mechanism comes from the Schrödinger equation shown below:

[0179] ;

[0180] Among them, represents the imaginary unit, represents the reduced Planck constant, is the wave function of the quantum system, representing the probability amplitude of a particle at a certain position and time, represents the time variable, represents the potential barrier function, represents the mass of the particle;

[0181] The quantum tunneling effect mechanism is through non-linear operation of the controlled rotation gate and two-qubit entanglement:

[0182] ;

[0183] Among them, represents the controlled rotation gate, represents the phase rotation of the complex number, represents the rotation angle or phase angle.

[0184] In some embodiments, the function evaluation unit is further configured to:

[0185] Use a quantum observer to map the objective function value to a measurement result M , and give the quality of the solution through the probability amplitude:

[0186] ;

[0187] Among them, represents the probability that the quantum state is measured, represents the quantum state 's probability amplitude, and argmax represents returning the index corresponding to the maximum probability in a probability distribution.

[0188] In some embodiments, the multi-layer optimization unit is further configured to introduce an adaptive multi-layer optimization strategy, and adjust the learning rate of the parameters through the following formula, gradually converging to the global optimal value:

[0189] ;

[0190] where, represents the updated optimization parameter at the (t + 1)-th iteration, represents the optimization parameter at the t-th iteration, represents the estimated value of the gradient of the objective function, represents the learning rate, represents under the parameter the quantum state obtained through the quantum circuit.

[0191] In some embodiments, the optimal solution determination unit is further configured to, after the quantum circuit is optimized, measure and extract the observed value through the following formula:

[0192] ;

[0193] where, represents the observed value; represents under the optimal parameter the quantum state generated through the quantum circuit.

[0194] In some embodiments, the apparatus further includes a feedback adjustment unit, and the feedback adjustment unit is configured to:

[0195] Based on the set optimization requirements, verify whether the objective function value meets the optimization requirements, and in the case where the optimization requirements are not met, adjust the circuit parameters through a feedback mechanism until the objective function value meets the optimization requirements.

[0196] It should be noted that the structures of the various optimizer design apparatuses using the quantum tunneling effect described in this embodiment belong to the same technical concept as the previously described optimizer design method using the quantum tunneling effect, and achieve the same beneficial effects through the same principle, which will not be elaborated here.

[0197] An embodiment of the present invention further provides a readable storage medium, and the readable storage medium stores one or more programs, and the one or more programs can be executed by one or more processors to implement the method described in any one of the above embodiments.

[0198] The foregoing description is intended to be illustrative and not restrictive. For example, the above examples (or one or more aspects thereof) may be used in combination with each other. For instance, other embodiments may be utilized by those of ordinary skill in the art upon reading the above description. Additionally, in the foregoing detailed description, various features may be grouped together to simplify the present invention. This should not be construed as an intention that the features of an unclaimed invention are necessary for any claim. On the contrary, the subject matter of the present invention may be less than all of the features of a particular embodiment of the invention. Thus, the following claims are hereby incorporated into the detailed description by way of example or embodiment, where each claim stands on its own as a separate embodiment, and it is contemplated that these embodiments may be combined with each other in various combinations or permutations. The scope of the present invention should be determined with reference to the appended claims and the full scope of equivalents to which those claims are entitled.

Claims

1. A method for designing an optimizer using the quantum tunneling effect, characterized in that: The method comprises: Convert the optimization problem into quantum state through mathematical modeling; Iteratively optimizing the quantum state by parameterizing the quantum circuit; Introduce quantum tunneling effect mechanism to escape from the local optimal solution; After each quantum state evolution, the quality of the current solution is evaluated by observing the value of the objective function; Introducing an adaptive multi-layer optimization strategy, by adjusting the learning rate of the parameters, gradually converges to the global optimal value, thereby balancing the capabilities of global search and local optimization; After the quantum circuit is optimized, the observed values ​​are measured and extracted, and the global optimal solution is determined based on the observed values; Introducing the quantum tunneling effect mechanism to jump out of the local optimal solution, including: The basis of the quantum tunneling mechanism comes from the Schrödinger equation as shown below: ； in, represents the imaginary unit, represents the reduced Planck constant, The wave function of a quantum system represents the probability amplitude of a particle at a certain position and time. represents the time variable, represents the potential barrier function, represents the mass of the particle; Quantum tunneling effect mechanism via nonlinear operation of controlled rotation gate And double quantum state entanglement: ； in, Indicates a controlled revolving door, represents the phase rotation of a complex number, Indicates the rotation angle or phase angle; The particle wave function exhibits exponential decay in the potential barrier region: ； Among them, A and B represent the constants of the wave function in the potential barrier region, represents the exponential decay rate of the wave function in the potential barrier region, represents the input parameter, E represents the total energy of the particle; The transmission coefficient of the potential barrier, that is, the probability of a particle passing through the barrier, is: ； Where T is the transmission coefficient, represents the width of the potential barrier; The probability of particle penetration varies with the barrier width and barrier height Increase and decrease; The transmission coefficient of the barrier region is controlled by a parameterized rotation gate, and the completion of tunneling is determined by the results of quantum measurement.

2. The optimizer design method using the quantum tunneling effect according to claim 1, characterized in that: The optimization problem is converted into quantum state through mathematical modeling, including: For variables ,in represents the real number space, n Represents the dimension of the problem, the objective function of the variable To perform operations, quantum bits are introduced to represent the state of each variable; Through quantum amplitude encoding, variables x Each possible state of is mapped to a quantum state ,in: ； in, represents the index of the qubit state, Represents the components of a quantum state; Mapping the optimization problem into a quantum state construction problem, weights , represents the possibility of each solution; When initializing the quantum circuit, the Hadamard gate is applied to each bit to generate the initial uniform superposition state through the following formula: ； in, represents the initial uniform superposition state.

3. The optimizer design method using quantum tunneling effect according to claim 2, characterized in that: Iterative optimization of the quantum state is achieved through parameterized quantum circuits, including: Through a series of parametric revolving doors and controlled doors CX The quantum variational circuit is formed, which is expressed as: ； in, represents a composite operation consisting of a series of parameterized quantum gates, Represents a quantum gate that rotates along the y-axis, with the rotation angle determined by the parameter Decide, represents the index of the rotating gate in the quantum circuit, represents the number of parameterized quantum gates in the quantum circuit; The parameterized circuit is used to update the quantum state, and the parameterized target state is formed by the following formula: ； in, It is composed of revolving door, controlled door CX And the composite operation composed of CZ gate, CZ gate is a control gate, represents the quantum state after optimization of the parameterized quantum circuit. The parameterized quantum circuit is optimized by adjusting the parameters accomplish.

4. The optimizer design method using quantum tunneling effect according to claim 1, characterized in that: After each quantum state evolution, the quality of the current solution is evaluated by observing the objective function value, including: Using quantum observers to map objective function values ​​to measurement results M , the goodness of the solution is given by the probability amplitude: ； in, Representing quantum states The probability of being measured, Representing quantum states The probability amplitude, argmax means returning the index corresponding to the maximum probability in a probability distribution.

5. The optimizer design method using quantum tunneling effect according to claim 1, characterized in that: An adaptive multi-layer optimization strategy is introduced to adjust the learning rate of the parameters through the following formula, gradually converging to the global optimal value: ； in, represents the updated optimization parameters at the t+1th iteration, represents the optimization parameter at the tth iteration, represents the estimated value of the objective function gradient, represents the learning rate, Indicated in the parameter Below, the quantum state obtained through the quantum circuit.

6. The optimizer design method using quantum tunneling effect according to claim 1, characterized in that: After the quantum circuit is optimized, the observed value is measured and extracted using the following formula: ； in, represents the observed value; Indicates the optimal parameters The quantum states generated by the quantum circuit.

7. The optimizer design method using quantum tunneling effect according to any one of claims 1 to 6, characterized in that: The method further comprises: Based on the set optimization requirements, check whether the objective function value meets the optimization requirements. If the optimization requirements are not met, adjust the circuit parameters through the feedback mechanism until the objective function value meets the optimization requirements.

8. An optimizer design device using quantum tunneling effect, characterized in that: The device comprises: A quantum state conversion unit, configured to convert the optimization problem into a quantum state through mathematical modeling; An iterative optimization unit, configured to implement iterative optimization of the quantum state through a parameterized quantum circuit; A mechanism introduction unit, configured to introduce a quantum tunneling effect mechanism to escape from a local optimal solution; A function evaluation unit, configured to evaluate the quality of the current solution by observing the target function value after each quantum state evolution; The multi-layer optimization unit is configured to introduce an adaptive multi-layer optimization strategy, which gradually converges to the global optimum by adjusting the learning rate of the parameters, thereby balancing the capabilities of global search and local optimization; The optimal solution determination unit is configured to measure and extract observation values ​​after the quantum circuit is optimized, and determine the global optimal solution according to the observation values; The mechanism introduction unit is further configured to: The basis of the quantum tunneling mechanism comes from the Schrödinger equation as shown below: ； in, represents the imaginary unit, represents the reduced Planck constant, The wave function of a quantum system represents the probability amplitude of a particle at a certain position and time. represents the time variable, represents the potential barrier function, represents the mass of the particle; Quantum tunneling effect mechanism via nonlinear operation of controlled rotation gate And double quantum state entanglement: ； in, Indicates a controlled revolving door, represents the phase rotation of a complex number, Indicates the rotation angle or phase angle; The particle wave function exhibits exponential decay in the potential barrier region: ； Among them, A and B represent the constants of the wave function in the potential barrier region, represents the exponential decay rate of the wave function in the potential barrier region, Represents the input parameters, E represents the total energy of the particle; The transmission coefficient of the potential barrier, that is, the probability of a particle passing through the barrier, is: ； Where T is the transmission coefficient, represents the width of the potential barrier; The probability of particle penetration varies with the barrier width and barrier height Increase and decrease; The transmission coefficient of the barrier region is controlled by a parameterized rotation gate, and the completion of tunneling is determined by the results of quantum measurement.

9. A non-transitory computer-readable storage medium storing instructions, which, when executed by a processor, executes the method according to any one of claims 1 to 7.

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