Quantum gate simulation and control parameter optimization method based on numerical calculation

Abstract

The invention relates to a quantum gate simulation and control parameter optimization method based on numerical calculation, and the method sequentially comprises the following three modules: a model Hamiltonian matrix representation module can calculate the matrix representation of a model Hamiltonian according to a specific problem; a time evolution and fidelity calculation module of the system discretely solves a Schrodinger equation by using a Hamiltonian matrix, gives a corresponding time evolution matrix, and calculates gate operation fidelity by using the obtained time evolution matrix; and the control parameter optimization module calls the first two modules, optimizes control parameters and quantum gate operation time by adopting a local optimization algorithm or a global optimization algorithm, and gives optimal control parameters and gate operation time. The problem that the gate fidelity of a current superconducting quantum computing system cannot meet the requirement for reliable operation of a practical quantum algorithm is solved, the detailed process of quantum gate operation can be simulated through a numerical calculation method, and the quantum gate operation fidelity is improved by optimizing control parameters.

Description

Technical Field

[0001] The present invention relates to a quantum computing technology, and in particular to a method for numerical simulation of quantum gate operations and optimization of quantum gate control parameters applicable to superconducting quantum computers. Background Art

[0002] Quantum computing is a new computing model based on the basic principles of quantum mechanics. Different from traditional computing theory, its basic unit is the quantum bit. It uses quantum effects such as superposition, interference and quantum entanglement to process information, which can greatly improve computing efficiency. The inherent parallelism of quantum computing makes it possible to outperform classical computers in many computing problems, such as code breaking, artificial intelligence, chemistry and pharmaceuticals, quantum finance, aerospace, etc. Since the concept of quantum computing was proposed, people have been committed to building a general-purpose quantum computer that can solve practical problems and has a significant acceleration effect relative to classical computers. The current mainstream technical routes include superconducting quantum computing, optical quantum computing, ion trap quantum computing, neutral atom quantum computing, topological quantum computing, semiconductor quantum computing, diamond nitrogen vacancy color center quantum computing, nuclear magnetic resonance quantum computing, etc. Each technical route has its own advantages and disadvantages. At present, no technical route can fully meet the requirements of practical application and tend to be technically mature. The key indicators for measuring the performance of quantum computers include the number of quantum bits, the decoherence time of quantum bits, and the fidelity of quantum gates. For superconducting quantum computing, the current mainstream quantum computing team has successfully built a quantum computer with a scale of 100 qubits; in terms of decoherence time, the current mainstream technology level is about one hundred microseconds; in terms of gate fidelity, the single-qubit gate fidelity of the most advanced quantum computing system can reach more than 99.9%, and the double-qubit gate fidelity can reach more than 99%. Although people have made great progress in various key technical indicators of quantum computing, it is still not enough for quantum computing. In terms of quantum gate fidelity, for large-scale general quantum computing, the quantum gate error needs to be lower than the fault tolerance threshold, which is conservatively estimated to be 0.01%. At present, the main limiting factor for running quantum algorithms is the relatively unreliable double-qubit gate. Therefore, improving the double-qubit gate fidelity is a top priority for realizing large-scale general quantum computing.

[0003] The fidelity of single-qubit gates in current superconducting quantum computing systems is about 99.9%, and the fidelity of dual-qubit gates is about 99%, which cannot meet the requirements for reliable operation of practical quantum algorithms. In order to ensure the reliability of the final result, in addition to improving the fidelity of isolated quantum gates, it is also necessary to effectively suppress the crosstalk between simultaneously executed quantum gates. Summary of the invention

[0004] In order to solve the problem that the gate fidelity of current superconducting quantum computing systems cannot meet the requirements for reliable operation of practical quantum algorithms, a quantum gate simulation and control parameter optimization method based on numerical calculation is proposed. Starting from the model Hamiltonian describing the multi-qubit system and the Hamiltonian of the interaction between the qubit and the control system, this method can simulate the detailed process of quantum gate operation through numerical calculation. At the same time, by optimizing the control parameters, it can reduce the errors that may occur during the quantum gate operation and improve the fidelity of quantum gate operation, providing theoretical guidance for the realization of high-fidelity quantum gate operation.

[0005] The technical solution of the present invention is:

[0006] A quantum gate simulation and control parameter optimization method based on numerical calculation 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 can calculate the matrix representation of the model Hamiltonian according to specific problems, and the module can receive a series of parameters, and then give 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 the Schrödinger equation, give the corresponding time evolution matrix, and use 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, and uses a local optimization algorithm or a global optimization algorithm to optimize the control parameters and quantum gate operation time, and gives the optimal control parameters and gate operation time; the optimization steps are as follows:

[0007] Single qubit gate:

[0008] This method starts from describing the Hamiltonian H that describes the interaction between a single qubit and the qubit and the control system. RWA (t), first use the model Hamiltonian matrix representation module to represent H RWA (t) is expressed in matrix form, and then a set of initial δ(t),Ω is given x (t) and Ω y (t) parameter, using the system's time evolution and fidelity calculation module to calculate the evolution matrix U ctrl AND gate fidelity F g ; On this basis, define the error rate function E g =1-F g Then use the local optimization algorithm or the global optimization algorithm to find the optimal control parameters δ(t),Ω x (t) and Ω y (t), thus providing a high-fidelity gate implementation method; at the same time, the fidelity of single quantum gate operations under different gate operation times can be compared to 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 the control system, first use the model Hamiltonian matrix representation module to represent H(t) in matrix form, and then select the functional relationship of ω c (t) varying with time and related parameters. Given a set of initial parameters, use the time evolution and fidelity calculation module of the system to calculate the evolution matrix U actual and the gate fidelity F g ; On this basis, define the error rate function E g = 1 - F g , and then use the local optimization algorithm or the global optimization algorithm 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 of 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 successively denoted 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 Δ j is the so-called anharmonicity of the oscillator; taking the energy of the |0> state as the reference, i.e., E0 = 0, the Hamiltonian H lf of this oscillator is:

[0013]

[0014] where j is the energy level index, and Π j = |j><j| is the projection operator projected onto the |j> state;

[0015] For a single-qubit gate, the coupling Hamiltonian H ct (t) between the oscillator and the control microwave is:

[0016]

[0017] where is the transition operator between the |j - 1> state and the |j> state, and λ jis the transition intensity between the |j-1> state and the |j> state; ε(t) is the amplitude of the driving microwave, which is usually in the following form:

[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 is the frequency of the driving microwave, φ0 is the initial phase of the driving microwave;

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

[0021]

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

[0023]

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

[0025] In order to realize any single-qubit gate operation in the subspace composed of |0> state and |1> state, it is necessary to optimize the parameters δ(t),Ω x (t) and Ω y (t), so that the time evolution matrix U ideal Has the following form:

[0026]

[0027] Among them, the operator represents the time integral, is a 2*2 dimensional unitary matrix, 0 (2,m-2)is a 2*(m-2) dimensional all-zero matrix, 0 (m-2,2) is a (m-2)*2 dimensional all-zero matrix, is a unitary matrix of (m-2)*(m-2) dimensions; in order to calculate the timing integral, the entire gate operation time t g Divide into N equal parts, the time interval between each part is Δt=t g / N; Assume that within the time interval Δt, the parameters δ(t),Ω x (t) and Ω y (t) remains unchanged, that is, the Hamiltonian H RWA (t) remains unchanged, then the time evolution matrix U in the nth time interval is 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] Gate Fidelity F g Defined as:

[0032]

[0033] in is the Hermitian conjugate of the matrix representation of the single quantum gate operation you want to implement.

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

[0035] For a two-qubit gate implemented with the help of a coupler, the system Hamiltonian H can be written as follows:

[0036]

[0037] where i is the qubit index, and a j are the creation and annihilation operators respectively, ω1 and ω2 are the bit frequencies of the fixed-frequency quantum bits Q1 and Q2 respectively, ω c is the bit frequency of coupler C, ω c Can be adjusted by changing the external magnetic flux; α1, α2 and α c are the anharmonicity of the qubits Q1, Q2 and the coupler C, g 1c and g 2c is the coupling strength between qubits Q1 and Q2 and coupler C, g 12is the direct coupling strength between quantum bits Q1 and Q2; to achieve gate operation, ω1, ω2, α1, α2, and α c The parameters remain unchanged, and the bit frequency ω of the coupler C is adjusted c , so that ω c Satisfies the given time-dependent function relation ω c (t), the system Hamiltonian H will also change with time, that is, H becomes the time-dependent Hamiltonian H(t); the time evolution operator U evolution It can be written as follows:

[0038]

[0039] where t gate is the double quantum gate operation time;

[0040] The above evolution operator U evolution Projecting it into the subspace spanned by the computational basis vectors |000>, |001>, |100>, and |101>, we can obtain the corresponding gate operator U impelmented The matrix representation of is:

[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 realize the gate operation, in addition to performing the above time evolution, it is also necessary to perform an auxiliary single-qubit Z rotation gate operation U pre and U post :

[0044]

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

[0046] Execution-assisted single-qubit Z rotation-gate operation U pre and U post After that, the realized quantum gate operation U actual for:

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

[0048] Gate fidelity is defined as:

[0049]

[0050] Among them U target is the gate operation we want to achieve, d is U target The dimensions of the matrix; by optimizing the parameters φ′1, φ′2, φ1, φ2, and ω c (t) contains the parameters that maximize the fidelity of the two-qubit gate.

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

[0052] The model Hamiltonian matrix representation module is used to convert the model Hamiltonian describing the multi-qubit system and the Hamiltonian of the interaction between the qubit and the control system into a matrix form; specifically, by selecting a set of basis vectors of the Hilbert space and then calculating the matrix representation of the generation operator and the annihilation operator under this set of basis vectors, the model Hamiltonian can be converted into a matrix form, in preparation for the 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 system state over time under the drive of the model Hamiltonian. It can also evaluate the gap between the final state of the system 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 the discretization method to numerically solve the time-dependent Schrödinger equation to show the intermediate state of the system's evolution over time. For single- and double-qubit gate operations, the quantum gate fidelity calculation formula is defined respectively to quantitatively evaluate the similarity between the final state of the evolution and the target state. This prepares for the subsequent optimization of quantum gate operation control parameters and the improvement of quantum gate fidelity.

[0054] The control parameter optimization module is used to find the optimal quantum gate operation control parameters and quantum gate operation time, so that the quantum gate operation has the highest theoretical fidelity; specifically, firstly, the quantum gate operation control parameters, gate operation time and other necessary model parameters are given, and the model Hamiltonian matrix representation module is called to convert the model Hamiltonian into a matrix form, and 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 calculated results, the control parameters and gate operation time are updated according to specific rules and the above steps are repeated until the convergence conditions are met, and the optimal control waveform and gate operation time can be obtained.

[0055] The beneficial effects of the present invention are:

[0056] The present invention is applied to the field of superconducting quantum computing, and provides a quantum gate simulation and control parameter optimization method based on numerical calculation, which is suitable for pulse-level simulation of common single- and double-qubit gate operation control. At the same time, the quantum gate operation control parameters can be optimized, and the optimal control waveform and quantum gate operation time can be given, so as to provide theoretical guidance for realizing high-fidelity quantum gate operation. This scheme is specifically 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 is used to calculate the matrix representation of the Hamiltonian, the system time evolution and fidelity calculation module is used to calculate the evolution law of the system state over time and the corresponding gate operation fidelity, and the control parameter optimization module is used to find the optimal quantum gate operation control parameters and quantum gate operation time, so that the quantum gate operation has the highest theoretical fidelity. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0058] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0059] The present invention is applied to the field of superconducting quantum computing and provides a quantum gate simulation and control parameter optimization method based on numerical calculation. It is suitable for pulse-level simulation of common single- and double-qubit gate operation control. At the same time, it can optimize the quantum gate operation control parameters, give the optimal control waveform and quantum gate operation time, and provide 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 convert the model Hamiltonian describing the multi-qubit system and the interaction Hamiltonian between the qubit and the control system (usually including coefficients, generation operators, annihilation operators and their products) into matrix form. Specifically, by selecting a set of basis vectors in the Hilbert space and then calculating the matrix representation of the generation operator and annihilation operator under this set of basis vectors, the model Hamiltonian can be converted into matrix form, preparing for the subsequent simulation of quantum gate operations and optimization of control parameters.

[0062] The system's time evolution and fidelity calculation module is used to simulate the evolution of the system state over time when the quantum system is driven by the model Hamiltonian; at the same time, it can also evaluate the gap between the final state of the system and the target state after the evolution ends. 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 to show the intermediate state of the system's evolution over time. For single- and double-qubit gate operations, the quantum gate fidelity calculation formulas are defined respectively to quantitatively evaluate the similarity between the final state of the evolution and the target state. This prepares for the subsequent optimization of quantum gate operation control parameters and the improvement of quantum gate fidelity.

[0063] The control parameter optimization module is used to find the optimal quantum gate operation control parameters and quantum gate operation time, so that the quantum gate operation has the highest theoretical fidelity. Specifically, firstly, the quantum gate operation control parameters, gate operation time and other necessary model parameters are given, and the model Hamiltonian matrix representation module is called to convert the model Hamiltonian into a matrix form, and then the system's time evolution and fidelity calculation module is called to calculate the gate operation fidelity under the given parameters. According to the calculated results, the control parameters and gate operation time are updated according to specific rules (see the specific implementation method for details) and the above steps are repeated until the convergence conditions are met, and the optimal control waveform and gate operation time can be obtained.

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

[0065]

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

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

[0068]

[0069] in is the transition operator between the |j-1> state and the |j> state, and λ j is the transition intensity between the |j-1> state and the |j> state. ε(t) is the amplitude of the driving microwave, usually in the following form:

[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 is the frequency of the driving microwave, and φ0 is the initial phase of the driving microwave.

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

[0073]

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

[0075]

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

[0077] In order to realize any single-qubit gate operation in the subspace composed of |0> state and |1> state, it is necessary to optimize the parameters δ(t),Ω x (t) and Ω y (t), so that the time evolution matrix U ideal Has the following form:

[0078]

[0079] Among them, the operator represents the time integral, is a 2*2 dimensional unitary matrix, 0 (2,m-2) is a 2*(m-2) dimensional all-zero matrix, 0 (m-2,2) is a (m-2)*2 dimensional all-zero matrix, is a unitary matrix of (m-2)*(m-2) dimensions. In order to calculate the timing integral, the entire gate operation time t g Divide into N equal parts, the time interval between each part is Δt=t g / N. Assume that within the time interval Δt, the parameters δ(t),Ω x (t) and Ω y (t) remains unchanged, that is, the Hamiltonian H RWA (t) remains unchanged, then the time evolution matrix U in the nth time interval is 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] Gate Fidelity F g Defined as:

[0084]

[0085] in is the Hermitian conjugate of the matrix representation of the single quantum gate operation you want to implement.

[0086] According to the above description, this method starts from describing the Hamiltonian H between a single quantum bit and the interaction between the quantum bit and the control system. RWA (t), first use the model Hamiltonian matrix representation module to represent H RWA (t) is expressed in matrix form, and then a set of initial δ(t),Ω is given x (t) and Ω y (t) parameter, using the system's time evolution and fidelity calculation module to calculate the evolution matrix U ctrl AND gate fidelity F g On this basis, the error rate function E is defined g =1-F gThen, we use local optimization algorithms such as Nelder-Mead and BFGS or global optimization algorithms such as basinhopping and differential-evolution to find the optimal control parameters δ(t),Ω x (t) and Ω y (t), etc., thus providing a high-fidelity gate implementation method. At the same time, the fidelity of single quantum gate operations under different gate operation times can be compared to find the optimal gate operation time.

[0087] Two-qubit gate:

[0088] For a two-qubit gate implemented with a coupler, the system Hamiltonian t can be written as follows:

[0089]

[0090] where i is the qubit index, and a i are the creation and annihilation operators respectively, ω1 and ω2 are the bit frequencies of the fixed-frequency quantum bits Q1 and Q2 respectively, ω c is the bit frequency of coupler C, ω c It can be adjusted by changing the external magnetic flux. α1, α2 and α c are the anharmonicity of the qubits Q1, Q2 and the coupler C, g 1c and g 2c is the coupling strength between qubits Q1 and Q2 and coupler C, g 12 is the direct coupling strength between qubits Q1 and Q2. To implement gate operations (such as CZ gates), keep ω1, ω2, α1, α2, and α c The same parameters remain unchanged, adjust the bit frequency ω of coupler C c , so that ω c Satisfies the given time-dependent function relation ω c (t), then the system Hamiltonian H will also change with time, that is, H becomes the time-dependent Hamiltonian H(t). The time evolution operator U of the system evolution It can be written as follows:

[0091]

[0092] where t gate is the double quantum gate operation time.

[0093] The above evolution operator U evolution Projecting it into the subspace spanned by the computational basis vectors |000>, |001>, |100>, and |101>, we can obtain the corresponding gate operator U impelmented The matrix representation of is:

[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 realize the gate operation, in addition to performing the above time evolution, it is also necessary to perform an auxiliary single-qubit Z rotation gate operation U pre and U post :

[0097]

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

[0099] Perform an auxiliary single-qubit Z rotation gate operation U pre and U post After that, the realized quantum gate operation U actual for:

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

[0101] Gate fidelity is defined as:

[0102]

[0103] Among them U target is the gate operation we want to achieve, d is U target The dimensions of the matrix. By optimizing the parameters φ′1, φ′2, φ1, φ2 and ω c (t) contains the parameters that maximize the fidelity of the two-qubit gate.

[0104] According to the above description, this method starts from the Hamiltonian H(t) that describes the interaction between the two quantum bits and the quantum bits and the control system. First, t(t) is expressed in matrix form using the model Hamiltonian matrix representation module, and then ω is selected. c (t) The functional relationship and related parameters that change with time. Given a set of initial parameters, the system's time evolution and fidelity calculation module is used to calculate the evolution matrix U actualAND gate fidelity F g On this basis, the error rate function E is defined g =1-F g Then, we use local optimization algorithms such as Nelder-Mead and BFGS or global optimization algorithms such as basinhopping and differential-evolution to find the optimal control parameters and the corresponding Z rotation angles φ′1, φ′2, φ1, φ2, thus providing a high-fidelity gate implementation solution. At the same time, we can also compare the fidelity of dual quantum gate operations under different gate operation times to find the optimal gate operation time.

[0105] The above-mentioned embodiment only expresses one implementation mode of the present invention, and its description is relatively specific and detailed, but it cannot be understood as limiting the scope of the invention patent. It should be pointed out that for ordinary technicians in this field, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be based on the attached claims.

Claims

1. A quantum gate simulation and control parameter optimization method based on numerical calculation, characterized in that: It 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 can calculate the matrix representation of the model Hamiltonian according to specific problems. The module can receive a series of parameters and then give 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 the Schrödinger equation, give the corresponding time evolution matrix, and use 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, and uses the local optimization algorithm or the global optimization algorithm to optimize the control parameters and quantum gate operation time, and gives the optimal control parameters and gate operation time; the optimization steps are as follows: Single qubit gate: This method starts from describing the Hamiltonian H that describes the interaction between a single qubit and the qubit and the control system. RWA (t), first use the model Hamiltonian matrix representation module to represent H RWA (t) is expressed in matrix form, and then a set of initial δ(t),Ω is given x (t) and Ω y (t) parameter, using the system's time evolution and fidelity calculation module to calculate the evolution matrix U ctrl AND gate fidelity F g ; On this basis, define the error rate function E g =1-F g Then use the local optimization algorithm or the global optimization algorithm to find the optimal control parameters δ(t),Ω x (t) and Ω y (t), thus providing a high-fidelity gate implementation method; at the same time, the fidelity of single quantum gate operations under different gate operation times can be compared to find the optimal gate operation time; Two-qubit gate: This method starts with the Hamiltonian H(t) that describes the two qubits and the interaction between the qubits and the control system. First, H(t) is expressed in matrix form using the model Hamiltonian matrix representation module, and then ω is selected. c (t) The functional relationship and related parameters that change with time. Given a set of initial parameters, the system's time evolution and fidelity calculation module is used to calculate the evolution matrix U actual AND gate fidelity F g ; On this basis, define the error rate function E g =1-F g , and then use the local optimization algorithm or the global optimization algorithm 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 solution; at the same time, the fidelity of the double 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 calculation according to claim 1, characterized in that: The specific optimization steps for a single qubit gate are as follows: Consider an oscillator with certain anharmonicity. Assume that the oscillator has a total of m energy levels, which are recorded from low to high energy as: |0>, |1>, |2>, …, |m-2>, |m-1> states. The two lowest energy levels constitute the |0> state and |1> state of the quantum bit respectively. is the energy difference between the |1> state and the |0> state, 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 is the so-called anharmonicity of the oscillator. Taking the energy of the |0> state as the reference, that is, E0 = 0, the Hamiltonian H of the oscillator lf for: where j is the energy level index, and Π j = |j><j| is the projection operator projecting onto the |j> state; For a single-qubit gate, the coupling Hamiltonian H between the oscillator and the control microwave ct (t) is: in is the transition operator between the |j-1> state and the |j> state, and λ j is the transition intensity between the |j-1> state and the |j> state; ε(t) is the amplitude of the driving microwave, which is usually in 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 is the frequency of the driving microwave, φ0 is the initial phase of the driving microwave; In the rotating coordinate system, the system Hamiltonian H R (t) is: in is an imaginary unit, t is the time index, and the rotation operator is the Hermitian conjugate of R(t), H S is the Hamiltonian in the laboratory coordinate system defined above: H S =H lf +H ct (t); After adopting the rotating wave approximation RWA, the system Hamiltonian is: in j and k are energy level indicators; from the above formula, it can be seen that in the rotating coordinate system, the single-qubit gate has three independent control parameters: δ(t) = ω-ω d ,Ω x (t) and Ω y (t); In order to realize any single-qubit gate operation in the subspace composed of |0> state and |1> state, it is necessary to optimize the parameters δ(t),Ω x (t) and Ω y (t), so that the time evolution matrix U ideal Has the following form: Among them, the operator represents the time integral, is a 2*2 dimensional unitary matrix, 0 (2,m-2) is a 2*(m-2) dimensional all-zero matrix, 0 (m-2,2) is a (m-2)*2 dimensional all-zero matrix, is a unitary matrix of (m-2)*(m-2) dimensions; in order to calculate the timing integral, the entire gate operation time t g Divide into N equal parts, the time interval between each part is Δt=t g / N; Assume that within the time interval Δt, the parameters δ(t),Ω x (t) and Ω y (t) remains unchanged, that is, the Hamiltonian H RWA (t) remains unchanged, then the time evolution matrix U in the nth time interval is n for: The complete evolution matrix U during the gate operation time ctrl for: IN ctrl =U N-1 IN N-2 …U1U0 Gate Fidelity F g Defined as: in is the Hermitian conjugate of the matrix representation of the single quantum gate operation you want to implement.

3. The method for quantum gate simulation and control parameter optimization based on numerical calculation 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 help of a coupler, the system Hamiltonian H can be written as follows: where i is the qubit index, and a i are the creation and annihilation operators respectively, ω1 and ω2 are the bit frequencies of the fixed-frequency quantum bits Q1 and Q2 respectively, ω c is the bit frequency of coupler C, ω c Can be adjusted by changing the external magnetic flux; α1, α2 and α c are the anharmonicity of the qubits Q1, Q2 and the coupler C, g 1c and g 2c is the coupling strength between qubits Q1 and Q2 and coupler C, g 12 is the direct coupling strength between quantum bits Q1 and Q2; to achieve gate operation, ω1, ω2, α1, α2, and α c The parameters remain unchanged, and the bit frequency ω of the coupler C is adjusted c , so that ω c Satisfies the given time-dependent function relation ω c (t), the system Hamiltonian H will also change with time, that is, H becomes the time-dependent Hamiltonian H(t); the time evolution operator U evolution It can be written as follows: where t gate is the double quantum gate operation time; The above evolution operator U evolution Projecting it into the subspace spanned by the computational basis vectors |000>, |001>, |100>, and |101>, we can obtain the corresponding gate operator U impelmented The matrix representation of is: 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 realize the gate operation, in addition to performing the above time evolution, it is also necessary to perform an auxiliary single-qubit Z rotation gate operation U pre and U post : Among them, φ1, φ2, φ′1 and φ′2 are the rotation angles and are the parameters to be optimized; and is the Pauli-z matrix, I1 and I2 are identity matrices; Execution-assisted single-qubit Z rotation-gate operation U pre and U post After that, the realized quantum gate operation U actual for: IN actual =U post ×U impelmented ×U pre Gate fidelity is defined as: Among them U target is the gate operation we want to achieve, d is U target The dimensions of the matrix; by optimizing the parameters φ′1, φ′2, φ1, φ2, and ω c (t) contains the parameters that maximize the fidelity of the two-qubit gate.

4. The method for quantum gate simulation and control parameter optimization based on numerical calculation according to claim 1, characterized in that: The model Hamiltonian matrix representation module, the system time evolution and fidelity calculation module, and the control parameter optimization module are described as follows: The model Hamiltonian matrix representation module is used to convert the model Hamiltonian describing the multi-qubit system and the Hamiltonian of the interaction between the qubit and the control system into a matrix form; specifically, by selecting a set of basis vectors of the Hilbert space and then calculating the matrix representation of the generation operator and the annihilation operator under this set of basis vectors, the model Hamiltonian can be converted into a matrix form, in preparation for the 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 system state over time under the drive of the model Hamiltonian. It can also evaluate the gap between the final state of the system 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 the discretization method to numerically solve the time-dependent Schrödinger equation to show the intermediate state of the system's evolution over time. For single- and double-qubit gate operations, the quantum gate fidelity calculation formula is defined respectively to quantitatively evaluate the similarity between the final state of the evolution and the target state. This prepares for the subsequent optimization of quantum gate operation control parameters and the improvement of quantum gate fidelity. The control parameter optimization module is used to find the optimal quantum gate operation control parameters and quantum gate operation time, so that the quantum gate operation has the highest theoretical fidelity; specifically, firstly, the quantum gate operation control parameters, gate operation time and other necessary model parameters are given, and the model Hamiltonian matrix representation module is called to convert the model Hamiltonian into a matrix form, and 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 calculated results, the control parameters and gate operation time are updated according to specific rules and the above steps are repeated until the convergence conditions are met, and the optimal control waveform and gate operation time can be obtained.

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