A numerical calculation-based quantum gate simulation and control parameter optimization method

Abstract

The application relates to a quantum gate simulation and control parameter optimization method based on numerical calculation, which sequentially comprises the following three modules: a model Hamiltonian matrix representation module which can calculate the matrix representation of the model Hamiltonian according to specific problems; a system time evolution and fidelity calculation module which uses the Hamiltonian matrix to discretely solve the Schrodinger equation, gives the corresponding time evolution matrix, and calculates the gate operation fidelity by using the obtained time evolution matrix; and a control parameter optimization module which calls the previous two modules, adopts a local optimization algorithm or a global optimization algorithm to optimize the control parameters and the quantum gate operation time, and gives the optimal control parameters and the gate operation time. The application solves the problem that the gate fidelity of the current superconducting quantum computing system cannot meet the requirements of reliable operation of practical quantum algorithms, can simulate the detailed process of quantum gate operation through the numerical calculation method, and improves the quantum gate operation fidelity through the optimization of the control parameters.

Description

Technical Field

[0001] This invention relates to a quantum computing technology, and more particularly to a numerical simulation of quantum gate operations suitable for superconducting quantum computers and a method for optimizing quantum gate control parameters. Background Technology

[0002] Quantum computing is a novel computational model based on the fundamental principles of quantum mechanics. Unlike traditional computing theories, its basic unit is the qubit (qubit). It utilizes quantum effects such as superposition, interference, and quantum entanglement for information processing, which can significantly improve computational efficiency. The inherent parallelism of quantum computing allows it to potentially outperform classical computers in many computational problems, such as cryptography, artificial intelligence, chemistry and pharmaceuticals, quantum finance, and aerospace. Since the concept of quantum computing was proposed, researchers have been dedicated to building general-purpose quantum computers capable of solving practical problems and offering significant speedups compared to classical computers. Currently, the mainstream technological approaches include superconducting quantum computing, optical quantum computing, ion trap quantum computing, neutral atom quantum computing, topological quantum computing, semiconductor quantum computing, diamond nitrogen-vacancy center quantum computing, and nuclear magnetic resonance quantum computing. Each approach has its own advantages and disadvantages, and currently, no single approach fully meets the requirements for practical application and is approaching technological maturity. Key performance indicators for quantum computers include the number of qubits, qubit decoherence time, and quantum gate fidelity. For superconducting quantum computing, mainstream quantum computing teams have successfully built quantum computers with a scale of 100 qubits. Regarding decoherence time, the current mainstream technology is around 100 microseconds. In terms of gate fidelity, the most advanced quantum computing systems currently achieve single-qubit gate fidelity of over 99.9% and two-qubit gate fidelity of over 99%. Despite significant progress in key technical indicators of quantum computing, it is still insufficient for large-scale universal quantum computing. Regarding gate fidelity, for large-scale universal quantum computing, the gate error needs to be below the fault-tolerance threshold, conservatively estimated at 0.01%. Currently, the main limiting factor for running quantum algorithms is the relatively unreliable two-qubit gate. Therefore, improving the two-qubit gate fidelity is an urgent priority for realizing large-scale universal quantum computing.

[0003] Current superconducting quantum computing systems achieve fidelity of approximately 99.9% for single-qubit gates and approximately 99% for two-qubit gates, which is insufficient to meet the requirements for reliably running practical quantum algorithms. To ensure the reliability of the final results, in addition to improving the fidelity of isolated quantum gates, it is also necessary to effectively suppress crosstalk between simultaneously executed quantum gates. Summary of the Invention

[0004] To address the issue that the gate fidelity of current superconducting quantum computing systems cannot meet the requirements for reliable operation of practical quantum algorithms, a numerical computation-based method for quantum gate simulation and control parameter optimization is proposed. This method starts with the model Hamiltonian describing a multi-qubit system and the Hamiltonian of the interaction between the qubit and the control system. Through numerical computation, the detailed process of quantum gate operation can be simulated. Simultaneously, by optimizing the control parameters, potential errors during quantum gate operation can be reduced, thereby improving the fidelity of quantum gate operation and providing theoretical guidance for achieving high-fidelity quantum gate operation.

[0005] The technical solution of this invention is as follows:

[0006] A numerical computation-based method for quantum gate simulation and control parameter optimization is proposed, comprising a model Hamiltonian matrix representation module, a system time evolution and fidelity calculation module, and a control parameter optimization module. The model Hamiltonian matrix representation module calculates the matrix representation of the model Hamiltonian based on the specific problem. This module can receive a series of parameters and then provide the matrix representation of the model Hamiltonian under the corresponding parameters. The system time evolution and fidelity calculation module uses the Hamiltonian matrix generated by the model Hamiltonian matrix representation module to discretize and solve the Schrödinger equation, providing the corresponding time evolution matrix, and uses the obtained time evolution matrix to calculate the gate operation fidelity. The control parameter optimization module calls the model Hamiltonian matrix representation module and the system time evolution and fidelity calculation module, employing local or global optimization algorithms to optimize the control parameters and quantum gate operation time, providing the optimal control parameters and gate operation time. The optimization steps are as follows:

[0007] Single qubit gate:

[0008] This method describes the Hamiltonian H, which describes a single qubit and the interaction between the qubit and the control system. RWA Starting from (t), firstly, the Hamiltonian matrix representation module of the model is used to represent H RWA (t) is represented in matrix form, and then given an initial set of δ(t), Ω x (t) and Ω y (t) parameters, using the system's time evolution and fidelity calculation module to calculate the evolution matrix U. ctrl Door fidelity F g Based on this, the error rate function E is defined. g =1-F g Then, the optimal control parameters δ(t) and Ω are found using local or global optimization algorithms. x (t) and Ω y (t), thus providing a high-fidelity gate implementation method; at the same time, it can also compare the fidelity of single quantum gate operation under different gate operation times and find the optimal gate operation time;

[0009] Two-qubit gate:

[0010] Starting from the Hamiltonian H(t) that describes the interaction between two qubits and between qubits and the control system, first, the model Hamiltonian matrix representation module is used to represent H(t) in matrix form. Then, the functional relationship of ω c (t) varying with time and related parameters are selected, and a set of initial parameters are given. The time evolution and fidelity calculation module of the system is used to calculate the evolution matrix U actual and the gate fidelity F g ; On this basis, the error rate function E g =1 - F g is defined. Then, the local optimization algorithm or the global optimization algorithm is used to find the optimal control parameters and the corresponding Z-rotation angles φ′1, φ′2, φ1, φ2, so as to give a high-fidelity gate implementation scheme; at the same time, the two-qubit gate operation fidelity under different gate operation times can also be compared to find the optimal gate operation time.

[0011] Furthermore, the specific optimization steps for a single-qubit gate are as follows:

[0012] Consider an oscillator with a certain anharmonicity. Assume that the oscillator has a total of m energy levels, which are sequentially recorded as: |0>, |1>, |2>, …, |m - 2>, |m - 1> states from low to high energy. The lowest two energy levels respectively form the |0> state and the |1> state of the qubit; is the energy difference between the |1> state and the |0> state, is the reduced Planck constant, ω is the qubit frequency, and the energy difference between the |j> state and the |0> state<​​​​​​​​​​​​​​​​​​​​​​​​​​​ε is the transition strength between the |j-1> state and the |j> state; ε(t) is the amplitude of the driving microwave, which is usually taken as follows:

[0018] ε(t)=Ω x (t)cos(ω d t+φ0)+Ω y (t)sin(ω d t+φ0)

[0019] Where Ω x (t) and Ω y (t) is the amplitude of the driving microwave, ω b φ0 is the frequency that drives the microwave, and φ0 is the initial phase of the driving microwave.

[0020] In the rotating coordinate system, the Hamiltonian H of the system R (t) is:

[0021]

[0022] in It is a virtual unit, t is a time index, and it is a rotation operator. It is the Hermitian conjugate of R(t), H s It is the Hamiltonian in the laboratory coordinate system defined above: H s =H lf +H ct (t); After applying the rotating wave approximation RWA, the system Hamiltonian is:

[0023]

[0024] in j and k are energy level indices; as can be seen from the above equation, in the rotating coordinate system, a single-qubit gate has three independent control parameters: δ(t) = ω - ω d ,Ω x (t) and Ω y (t);

[0025] To implement arbitrary single-qubit gate operations within the subspace composed of the |0> and |1> states, it is necessary to optimize the parameters δ(t) and Ω. x (t) and Ω y (t), so that the time evolution matrix U ideal It has the following form:

[0026]

[0027] Among them, operators Represents time-integrated integral, It is a 2x2 unitary matrix, 0 (2,m-2)It is a 2*(m-2) dimensional all-zero matrix, 0 (m-2,2) It is a (m-2)*2 dimensional matrix of all zeros. It is a unitary matrix of (m-2)*(m-2) dimensions; in order to calculate the timing integral, the entire gate operation time t is used. g Divide the material into N equal parts, with each part having a time interval of Δt = t. g / N; Assuming that within the time interval Δt, the parameters δ(t), Ω x (t) and Ω y (t) remains unchanged, i.e., the Hamiltonian H RWA If (t) remains constant, then the time evolution matrix U in the nth time interval... n for:

[0028]

[0029] The complete evolution matrix U during the gate operation time ctrl for:

[0030] U ctrl =U N-1 U N-2 …U1U0

[0031] Door fidelity F g Defined as:

[0032]

[0033] in Hermitian conjugates are the matrix representations of the single quantum gate operations to be implemented.

[0034] Furthermore, the specific optimization steps for the two-qubit gate are as follows:

[0035] For a two-qubit gate implemented with the aid of a coupler, the system Hamiltonian H can be written in the following form:

[0036]

[0037] Where i is the qubit index. and a j These are the creation and annihilation operators, respectively. ω1 and ω2 are the bit frequencies of the fixed-frequency qubits Q1 and Q2, respectively. c ω is the bit frequency of coupler C. c The values ​​α1, α2, and α can be adjusted by changing the applied magnetic flux. c These are the anharmonicity of qubits Q1 and Q2 and coupler C, respectively, and g 1c and g 2c It is the coupling strength between qubits Q1 and Q2 and coupler C, g 12It is the direct coupling strength between qubits Q1 and Q2; in order to achieve gate operations, ω1, ω2, α1, α2, and α... c With parameters unchanged, adjust the bit frequency ω of coupler C. c , so that ω c Satisfying the given time-dependent functional relationship ω c If (t), then the system Hamiltonian H will also change with time, that is, H becomes the time-dependent Hamiltonian H(t); the system's time evolution operator U evolution It can be written in the following form:

[0038]

[0039] Where t gate It is the operation time of two quantum gates;

[0040] The above evolution operator U evolution Projecting the computational basis vectors |000>, |001>, |100>, and |101> into the subspace spanned by these basis vectors yields the corresponding gate operator U. impelmented Matrix representation:

[0041] U impelmented = <n1n c n2|U evolution |n′1n′ c n′2>

[0042] Where |n′1n′ c n′2> and |n1n c n2> takes one of the calculation basis vectors |000>, |001>, |100>, and |101> respectively;

[0043] In order to perform the gate operation, in addition to performing the time evolution described above, an auxiliary single-qubit Z-rotation gate operation U is also required. pre and U post :

[0044]

[0045] Where φ1, φ2, φ′1, and φ′2 are rotation angles, which are parameters to be optimized; and It is a Pauli-z matrix, and I1 and I2 are identity matrices;

[0046] Performing auxiliary single-qubit Z-rotation gate operation U pre and U post Subsequently, the quantum gate operation U was implemented. actual for:

[0047] U actual =U post ×Uimpelmented ×U pre

[0048] Door fidelity is defined as:

[0049]

[0050] Among them U target The desired gate operation is d, where d is U. target The dimension of the matrix; by optimizing parameters φ′1, φ′2, φ1, φ2, and ω. c The parameters included in (t) maximize the fidelity of the two-qubit gate.

[0051] Furthermore, the specific descriptions of the model Hamiltonian matrix representation module, the system time evolution and fidelity calculation module, and the control parameter optimization module are as follows:

[0052] The Model Hamiltonian Matrix Representation module is used to transform the model Hamiltonian describing the multi-qubit system and the Hamiltonian of the interaction between the qubit and the control system into matrix form. Specifically, by selecting a set of basis vectors in the Hilbert space, and then calculating the matrix representation of the generating operator and the annihilation operator under this set of basis vectors, the model Hamiltonian can be transformed into matrix form, which is used to prepare for subsequent simulation of quantum gate operations and optimization of control parameters.

[0053] The system's time evolution and fidelity calculation module is used to simulate the evolution of the quantum system's state over time under the driving force of the model Hamiltonian. It can also evaluate the difference between the final state and the target state after the evolution. Specifically, the system's time evolution requires solving the time-dependent Schrödinger equation. This method divides the entire evolution process into a series of time segments and uses a discretization method to numerically solve the time-dependent Schrödinger equation, demonstrating the intermediate states of the system's evolution over time. For single-qubit and two-qubit gate operations, quantum gate fidelity calculation formulas are defined to quantitatively evaluate the similarity between the final and target states. This prepares the groundwork for subsequent optimization of quantum gate operation control parameters and improvement of quantum gate fidelity.

[0054] The control parameter optimization module is used to find the optimal control parameters and operation time of the quantum gate operation, so that the quantum gate operation has the highest theoretical fidelity. Specifically, given the control parameters, operation time, and other necessary model parameters, the model Hamiltonian matrix representation module is called to convert the model Hamiltonian into matrix form. Then, the system's time evolution and fidelity calculation module is called to calculate the gate operation fidelity under the given parameters. Based on the calculation, the control parameters and operation time are updated according to specific rules, and the above steps are repeated until the convergence condition is met, thus obtaining the optimal control waveform and operation time.

[0055] The beneficial effects of this invention are as follows:

[0056] This invention applies to the field of superconducting quantum computing, providing a numerical computation-based method for quantum gate simulation and control parameter optimization. It is applicable to pulse-level simulation of common single- and double-qubit gate operations, and can optimize quantum gate operation control parameters, providing optimal control waveforms and quantum gate operation times, thus offering theoretical guidance for achieving high-fidelity quantum gate operations. Specifically, this scheme is divided into a model Hamiltonian matrix representation module, a system time evolution and fidelity calculation module, and a control parameter optimization module. The model Hamiltonian matrix representation module calculates the matrix representation of the Hamiltonian; the system time evolution and fidelity calculation module calculates the evolution of the system state over time and the corresponding gate operation fidelity; and the control parameter optimization module finds the optimal quantum gate operation control parameters and quantum gate operation time, thereby achieving the highest theoretical fidelity for quantum gate operations. Attached Figure Description

[0057] Figure 1 This is a block diagram of the module structure used in the quantum gate simulation and control parameter optimization method of the present invention. Detailed Implementation

[0058] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0059] This invention is applied to the field of superconducting quantum computing, providing a method for quantum gate simulation and control parameter optimization based on numerical calculation. It is applicable to pulse-level simulation of common single and double qubit gate operation control, and can optimize the quantum gate operation control parameters, providing the optimal control waveform and quantum gate operation time, thus providing theoretical guidance for realizing high-fidelity quantum gate operation.

[0060] The quantum gate pulse-level simulation and control parameter optimization method applied to superconducting quantum computers is specifically divided into a model Hamiltonian matrix representation module, a system time evolution and fidelity calculation module, and a control parameter optimization module.

[0061] The Model Hamiltonian Matrix Representation module is used to transform the model Hamiltonians describing multi-qubit systems and the interaction Hamiltonians between qubits and the control system (typically including coefficients, production operators, annihilation operators, and their products) into matrix form. Specifically, by selecting a set of basis vectors in a Hilbert space and then calculating the matrix representations of the production and annihilation operators under this set of basis vectors, the model Hamiltonians can be transformed into matrix form, preparing for subsequent simulation of quantum gate operations and optimization of control parameters.

[0062] The system's time evolution and fidelity calculation module simulates the evolution of a quantum system's state over time under the influence of the model Hamiltonian. It also assesses the difference between the final and target states after the evolution. Specifically, the system's time evolution requires solving the time-dependent Schrödinger equation. This method divides the entire evolution process into a series of time segments and uses a discretization method to numerically solve the time-dependent Schrödinger equation, demonstrating the intermediate states of the system's evolution over time. For single-qubit and two-qubit gate operations, quantum gate fidelity calculation formulas are defined to quantitatively evaluate the similarity between the final and target states. This prepares the groundwork for subsequent optimization of quantum gate operation control parameters and improvement of quantum gate fidelity.

[0063] The control parameter optimization module is used to find the optimal control parameters and operation time for quantum gate operations, thereby achieving the highest theoretical fidelity. Specifically, given the control parameters, operation time, and other necessary model parameters, the model Hamiltonian matrix representation module is called to convert the model Hamiltonian into matrix form. Then, the system's time evolution and fidelity calculation module is called to calculate the gate operation fidelity under the given parameters. Based on the calculation, the control parameters and operation time are updated according to specific rules (see detailed implementation method), and the above steps are repeated until the convergence condition is met, thus obtaining the optimal control waveform and operation time.

[0064] Consider an oscillator with a certain degree of anharmonicity. Suppose that the oscillator has a total of m energy levels, which are denoted as the states |0>,|1>,|2>,…,|m-2>,|m-1> in order of energy from low to high. The two lowest energy levels constitute the |0> state and the |1> state of the qubit, respectively. It is the energy difference between the |1> state and the |0> state. (where ω is the reduced Planck constant and ω is the bit frequency), and the energy difference between the |j> state and the |0> state. Δ j This refers to the anharmonicity of the oscillator, as commonly understood. Taking the energy of the |0> state as a reference (i.e., e0 = 0), the Hamiltonian H of this oscillator... lf for:

[0065]

[0066] Where j is the energy level index, Π j =|j><| is the projection operator projected onto the state |j>.

[0067] For a single-qubit gate, the coupling Hamiltonian H between the oscillator and the control microwave is... ct (t) is:

[0068]

[0069] in It is the transition operator between the |j-1> state and the |j> state, while λ j It represents the transition strength between the |j-1> state and the |j> state. ε(t) is the amplitude of the driving microwave, typically taken as follows:

[0070] ε(t)=Ω x (t)cos(ω d t+φ0)+Ω y (t)sin(ω d t+φ0)

[0071] Where Ω x (t) and Ω y (t) is the amplitude of the driving microwave, ω d φ0 is the frequency driving the microwave, and φ0 is the initial phase of the driving microwave.

[0072] In the rotating coordinate system, the Hamiltonian H of the system R (t) is:

[0073]

[0074] in It is a virtual unit, t is a time index, and it is a rotation operator. It is the Hermitian conjugate of R(t), H S It is the Hamiltonian in the laboratory coordinate system defined above: H S =H lf +H ct (t). After applying the rotating-wave approximation (RWA), the Hamiltonian of the system is:

[0075]

[0076] in j and k are energy level indices. As can be seen from the above equation, in a rotating coordinate system, a single-qubit gate has three independent control parameters: δ(t) = ω - ω d ,Ω x (t) and Ω y (t).

[0077] To implement arbitrary single-qubit gate operations within the subspace composed of the |0> and |1> states, it is necessary to optimize the parameters δ(t) and Ω. x (t) and Ω y (t), so that the time evolution matrix U ideal It has the following form:

[0078]

[0079] Among them, operators Represents time-integrated integral, It is a 2x2 unitary matrix, 0 (2,m-2) It is a 2*(m-2) dimensional all-zero matrix, 0 (m-2,2) It is a (m-2)*2 dimensional matrix of all zeros. It is a unitary matrix of (m-2)*(m-2) dimensions. To calculate the timing integral, the entire gate operation time t is... g Divide the material into N equal parts, with each part having a time interval of Δt = t. g / N. Assume that within the time interval Δt, the parameters δ(t), Ω x (t) and Ω y (t) remains unchanged, i.e., the Hamiltonian H RWA If (t) remains constant, then the time evolution matrix U in the nth time interval... n for:

[0080]

[0081] The complete evolution matrix U during the gate operation time ctrl for:

[0082] U ctrl =U N-1 U N-2 …U1U0

[0083] Door fidelity F g Defined as:

[0084]

[0085] in Hermitian conjugates are the matrix representations of the single quantum gate operations to be implemented.

[0086] Based on the above description, this method describes the Hamiltonian H, which describes a single qubit and the interaction between the qubit and the control system. RWA Starting from (t), firstly, the Hamiltonian matrix representation module of the model is used to represent H RWA (t) is represented in matrix form, and then given an initial set of δ(t), Ω x (t) and Ω y (t) parameters, using the system's time evolution and fidelity calculation module to calculate the evolution matrix U. ctrl Door fidelity F g Based on this, the error rate function E is defined. g =1-F gThen, local optimization algorithms such as Nelder-Mead and BFGS, or global optimization algorithms such as bassinhopping and differential-evolution, are used to find the optimal control parameters δ(t) and Ω. x (t) and Ω y (t) etc., thus providing a high-fidelity gate implementation method. It can also compare the fidelity of single-quantum gate operations under different gate operation times to find the optimal gate operation time.

[0087] Two-qubit gate:

[0088] For a two-qubit gate implemented with the aid of a coupler, the system Hamiltonian t can be written in the following form:

[0089]

[0090] Where i is the qubit index. and a i These are the creation and annihilation operators, respectively. ω1 and ω2 are the bit frequencies of the fixed-frequency qubits Q1 and Q2, respectively. c ω is the bit frequency of coupler C. c It can be adjusted by changing the applied magnetic flux. α1, α2, and α c These are the anharmonicity of qubits Q1 and Q2 and coupler C, respectively, and g 1c and g 2c It is the coupling strength between qubits Q1 and Q2 and coupler C, g 12 This represents the direct coupling strength between qubits Q1 and Q2. To implement gate operations (such as CZ gates), ω1, ω2, α1, α2, and α... c With parameters remaining constant, adjust the bit frequency ω of coupler C. c , so that ω c Satisfying the given time-dependent functional relationship ω c If (t), then the system's Hamiltonian H will also change with time, that is, H becomes a time-dependent Hamiltonian H(t). The system's time evolution operator U evolution It can be written in the following form:

[0091]

[0092] Where t gate It is the operation time of a two-quantum gate.

[0093] The above evolution operator U evolution Projecting the computational basis vectors |000>, |001>, |100>, and |101> into the subspace spanned by these basis vectors yields the corresponding gate operator U. impelmented Matrix representation:

[0094] U impelmented = <n1n c n2|U evolution |n′1n′ c n′2>

[0095] Where |n′1n′ c n′2> and |n1n c n2< takes one of the calculation basis vectors |000<, |001<, |100< and |101< respectively.

[0096] In order to perform the gate operation, in addition to performing the time evolution described above, an auxiliary single-qubit Z-rotation gate operation U is also required. pre and U post :

[0097]

[0098] Where φ1, φ2, φ′1, and φ′2 are rotation angles, which are parameters to be optimized; and It is a Pauli-z matrix, and I1 and I2 are identity matrices.

[0099] Performing auxiliary single-qubit Z-rotation gate operation U pre and U post Subsequently, the quantum gate operation U was implemented. actual for:

[0100] U actual =U post ×U impelmented ×U pre

[0101] Door fidelity is defined as:

[0102]

[0103] Among them U target The desired gate operation is d, where d is U. target The dimension of the matrix. This is achieved by optimizing the parameters φ′1, φ′2, φ1, φ2, and ω. c The parameters included in (t) maximize the fidelity of the two-qubit gate.

[0104] Based on the above description, this method starts with the Hamiltonian H(t) describing the interaction between two qubits and the control system. First, it uses the model Hamiltonian matrix representation module to represent t(t) in matrix form, and then selects ω. c (t) The functional relationship and related parameters of the system over time. Given a set of initial parameters, the evolution matrix U is calculated using the system's time evolution and fidelity calculation module. actualDoor fidelity F g Based on this, the error rate function E is defined. g =1-F g Then, local optimization algorithms such as Nelder-Mead and BFGS, or global optimization algorithms such as bassing and differential-evolution, are used to find the optimal control parameters and the corresponding Z rotation angles φ′1, φ′2, φ1, and φ2, thereby providing a high-fidelity gate implementation scheme. Simultaneously, the fidelity of dual-quantum gate operations under different gate operation times can be compared to find the optimal gate operation time.

[0105] The above-described embodiments are merely one implementation of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention should be determined by the appended claims.

Claims

1. A method for quantum gate simulation and control parameter optimization based on numerical computation, characterized in that, The system is divided into three modules: a model Hamiltonian matrix representation module, a system time evolution and fidelity calculation module, and a control parameter optimization module. The model Hamiltonian matrix representation module calculates the matrix representation of the model Hamiltonian based on the specific problem. This module can receive a series of parameters and then provide the matrix representation of the model Hamiltonian under the corresponding parameters. The system time evolution and fidelity calculation module uses the Hamiltonian matrix generated by the model Hamiltonian matrix representation module to discretize and solve the Schrödinger equation, providing the corresponding time evolution matrix, and uses the obtained time evolution matrix to calculate the gate operation fidelity. The control parameter optimization module calls the model Hamiltonian matrix representation module and the system time evolution and fidelity calculation module, using local or global optimization algorithms to optimize the control parameters and quantum gate operation time, providing the optimal control parameters and gate operation time. The optimization steps are as follows: Single-qubit gate: This method uses the Hamiltonian H, which describes the interaction between a single qubit and the control system, to... RWA Starting from (t), firstly, the Hamiltonian matrix representation module of the model is used to represent H RWA (t) is represented in matrix form, and then given an initial set of δ(t), Ω x (t) and Ω y (t) parameters, using the system's time evolution and fidelity calculation module to calculate the evolution matrix U. ctrl Door fidelity F g Based on this, the error rate function E is defined. g =1-F g Then, the optimal control parameters δ(t) and Ω are found using local or global optimization algorithms. x (t) and Ω y (t), thus providing a high-fidelity gate implementation method; at the same time, it can also compare the fidelity of single quantum gate operation under different gate operation times and find the optimal gate operation time; Two-qubit gate: This method starts with the Hamiltonian H(t) describing two qubits and the interaction between qubits and the control system. First, it uses the model Hamiltonian matrix representation module to represent H(t) in matrix form, and then selects ω. c (t) The functional relationship and related parameters of the system over time. Given a set of initial parameters, the evolution matrix U is calculated using the system's time evolution and fidelity calculation module. actual Door fidelity F g Based on this, the error rate function E is defined. g =1-F g Then, by using local or global optimization algorithms, the optimal control parameters and the corresponding Z rotation angles φ′1, φ′2, φ1, and φ2 are found, thus providing a high-fidelity gate implementation scheme. At the same time, the fidelity of the dual quantum gate operation under different gate operation times can be compared to find the optimal gate operation time.

2. The method for quantum gate simulation and control parameter optimization based on numerical computation according to claim 1, characterized in that, The specific optimization steps for a single qubit gate are as follows: Consider an oscillator with a certain degree of anharmonicity. Suppose that the oscillator has a total of m energy levels, which are denoted as the states |0>,|1>,|2>,…,|m-2>,|m-1> in order of energy from low to high. The two lowest energy levels constitute the |0> state and the |1> state of the qubit, respectively. It is the energy difference between the |1> state and the |0> state. It is the reduced Planck constant, ω is the bit frequency, and the energy difference between the |j> state and the |0> state. Δ j This relates to the anharmonicity of the oscillator; taking the energy of the |0> state as a reference, i.e., E0 = 0, the Hamiltonian H of the oscillator is... lf for: where j is the energy level index, and Π j = |j><j| is the projection operator projected onto the |j> state; For a single-qubit gate, the coupling Hamiltonian H between the oscillator and the control microwave is... ct (t) is: in It is the transition operator between the |j-1> state and the |j> state, while λ j ε is the transition strength between the |j-1> state and the |j> state; ε(t) is the amplitude of the driving microwave, taking the following form: ε(t)=Ω x (t)cos(ω d t+φ0)+Ω y (t)sin(ω d t+φ0) Where Ω x (t) and Ω y (t) is the amplitude of the driving microwave, ω d φ0 is the frequency that drives the microwave, and φ0 is the initial phase of the driving microwave. In the rotating coordinate system, the Hamiltonian H of the system R (t) is: in It is a virtual unit, t is a time index, and it is a rotation operator. It is the Hermitian conjugate of R(t), H S It is the Hamiltonian in the laboratory coordinate system defined above: H S =H lf +H ct (t); After applying the rotating wave approximation RWA, the system Hamiltonian is: in j and k are energy level indices; as can be seen from the above equation, in the rotating coordinate system, a single-qubit gate has three independent control parameters: δ(t) = ω - ω d ,Ω x (t) and Ω y (t); To implement arbitrary single-qubit gate operations within the subspace composed of the |0> and |1> states, it is necessary to optimize the parameters δ(t) and Ω. x (t) and Ω y (t), so that the time evolution matrix U ideal It has the following form: Among them, operators Represents time-integrated integral, It is a 2x2 unitary matrix, 0 (2,m-2) It is a 2*(m-2) dimensional all-zero matrix, 0 (m-2,2) It is a (m-2)*2 dimensional matrix of all zeros. It is a unitary matrix of (m-2)*(m-2) dimensions; in order to calculate the timing integral, the entire gate operation time t is used. g Divide the material into N equal parts, with each part having a time interval of Δt = t. g / N; Assuming that within the time interval Δt, the parameters δ(t), Ω x (t) and Ω y (t) remains unchanged, i.e., the Hamiltonian H RWA If (t) remains constant, then the time evolution matrix U in the nth time interval... n for: The complete evolution matrix U during the gate operation time ctrl for: IN ctrl =U N-1 IN N-2 …U1U0 Door fidelity F g Defined as: in Hermitian conjugates are the matrix representations of the single quantum gate operations to be implemented.

3. The method for quantum gate simulation and control parameter optimization based on numerical computation according to claim 1, characterized in that, The specific optimization steps for the two-qubit gate are as follows: For a two-qubit gate implemented with the aid of a coupler, the system Hamiltonian H can be written in the following form: Where i is the qubit index. and a i These are the creation and annihilation operators, respectively. ω1 and ω2 are the bit frequencies of the fixed-frequency qubits Q1 and Q2, respectively. c ω is the bit frequency of coupler C. c The values ​​α1, α2, and α can be adjusted by changing the applied magnetic flux. c These are the anharmonicity of qubits Q1 and Q2 and coupler C, respectively, and g 1c and g 2c It is the coupling strength between qubits Q1 and Q2 and coupler C, g 12 It is the direct coupling strength between qubits Q1 and Q2; in order to achieve gate operations, ω1, ω2, α1, α2, and α... c With parameters unchanged, adjust the bit frequency ω of coupler C. c , so that ω c Satisfying the given time-dependent functional relationship ω c If (t), then the system Hamiltonian H will also change with time, that is, H becomes the time-dependent Hamiltonian H(t); the system's time evolution operator U evolution It can be written in the following form: Where t gate It is the operation time of two quantum gates; The above evolution operator U evolution Projecting the computational basis vectors |000>, |001>, |100>, and |101> into the subspace spanned by these basis vectors yields the corresponding gate operator U. impelmented Matrix representation: U impelmented = <n1n c n2|U evolution |n′1n′ c n′2> Where |n′1n′ c m′2> and |n1n c n2> takes one of the calculation basis vectors |000>, |001>, |100>, and |101> respectively; In order to perform the gate operation, in addition to performing the time evolution described above, an auxiliary single-qubit Z-rotation gate operation U is also required. pre and U post : Where φ1, φ2, φ′1, and φ′2 are rotation angles, which are parameters to be optimized; and It is a Pauli-z matrix, and I1 and I2 are identity matrices; Performing auxiliary single-qubit Z-rotation gate operation U pre and U post Subsequently, the quantum gate operation U was implemented. actual for: IN actual =U post ×U impelmented ×U pre Door fidelity is defined as: Among them U target The desired gate operation is d, where d is U. target The dimension of the matrix; by optimizing parameters φ′1, φ′2, φ1, φ2, and ω. c The parameters included in (t) maximize the fidelity of the two-qubit gate.

4. The method for quantum gate simulation and control parameter optimization based on numerical computation according to claim 1, characterized in that, The specific descriptions of the model Hamiltonian matrix representation module, the system time evolution and fidelity calculation module, and the control parameter optimization module are as follows: The Model Hamiltonian Matrix Representation module is used to transform the model Hamiltonian describing the multi-qubit system and the Hamiltonian of the interaction between the qubit and the control system into matrix form. Specifically, by selecting a set of basis vectors in the Hilbert space, and then calculating the matrix representation of the generating operator and the annihilation operator under this set of basis vectors, the model Hamiltonian can be transformed into matrix form, which is used to prepare for subsequent simulation of quantum gate operations and optimization of control parameters. The system's time evolution and fidelity calculation module is used to simulate the evolution of the quantum system's state over time under the driving force of the model Hamiltonian. It can also evaluate the difference between the final state and the target state after the evolution. Specifically, the system's time evolution requires solving the time-dependent Schrödinger equation. This method divides the entire evolution process into a series of time segments and uses a discretization method to numerically solve the time-dependent Schrödinger equation, demonstrating the intermediate states of the system's evolution over time. For single-qubit and two-qubit gate operations, quantum gate fidelity calculation formulas are defined to quantitatively evaluate the similarity between the final and target states. This prepares the groundwork for subsequent optimization of quantum gate operation control parameters and improvement of quantum gate fidelity. The control parameter optimization module is used to find the optimal control parameters and operation time of the quantum gate operation, so that the quantum gate operation has the highest theoretical fidelity. Specifically, given the control parameters, operation time, and other necessary model parameters, the model Hamiltonian matrix representation module is called to convert the model Hamiltonian into matrix form. Then, the system's time evolution and fidelity calculation module is called to calculate the gate operation fidelity under the given parameters. Based on the calculation, the control parameters and operation time are updated according to specific rules, and the above steps are repeated until the convergence condition is met, thus obtaining the optimal control waveform and operation time.

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