Superconducting quantum bit physical simulation and line simulation method with noise modeling

Abstract

The invention discloses a superconducting quantum bit physical-level simulation and line simulation method with noise modeling, and relates to the technical field of quantum calculation and quantum simulation, and the method comprises the steps: under the Schrodinger representation, according to the physical parameters of superconducting quantum bits of a quantum system and the gate operation type, calculating the physical-level simulation of the superconducting quantum bits of the quantum system; constructing a time-dependent Hamiltonian sequence which is corresponding to the quantum system and changes along with time; according to the noise parameter of each superconducting quantum bit in the quantum system, constructing a noise operator corresponding to each superconducting quantum bit; and introducing the time-dependent Hamiltonian sequence and all noise operators into a LINDBLAD main equation, and carrying out evolution on a density matrix of the quantum system to obtain a quantum state of the quantum system under the influence of noise. According to the method, the finally obtained noise-containing quantum state provides an accurate basis for quantum circuit performance evaluation, and design optimization of a superconducting quantum chip, improvement of a gate operation control strategy and performance prediction of a quantum algorithm on actual hardware can be effectively guided.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of quantum computing and quantum simulation, and particularly relates to a superconducting quantum bit physical level simulation and circuit simulation method with noise modeling. BACKGROUND

[0002] In the field of superconducting quantum computing, reliable simulation of quantum circuits is crucial for algorithm verification and hardware design. However, existing mainstream superconducting quantum circuit simulators face severe challenges in accurately predicting the behavior of real quantum devices. These simulators are mostly based on idealized quantum gate models and cannot fully reflect various physical noises and error propagation effects that exist during the operation of real superconducting quantum devices. As the scale of quantum processors expands and the complexity of circuits increases, the gap between this ideal model and the actual physical system becomes increasingly prominent, severely restricting the guiding value of simulation results for experiments.

[0003] To solve the above problems, existing technical solutions mainly fall into two categories. One is to directly use ideal quantum gate models for circuit-level simulation, which is computationally efficient but completely ignores the details of physical implementation. The other, more advanced, solution attempts to perform physical-level simulation in the Schrödinger representation by introducing Transmon physical parameters and frequency-modulated controlled-Z gates, completing noise-free physical-level simulation. This type of solution also proposes phase correction and gate fidelity evaluation methods in the interaction representation, to some extent bridging the gap between the ideal model and physical reality, providing an important foundation for more accurate quantum simulation.

[0004] However, these existing technical solutions still have obvious deficiencies. In particular, they fail to systematically incorporate key noise factors such as temperature, relaxation time, and decoherence time into the simulation framework. Even the most advanced physical-level simulation solutions mainly focus on gate operation implementation in ideal environments, ignoring the inevitable noise effects in real quantum systems. In addition, some solutions attempt to add noise approximations after ideal gate operations, which is a "gate before noise" approach that significantly differs from the actual physical process and cannot accurately describe the dynamic impact and cumulative effects of noise during gate operation.

[0005] Therefore, there is an urgent need in the field for a new simulation method that can organically combine noise modeling with the time evolution of physical-level gate operations. This method should be able to handle both ideal evolution and noise effects of quantum systems in a unified mathematical framework, thereby more accurately predicting the actual behavior of real quantum devices and providing reliable technical support for the transition of superconducting quantum computing from theoretical research to engineering application. SUMMARY

[0006] The technical problem solved by the present application is to overcome the deficiencies of the prior art by providing the following technical solutions: 1) In a first aspect, the present application provides a superconducting quantum bit physical level simulation and circuit simulation method with noise modeling, and the specific technical solutions are as follows: Under the Schrodinger representation, according to the physical parameters of the superconducting quantum bits of the quantum system and the types of gate operations, a time-dependent Hamiltonian sequence corresponding to the quantum system is constructed; According to the noise parameters of each superconducting quantum bit in the quantum system, a noise operator corresponding to each superconducting quantum bit is constructed. The time-dependent Hamiltonian sequence and all noise operators are jointly introduced into the Lindblad master equation to evolve the density matrix of the quantum system, and the quantum state of the quantum system under the influence of noise is obtained.

[0007] The superconducting quantum bit physical level simulation and circuit simulation method with noise modeling provided by the present application has the following beneficial effects: By jointly introducing the time-dependent Hamiltonian sequence and the noise operator into the Lindblad master equation to evolve the density matrix, integrated modeling is realized, which fundamentally avoids the artificial segmentation problem of prior art that noise is modeled after gate operations, so that the simulation process is closer to the real physical evolution process of the superconducting quantum bit. The corresponding noise operator can be constructed according to the noise parameters of each superconducting quantum bit, including relaxation noise operator, pure dephasing noise operator and environmental temperature noise operator, so that key noise parameters such as temperature, relaxation time and dephasing time are included in the simulation framework, improving the authenticity and reliability of the simulation results. In addition, the time-dependent Hamiltonian sequence is constructed under the Schrodinger representation, ensuring the accuracy of the physical level simulation, and the mixed state characteristics of the quantum state under the influence of noise are completely described through the density matrix evolution. The final noise-containing quantum state (quantum state of the quantum system under the influence of noise) provides an accurate basis for performance evaluation of quantum circuits, effectively guides the design optimization of superconducting quantum chips, the improvement of gate operation control strategies and the performance prediction of quantum algorithms on actual hardware, and strongly promotes the conversion process from theoretical research to engineering application of quantum computing.

[0008] On the basis of the above-mentioned scheme, the superconducting quantum bit physical level simulation and circuit simulation method with noise modeling of the present application can be further improved as follows.

[0009] Further, under the Schrodinger representation, according to the physical parameters of the superconducting quantum bits of the quantum system and the types of gate operations, a time-dependent Hamiltonian sequence corresponding to the quantum system is constructed, including: Under the Schrodinger representation, according to the frequency modulation trajectory of the controlled Z gate operation of the quantum system, and according to the physical parameters of the superconducting quantum bits of the quantum system and the types of gate operations, the continuous time-dependent Hamiltonian of the quantum system is discretized into a time-dependent Hamiltonian sequence.

[0010] The beneficial effect of the above further scheme is that by discretizing the continuous time Hamiltonian of the quantum system into a sequence of time-dependent Hamiltonians, an accurate numerical implementation of the physical-level simulation is achieved. Based on the frequency modulation trajectory of the controlled Z gate operation of the quantum system and the physical parameters of the superconducting qubit and the type of gate operation, this method can accurately describe the dynamic evolution during the gate operation. By using the time slicing technique to convert the continuous time evolution into a discrete sequence, the authenticity of the physical process is preserved, and the feasibility of numerical calculation is provided. This discretization process allows the complex quantum system evolution to be solved by iterative methods, ensuring the numerical stability and calculation accuracy of the simulation process. At the same time, this method establishes an accurate dynamic basis for the subsequent introduction of noise operators and density matrix evolution, making the entire simulation process accurately reflect the actual physical behavior of the superconducting qubit during the gate operation, providing reliable technical support for evaluating quantum gate performance and optimizing control parameters.

[0011] Further, it further comprises: Comparing the quantum state of the quantum system under the influence of noise with the quantum state of the quantum system under ideal noise-free conditions, the state fidelity of the quantum state of the quantum system under the influence of noise is calculated.

[0012] The beneficial effect of the above further scheme is that by calculating the state fidelity of the quantum state of the quantum system under the influence of noise, an objective and effective evaluation basis is provided for evaluating the influence of noise on the quantum system. By accurately comparing the noisy quantum state with the ideal noise-free quantum state, the cumulative degree of noise effect in the quantum state evolution process can be quantitatively characterized. This evaluation method based on state fidelity can accurately reflect the influence of different noise sources on the performance of quantum gate operation and quantum circuit, providing a reliable performance metric for physical-level simulation of superconducting qubits. Through the calculation of state fidelity, direct guidance can be provided for quantum chip design optimization, helping to identify key links sensitive to noise, and also providing a unified evaluation standard for comparison and improvement of quantum gate operation schemes. This technical feature makes the simulation results have clear physical meaning and practical reference value, effectively supporting the performance evaluation and optimization of quantum computing systems.

[0013] Further, the noise operator corresponding to each superconducting qubit comprises a relaxation noise operator, a pure dephasing noise operator and an environmental temperature noise operator.

[0014] The beneficial effect of adopting the above further scheme is that by constructing the relaxation noise operator, the pure dephasing noise operator and the environmental temperature noise operator, the main noise mechanisms of the superconducting quantum bit are systematically covered. This comprehensive noise modeling can accurately describe the multiple physical effects faced by the quantum bit in actual operation, including energy relaxation process, phase coherence decay and thermal environment excitation effect. By considering the three types of noise operators at the same time, the simulation process can fully reflect the combined action of multiple noise sources in the real quantum device, improving the reality and accuracy of the physical level simulation. The modular noise operator design provides convenience for flexible configuration of different noise parameters, supporting adjustment of the noise operator according to the specific experimental conditions, thereby providing a more reliable simulation basis for performance evaluation and optimization of the superconducting quantum computing system.

[0015] 2) In a second aspect, the present application also provides a superconducting quantum bit physical level simulation and circuit simulation system with noise modeling, and the specific technical solutions are as follows: It comprises a construction module, a noise operator construction module and an evolution module. The construction module is used to: in the Schrodinger representation, according to the physical parameters of the superconducting quantum bit of the quantum system and the type of gate operation, construct the time-dependent Hamiltonian sequence corresponding to the quantum system; The noise operator construction module is used to: according to the noise parameters of each superconducting quantum bit in the quantum system, construct the noise operator corresponding to each superconducting quantum bit; The evolution module is used to: introduce the time-dependent Hamiltonian sequence and all noise operators into the Lindblad master equation, evolve the density matrix of the quantum system, and obtain the quantum state of the quantum system under the influence of noise.

[0016] On the basis of the above scheme, the superconducting quantum bit physical level simulation and circuit simulation system with noise modeling of the present application can also be improved as follows.

[0017] Further, the construction module is specifically used for: In the Schrodinger representation, according to the frequency modulation trajectory of the controlled Z gate operation of the quantum system, and according to the physical parameters of the superconducting quantum bit of the quantum system and the type of gate operation, the continuous time-dependent Hamiltonian of the quantum system is discretized into a time-dependent Hamiltonian sequence.

[0018] Further, it further comprises a state fidelity calculation module, which is used to: Compare the quantum state of the quantum system under the influence of noise with the quantum state of the quantum system in the ideal noise-free case, and calculate the state fidelity of the quantum state of the quantum system under the influence of noise.

[0019] Furthermore, the noise operators corresponding to each superconducting quantum bit include: relaxation noise operator, pure dephase noise operator, and ambient temperature noise operator.

[0020] 3) In a third aspect, the present invention also provides an electronic device, the electronic device including a processor coupled to a memory, the memory storing at least one computer program, the at least one computer program being loaded and executed by the processor, so as to enable the electronic device to implement any of the above-mentioned methods for physical-level simulation and circuit simulation of superconducting quantum bits with noise modeling.

[0021] 4) In a fourth aspect, the present invention also provides a computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor, implements any of the above-mentioned methods for physical-level simulation and circuit simulation of superconducting quantum bits with noise modeling.

[0022] It should be noted that the beneficial effects of the technical solutions of the second to fourth aspects of the present invention and their corresponding possible implementations can be found in the above description of the technical effects of the first aspect and its corresponding possible implementations, and will not be repeated here. Attached Figure Description

[0023] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments of the present invention will be briefly introduced below: Figure 1 This is a flowchart illustrating a method for physical-level simulation and circuit simulation of superconducting quantum bits with noise modeling, according to an embodiment of the present invention. Figure 2 This is a schematic diagram of a physical-level simulation and circuit simulation system for superconducting quantum bits with noise modeling, according to an embodiment of the present invention. Figure 3 This is a schematic diagram of the structure of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0024] The principles and features of the present invention are described below. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0025] The technical solution of the present invention and how the technical solution of the present invention solves the above-mentioned technical problems are described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of the present invention will now be described with reference to the accompanying drawings.

[0026] like Figure 1 As shown in the figure, a method for physical-level simulation and circuit simulation of superconducting quantum bits with noise modeling according to an embodiment of the present invention includes the following steps: S1, constructing a time-dependent Hamiltonian sequence of the quantum system according to the physical parameters of the superconducting qubits of the quantum system and the type of gate operation in the Schrödinger representation, specifically, discretizing the continuous time-dependent Hamiltonian of the quantum system into a time-dependent Hamiltonian sequence according to the frequency modulation trajectory of the controlled-Z gate operation of the quantum system and according to the physical parameters of the superconducting qubits of the quantum system and the type of gate operation in the Schrödinger representation, specifically comprising the following steps: S10, determining the basic Hamiltonian structure of the quantum system according to the physical parameters of the superconducting qubits of the quantum system and the type of gate operation. Specifically, the physical parameters of the superconducting qubits of the quantum system need to be analyzed in detail, including the energy level spacing of each qubit, the non-linear characteristics of the Josephson junction, and the coupling strength between qubits. The energy level spacing determines the eigenenergy structure of the qubit, the non-linear characteristics of the Josephson junction ensure the distinguishable energy levels of the qubit, and the coupling strength describes the degree of interaction between qubits. At the same time, according to the type of gate operation to determine the specific form of the Hamiltonian, for single-qubit gate operation, corresponding driving control terms need to be added to the Hamiltonian, which describe the interaction between external microwave field and qubit; for two-qubit gate operation, especially controlled-Z gate operation, in addition to considering single-qubit terms, coupling interaction terms also need to be added to the Hamiltonian, which reflect the energy exchange mechanism between two qubits. The final basic Hamiltonian structure contains the eigenenergy terms, driving control terms and coupling interaction terms of the qubits, providing a complete theoretical framework and mathematical model basis for subsequent construction of time-dependent Hamiltonian sequence.

[0027] S11, for the controlled-Z gate operation, the time dependence of the Hamiltonian needs to be defined according to its frequency modulation trajectory. The frequency modulation trajectory describes the precise path of the qubit frequency change over time when implementing the controlled-Z gate, which is usually designed based on the principle of fast near-adiabatic. Specifically, according to the energy level structure characteristics of the quantum system, especially the energy level avoidance characteristics of the qubits, a frequency variation curve is calculated that can maximize the fidelity of the gate operation while minimizing the leakage error. This frequency modulation trajectory needs to ensure that at the end of the gate operation, the quantum bit system can accumulate an accurate π phase difference, while avoiding excitation to non-computational energy levels. The design of the frequency modulation trajectory will directly determine the time evolution law of the relevant parameters in the Hamiltonian, and is a key factor to ensure the accuracy and high fidelity of the controlled-Z gate operation, which needs to be strictly optimized numerically and physically verified.

[0028] S12, based on the physical parameters and the frequency modulation trajectory, construct a continuous time-dependent Hamiltonian of the quantum system. The continuous time-dependent Hamiltonian is a complete mathematical description of the time dependence based on the basic Hamiltonian structure. For a Transmon superconducting qubit, the intrinsic energy term is described by a nonlinear harmonic oscillator model, which accurately reflects the energy level structure of the qubit; the driving control term corresponds to the interaction of the external control signal, its specific form depends on the type of gate operation and the corresponding control pulse parameters; the coupling interaction term accurately describes the energy exchange process between qubits, and its strength is dynamically adjusted with the change of the frequency modulation trajectory. The continuous time-dependent Hamiltonian needs to completely describe the evolution of the quantum system from the initial time to the end of the gate operation, where the Hamiltonian form at each time point is determined by the instantaneous values of the physical parameters, the gate operation state and the frequency modulation trajectory, ensuring accurate simulation of the real physical evolution process.

[0029] S13, in order to carry out numerical simulation, the continuous time-dependent Hamiltonian needs to be discretized into a time-dependent Hamiltonian sequence. The discretization process is realized by dividing the total gate operation time into multiple small time intervals, usually dividing the entire gate operation time into hundreds to thousands of small time steps. When dividing, the appropriate time step needs to be determined according to the dynamic characteristics of the system to ensure that the fastest dynamic process can be accurately captured. Within each time step, the Hamiltonian of the system is assumed to remain constant, and its value is the continuous time-dependent Hamiltonian value at the midpoint of the time interval. The accuracy of the discretization needs to be controlled by adjusting the time step, usually needs to ensure that the time step is much smaller than the fastest dynamic time scale of the system, while also considering the balance between calculation efficiency and numerical stability, to ensure that the discretized sequence can accurately reflect the dynamic characteristics of the original continuous Hamiltonian.

[0030] S14, the generated time-dependent Hamiltonian sequence will serve as the basis for quantum state evolution. This sequence is arranged in chronological order, and each element corresponds to the Hamiltonian value of the system at a specific time interval. The first element in the sequence corresponds to the Hamiltonian at the initial time, and the last element corresponds to the Hamiltonian at the end of the gate operation, and the elements in between are arranged in chronological order. This sequence completely describes the evolution of the system Hamiltonian during the gate operation, including all the interaction terms and the influence of the external control field. In numerical simulation, this time-dependent Hamiltonian sequence will be directly input into the numerical solver for step-by-step evolution of the quantum state calculation. The storage format of the sequence needs to be specially optimized to support efficient large-scale numerical calculation and fast data access, providing accurate and reliable physical basis for subsequent density matrix evolution, noise modeling and fidelity calculation.

[0031] The frequency modulation trajectory of the controlled Z gate operation refers to the path of adjusting the frequency of the superconducting qubit over time when implementing the controlled Z gate. This frequency modulation trajectory is usually designed based on the principle of fast near-adiabatic, by controlling the frequency of the qubit to evolve according to a specific curve, so that effective energy level crossing or avoidance occurs between two superconducting qubits, thereby inducing the required phase change of the controlled Z gate. The frequency modulation trajectory ensures the accuracy and high fidelity of the gate operation, while minimizing unnecessary energy level excitation and errors.

[0032] The physical parameters of the superconducting qubit include numerical values that describe the basic characteristics of the qubit, such as the intrinsic frequency of the qubit, the energy level spacing, the Josephson junction energy, the charging energy, the relaxation time, the decoherence time, and the pure decoherence time, etc. These parameters determine the energy level structure, dynamic behavior, and the strength of interaction with the environment of the qubit, and are the basis for constructing the Hamiltonian and noise model.

[0033] The type of gate operation of the superconducting qubit refers to various quantum logic gates performed in the quantum circuit, such as single-bit gates and two-bit gates. Single-bit gates include X gates, Y gates, and Z gates, etc., which are usually implemented through external microwave pulses; two-bit gates such as controlled Z gates are implemented through frequency modulation or coupling modulation. Each type of gate operation corresponds to a specific Hamiltonian form and control sequence, which is used to accurately describe the transformation of quantum states in simulation.

[0034] The continuous time-dependent Hamiltonian is a mathematical object that describes the continuous change of the energy operator of a quantum system over time. It contains all the interaction terms of the system and the influence of external control fields, such as the driving term, coupling term, and frequency modulation term of the qubit. In the Schrödinger representation, the continuous time-dependent Hamiltonian determines the continuous evolution dynamics of the quantum state, and is the core element of simulating the time behavior of quantum systems.

[0035] The time-dependent Hamiltonian sequence is obtained by discretizing the continuous time-dependent Hamiltonian in the time domain to obtain a series of Hamiltonian values. Each sequence element corresponds to an approximate constant Hamiltonian in a specific time interval, which is used to numerically solve the evolution equation. This discretization converts the complex continuous-time problem into a computable discrete step, facilitating the gradual advancement of quantum state evolution in simulation.

[0036] S2, according to the noise parameters of each superconducting qubit in the quantum system, constructing a noise operator corresponding to each superconducting qubit; The noise operator corresponding to each superconducting qubit includes a relaxation noise operator, a pure decoherence noise operator, and an environmental temperature noise operator.

[0037] The noise parameters of the superconducting qubit are a set of key physical quantities used to quantify the loss of coherence and state errors caused by the interaction with the environment, mainly including the relaxation time , decoherence time and pure decoherence time . Wherein, characterizes the energy relaxation process of a superconducting qubit from an excited state spontaneously transitions to the ground state , the inverse reflects the rate of energy dissipation; describes the overall decay of the phase coherence of a superconducting qubit, whose value is jointly limited by energy relaxation and pure phase noise, the relaxation time , decoherence time and pure decoherence time satisfy the physical relationship: ; In addition, the environmental temperature and the main frequency of the superconducting qubit jointly determine the thermal occupation number of the excited and relaxation processes in the thermal environment , which together constitute the basic input for constructing various superconducting noise operators and performing physical-level noise simulation.

[0038] Wherein, the specific implementation process of calculating the relaxation noise operator corresponding to each superconducting qubit is as follows: read the relaxation time of each superconducting qubit. The relaxation time is a physical quantity that describes the average time for the quantum bit to spontaneously decay from an excited state to the ground state , and is a key indicator of energy relaxation process. Let the relaxation time of the th superconducting qubit in the quantum system be . Substitute directly into the standard mathematical expression of the relaxation noise operator to calculate the relaxation noise operator corresponding to the th superconducting qubit : , execute this operation for all superconducting qubits participating in the simulation to ensure that the noise effect of each superconducting qubit is independently and accurately modeled, thereby obtaining the relaxation noise operator corresponding to each superconducting qubit.

[0039] wherein, is the annihilation operator of the th superconducting qubit. The annihilation operator is a basic concept in quantum mechanics, which functions to lower the energy level of the quantum bit by one level, for example, to convert the excited state to the ground state , which physically corresponds to the microscopic behavior of the quantum bit losing one energy quantum in the energy relaxation process. In the calculation, first, the inverse of the parameter is calculated , which represents the relaxation rate of the superconducting quantum bit. Then, the square root of the relaxation rate is taken to obtain the coefficient of the relaxation noise operator . Finally, the product of and the annihilation operator of the th quantum bit is calculated, and the relaxation noise operator describing the energy relaxation effect of the th superconducting quantum bit is finally constructed.

[0040] The calculated relaxation noise operators are integrated and stored, and the relaxation noise operator generated for each superconducting quantum bit is added to a unified noise operator set. This set will be called when constructing the Lindblad master equation later, as part of the noise term participating in the dynamic evolution of the entire quantum system. When storing, each relaxation noise operator is associated with its corresponding superconducting quantum bit index to ensure that it can correctly and accurately act on the corresponding superconducting quantum bit during evolution.

[0041] where the specific implementation process of calculating the pure dephasing noise operator corresponding to each superconducting quantum bit is as follows: Read the pure dephasing time of each superconducting quantum bit . The pure dephasing time is a physical quantity specifically describing the loss of coherence of a superconducting quantum bit caused by random phase fluctuations, which is independent of the energy relaxation process. Let the pure dephasing time of the th quantum bit in the quantum system be . According to whether the th quantum bit is a two-level system or a multi-level system, select the corresponding mathematical expression to calculate the pure dephasing noise operator. Specifically: 1) For a two-level system, its pure dephasing noise operator is calculated by the formula . In this formula, is the Pauli Z operator acting on the th superconducting quantum bit. The Pauli Z operator is a diagonal matrix in the computational basis, and its essential effect is to introduce a phase dependent on the energy level on the quantum state, thereby accurately simulating the random diffusion of phase information, represents the pure dephasing noise operator corresponding to the th quantum bit.

[0042] 2) For multi-level systems, such as Transmon qubits containing multiple energy levels, the pure dephase noise operator is given by the formula... Given. In this formula, It is a number operator, defined as ,in and They are the first The generation and annihilation operators for qubits. Number operators. The eigenvalues ​​are the energy level numbers of the qubit, thus this noise operator can describe the relative phase diffusion between different energy levels, which is crucial for accurately simulating high-level leakage effects beyond the two-level approximation. The calculation process is similar to the two-level case, but the coefficients are simplified to... Then combine it with the number operator Perform scalar multiplication. Indicates: the The pure dephase noise operator corresponding to each qubit.

[0043] Perform the above operation one by one for all superconducting qubits that require modeling pure decoherent noise, and calculate the pure decoherent noise operator corresponding to each superconducting qubit.

[0044] The calculated pure dephase noise operators are integrated and stored. The pure dephase noise operator generated for each superconducting qubit is added to a unified noise operator set, coexisting with other noise models such as relaxation noise operators. During storage, the operator is explicitly labeled with its corresponding qubit index. This is to ensure that it can be correctly called and applied when constructing the Lindblad master equations later.

[0045] The specific implementation process for calculating the ambient temperature noise operator for each superconducting quantum bit is as follows: Read the ambient temperature of each superconducting quantum bit And clock speed. Ambient temperature. It is a physical quantity describing the thermodynamic state of the working environment of a quantum system, while the dominant frequency is the frequency corresponding to the energy level interval between the ground state and the first excited state of a superconducting quantum bit. The decay rate parameter also needs to be obtained. The decay rate parameter Typically related to the relaxation time of superconducting qubits Related, defined as .

[0046] Calculate the first Hot occupation number of superconducting qubits Specifically, the Bose-Einstein distribution formula is used to calculate: where, is the reduced Planck constant, is the Boltzmann constant. When calculating, make sure that all physical quantities are unified to the International System of Units. is the main frequency of the th superconducting qubit. When calculating, first calculate the exponential term , then calculate the value of the natural exponential function, subtract 1 and take the reciprocal, and finally get the thermal occupation number of the th superconducting qubit . The thermal occupation number represents the average number of excited quanta of quantum modes with a main frequency of in a thermal equilibrium environment at temperature , which quantifies the strength of environmental thermal fluctuations on the superconducting qubit.

[0047] Then, based on the calculated thermal occupation number , the environmental temperature noise operator is constructed. The environmental temperature noise operator contains two parts: the down transition operator and the up transition operator. The down transition operator is used to simulate the relaxation process of the quantum bit from the high energy level to the low energy level in the thermal environment, and is calculated by the following formula: The up transition operator then simulates the process of quantum bit transition from low energy level to high energy level caused by environmental thermal excitation, and is calculated by the following formula: where, is the annihilation operator of the th superconducting qubit, is the corresponding creation operator. When calculating, the coefficients of the two operators need to be calculated respectively, where the coefficient of the down transition operator is , and the coefficient of the up transition operator is , and then these coefficients are multiplied by the corresponding operators respectively.

[0048] For all superconducting qubits that need to be modeled as environmental temperature noise operators, perform the above operations one by one to calculate the corresponding environmental temperature noise operator for each superconducting qubit.

[0049] Subsequently, the calculated environmental temperature noise operators are integrated and stored. The down transition operator and the up transition operator generated for each superconducting qubit are added as a noise pair to the unified noise operator set. When storing, the two operators will be stored with their corresponding superconducting qubit index Explicitly associate and mark as environmental temperature noise type to ensure that they can be properly co-invoked when building the Lindblad master equation later.

[0050] S3, jointly introduce the time-dependent Hamiltonian sequence and all noise operators into the Lindblad master equation to evolve the density matrix of the quantum system, and obtain the quantum state of the quantum system under the influence of noise, specifically: S30, the initial state of the quantum system needs to be initialized. According to the simulation requirements, the density matrix of the quantum system is set to a specific initial state, usually starting from a pure state such as the ground state, or set to other specific quantum states according to the line requirements. This initial density matrix will serve as the starting point for the evolution process.

[0051] S31, use the time slicing method to gradually advance the evolution of the quantum system according to the time sequence defined in the time-dependent Hamiltonian sequence. For each time slice in the sequence, obtain the corresponding Hamiltonian and all constructed noise operators within that time period. Then construct the complete Lindblad master equation: where the dissipative term has the specific form: where ρ represents the density matrix of the quantum system. It is a core mathematical quantity that describes the quantum state of the system, and its particularity lies in its ability to represent both pure states and mixed states. In an open quantum system with noise, due to the entanglement between the system and the environment, a single state vector is not sufficient to completely describe the system state, and the density matrix must be used. The diagonal elements of the density matrix represent the probability distribution of the system in each basis state, while the off-diagonal elements depict the coherence between different quantum states. represents the Hamiltonian operator corresponding to the kth time slice in the discrete time sequence. It is derived from the time-dependent Hamiltonian sequence generated in S13 . encapsulates all the energy information of the system within that specific time interval, including the intrinsic energy of the superconducting qubit, the interaction driven by the control field, and the coupling energy between qubits. It is the root of driving the system to undergo deterministic unitary evolution. refers to the kth noise operator, also commonly known as the Lindblad operator or jump operator. It is not a single operator, but a collection of all constructed noise operators. is the quantum jump term. It describes the actual impact of the physical process represented by the noise operator on ρ, which is the term that causes the sudden change in the quantum state. : This is the product of the adjoint operator of the noise operator and the original operator, forming a Hermitian operator. It can be understood as the "rate operator" or "noise intensity operator" associated with the noise channel, whose expectation value is proportional to the probability rate of the occurrence of the noise process. : This is the compensation term or dissipation term. In order to keep the trace of the density matrix (total probability) always equal to 1, and to be able to return to the standard von Neumann equation in the absence of noise, this term must be introduced. It mathematically ensures the complete positive definiteness and trace conservation properties of the evolution process.

[0052] At each time step, it is necessary to numerically solve this differential equation. Numerical integration methods such as the Runge-Kutta method are usually used to calculate the rate of change of the density matrix state under the action of the Lindblad master equation based on the current time step, and then update it to the density matrix state of the next time step. This process needs to ensure that the time step is small enough to meet the numerical stability requirements.

[0053] S32, During the evolution process, different types of noise operators need to be handled specially. For relaxation noise operators, they mainly affect the diagonal and off-diagonal elements of the density matrix; for pure dephasing noise operators, they mainly cause the decay of the off-diagonal elements of the density matrix; for environmental temperature noise operators, both the up transition and down transition operators need to be considered. All these noise effects are uniformly handled under the framework of the Lindblad master equation.

[0054] S33, After completing the evolution of all time slices, the final density matrix is output as the quantum state of the quantum system under the influence of noise. This density matrix contains the complete information of all Hamiltonian actions and noise accumulations during the entire evolution process, and can be used for subsequent fidelity calculation and quantum state analysis.

[0055] where the Lindblad master equation is the standard mathematical description of the dynamic evolution of open quantum systems, which can describe both the unitary evolution process of the quantum system and the non-unitary dissipation process. The equation contains two main parts, the first part is the Hamiltonian evolution term of the system, which describes the ideal evolution behavior of the quantum state under the action of the energy operator; the second part is the dissipation term, which is composed of a series of noise operators, used to model various dephasing and relaxation effects caused by the interaction between the system and the environment. The Lindblad master equation provides a rigorous and complete theoretical framework for the noise evolution of quantum systems.

[0056] The density matrix of the quantum system is a mathematical tool for describing the state of the quantum system, which can uniformly describe both pure states and mixed states. Unlike the state vector, which can only describe pure quantum states, the density matrix can describe the probability mixture of the system in different quantum states. This feature makes it particularly suitable for handling open quantum systems with noise and uncertainty. In the simulation, the matrix elements of the density matrix contain all the statistical information of the system, including the particle number distribution and the coherence intensity, and other important physical quantities.

[0057] Evolution in quantum mechanics refers to the dynamic process of the state of a quantum system changing over time. In the framework of the Lindblad master equation, evolution specifically refers to the continuous change of the density matrix under the influence of the Hamiltonian and noise operators. This process includes the natural evolution of the system energy, the logical transformation of quantum gate operations, and the decoherence effect caused by environmental noise. Numerical evolution is achieved by discretizing the time domain and using iterative calculations to approximate the continuous change process, ultimately obtaining the quantum state of the quantum system at a specific time.

[0058] Optionally, in the above technical solution, further comprising: S4, comparing the quantum state of the quantum system under the influence of noise with the quantum state of the quantum system under ideal noise-free conditions, and calculating the state fidelity of the quantum state of the quantum system under the influence of noise.

[0059] The quantum state of the quantum system under ideal noise-free conditions is obtained as follows: S40, the evolution framework of the quantum system under ideal conditions needs to be constructed. This process is carried out in the Schrödinger representation, using the same initial quantum state and time-dependent Hamiltonian sequence as the noisy evolution. The key difference is that the evolution under ideal conditions completely ignores the influence of all noise operators, i.e., it assumes that the quantum system is a closed system completely isolated from the external environment.

[0060] S41, the evolution of the quantum state is advanced by numerical integration of the Schrödinger equation. The form of the Schrödinger equation is: In actual numerical calculations, a sequence of time-dependent Hamiltonians is used in this process. For each time slice in the sequence, the system obtains the corresponding Hamiltonian , and uses numerical algorithms such as the Runge-Kutta method or an exact solver based on the matrix exponential to calculate the evolution operator for that time step, then applies this operator to the current state vector to update the state vector at the next time point.

[0061] In the evolution process, especially for the controlled Z gate which is realized by frequency modulation, phase correction is usually needed after the evolution. This is because the evolution of physical level may produce additional dynamic phase. The system corrects these phases by applying a virtual RZ gate operation, which is a mathematical process at the software level. It directly adjusts the phase factor of the state vector, so that the final quantum state is completely aligned with the target state defined by the ideal quantum logic gate in the sense of global phase consistency. After completing the evolution of all gate operations and implementing the phase correction, the obtained state vector is the quantum state of the quantum system in the ideal noiseless case. This pure state will be used as a reference for subsequent fidelity comparison with the noisy result.

[0062] The specific implementation process of calculating the state fidelity of the quantum state of the quantum system under the influence of noise is as follows: S42, the input of calculating the state fidelity is determined. The input includes two parts: the first part is the quantum state of the quantum system under the influence of noise obtained by the evolution of the Lindblad master equation, which is a density matrix , which describes the mixed state after the actual noise influence; the second part is the quantum state of the quantum system in the ideal noiseless case obtained by the above process, which is a pure state .

[0063] S43, according to the specific form of the two quantum states, select and apply the corresponding state fidelity mathematical definition for calculation: 1) when comparing the noisy density matrix with the ideal pure state , the calculation formula of the state fidelity is: This calculation is numerically equivalent to taking the diagonal matrix element of the density matrix corresponding to the ideal state . Its physical meaning is: in the mixed state prepared in the actual experiment or simulation, what proportion is in the ideal target state we expect.

[0064] 2) as a more general case, if it is necessary to calculate the fidelity of two density matrices and , for example, to compare the outputs under two different noise models, the generalized fidelity formula is used: This calculation involves the square root and multiplication of matrices, which needs to be completed through a linear algebra numerical library.

[0065] S44, the ideal state and the noisy density matrix As input, a predefined fidelity calculation function is called. The function first determines the type of the input quantum state. After confirming that one is a pure state and the other is a density matrix, the function selects the first formula for calculation. The calculation process includes multiplying the ideal state vector and the density matrix, then left multiplying the conjugate transpose of the ideal state vector, and finally obtaining a scalar real number between 0 and 1, which is the state fidelity . represents complete consistency, represents complete orthogonality.

[0066] S45, output and record the calculation result of the state fidelity. This value, as the core indicator for evaluating the impact of noise, is output to the simulation report or log. It can be used to analyze the degree of influence of different noise sources on quantum gate operations or the performance of the entire quantum circuit, providing important quantitative basis for optimizing quantum bit parameters and improving gate operation schemes. Through this series of steps, the complete technical implementation process from obtaining the ideal state to accurately calculating the state fidelity is completed.

[0067] In the field of quantum chip design, the quantum system can be a multi-bit superconducting quantum processor based on the Transmon architecture. Using the method of the present application, first, according to the quantum bit arrangement and coupling structure in the chip design scheme, the physical parameters of the superconducting quantum bits of the system are determined, including the energy level spacing and coupling strength of each quantum bit. Based on these parameters, the frequency modulation trajectory of the controlled Z gate operation is constructed, and the corresponding time-dependent Hamiltonian sequence is generated. At the same time, according to the noise parameters of each quantum bit in the chip design specification, including the relaxation time , decoherence time and environmental temperature , the corresponding relaxation noise operator, pure decoherence noise operator and environmental temperature noise operator are constructed. These Hamiltonian sequences and noise operators are introduced into the Lindblad master equation together, and the system density matrix is evolved, and finally the quantum state of the chip design under the influence of noise is obtained. Using the obtained noisy quantum state, its state fidelity can be calculated, and by comparing the fidelity indicators of the quantum states output by different chip design schemes, quantitative basis for optimizing the physical layout of the quantum chip and selecting materials is provided, thereby guiding the manufacture of quantum processors with higher performance.

[0068] In the field of quantum gate operation optimization, the quantum system can be a superconducting qubit system containing specific coupling pairs. Using the method of the present application, for different controlled Z gate control strategies, according to its specific frequency modulation trajectory and pulse waveform, combined with the physical parameters of the superconducting qubits of the quantum system, the corresponding time-dependent Hamiltonian sequence is constructed. At the same time, based on the measured noise parameters, a complete noise model including relaxation noise operators and pure dephasing noise operators is constructed. Through the Lindblad master equation evolution, the output quantum state under each control scheme is obtained. Using these noisy quantum states, the state fidelity of the ideal target state is calculated, which can accurately quantify the sensitivity of different frequency modulation trajectories to noise, and thus select the gate control scheme with the optimal anti-noise performance, providing reliable technical guidance for experimental implementation of high-fidelity quantum gate operations.

[0069] In the field of quantum algorithm evaluation, the quantum system can be a superconducting quantum processor running a specific quantum algorithm. Using the method of the present application, according to the quantum gate sequence involved in the algorithm, including single-bit gate and double-bit gate operation types, combined with specific superconducting qubit physical parameters, a complete time-dependent Hamiltonian sequence is constructed. At the same time, based on the actual noise parameters of the target quantum hardware, a comprehensive noise model including relaxation, dephasing and environmental temperature effects is constructed. Through the Lindblad master equation evolution, the noisy quantum state after algorithm execution is obtained. Using this quantum state, the state fidelity is calculated, which can accurately predict the execution effect of quantum chemical simulation or combinatorial optimization algorithms on real hardware, providing key technical basis for algorithm parameter adjustment, hardware selection and algorithm fault tolerance threshold analysis.

[0070] In the field of quantum error correction verification, the quantum system can be a superconducting quantum circuit integrated with a specific error correction code. Using the method of the present application, based on the basic quantum system, auxiliary bits and corresponding error correction operation gates are added to construct a time-dependent Hamiltonian sequence containing error correction steps. At the same time, based on the actual noise parameters, noise operators are constructed, and the quantum state after error correction is obtained through the Lindblad master equation evolution. Using this noisy quantum state, by comparing the state fidelity of the output quantum state after using different error correction schemes, the suppression effect of each error correction code on the specific noise pattern can be objectively evaluated, providing reliable technical guidance for selecting the most suitable error correction scheme for the noise characteristics of the hardware, and promoting the practical development of fault-tolerant quantum computing.

[0071] The overall goal of the present application is to propose a superconducting quantum bit physical level simulation and circuit simulation method with noise modeling, in the Schrödinger representation, according to the physical parameters of the superconducting quantum bits of the quantum system and the types of gate operations, a time-dependent Hamiltonian sequence corresponding to the quantum system is constructed. The physical parameters of the superconducting quantum bits include energy level spacing, coupling strength, Josephson junction energy, etc.; the types of gate operations include single-bit gate operations and double-bit gate operations, especially controlled Z gate operations. At the same time, according to the noise parameters of each superconducting quantum bit in the quantum system, the noise operator corresponding to each superconducting quantum bit is constructed; the noise parameters include relaxation time , decoherence time , pure decoherence time and environmental temperature , etc., the noise operator includes relaxation noise operator, pure decoherence noise operator and environmental temperature noise operator. Then, the time-dependent Hamiltonian sequence and all noise operators are jointly introduced into the Lindblad master equation to evolve the density matrix of the quantum system, and the quantum state of the quantum system under the influence of noise is obtained. The standard form of the Lindblad master equation is: wherein, represents the noise dissipation term. Finally, the quantum state of the quantum system under the influence of noise is compared with the quantum state of the quantum system under ideal noise-free conditions, and the state fidelity of the quantum state of the quantum system under the influence of noise is calculated, thereby completing the evaluation of the performance of the quantum circuit. This method realizes the integrated simulation of physical level gate operations and noise effects, and can more accurately predict the behavior of real quantum hardware.

[0072] In the present application, noise and physical gate operations are integrated modeled in the same time evolution framework, the time-dependent Hamiltonian sequence and noise operators are combined through the Lindblad master equation to realize the joint evolution of the density matrix of the quantum system. This modeling method avoids the artificial division of the traditional method of "gate first, noise second", and is more consistent with the physical process of superconducting quantum bits in actual devices, ensuring the authenticity and accuracy of the simulation results. Noise modeling is integrated into the simulation framework as an independent module, and according to the noise parameters (such as relaxation time , decoherence time , pure decoherence time and environmental temperature of the quantum bits,The noise module automatically generates different types of noise operators, including relaxation noise operators, pure dephasing noise operators, and environmental temperature noise operators. This modular design supports flexible configuration and extension of noise models by users, facilitating adaptation to the characteristics of different quantum hardware platforms. The simulation system automatically selects a solving strategy based on the presence or absence of noise operators. When at least one noise operator is constructed, the system solves the Lindblad master equation using density matrix evolution; when no noise operator is constructed, the system degenerates to Schrödinger equation evolution for state vectors. This adaptive mechanism ensures the accuracy of noise simulation while taking into account the computational efficiency in the absence of noise.

[0073] In the present application, first, in the Schrödinger representation, a time-dependent Hamiltonian sequence corresponding to the quantum system is constructed according to the physical parameters of the superconducting qubits of the quantum system and the types of gate operations. The physical parameters of the superconducting qubits include the energy level spacing of each qubit, the nonlinearity of the Josephson junction, and the coupling strength between qubits; the types of gate operations include single-qubit gate operations and two-qubit gate operations. For controlled-Z gate operations, the time dependence of the Hamiltonian needs to be defined according to its frequency modulation trajectory. The frequency modulation trajectory describes the path of the qubit frequency changing over time to ensure that the controlled-Z gate can be correctly implemented through frequency modulation. Based on these parameters, the continuous time-dependent Hamiltonian is discretized into a time-dependent Hamiltonian sequence. The discretization process is achieved by dividing the total gate operation time into multiple small time intervals, and the Hamiltonian is approximately constant within each time interval. Second, according to the noise parameters of each superconducting qubit in the quantum system, a noise operator corresponding to each superconducting qubit is constructed; the noise operator includes relaxation noise operators, pure dephasing noise operators, and environmental temperature noise operators. Then, the time-dependent Hamiltonian sequence and all noise operators are introduced into the Lindblad master equation to evolve the density matrix of the quantum system, obtaining the quantum state of the quantum system under the influence of noise. Finally, the state fidelity is calculated to evaluate the simulation results. The following will be described in detail through specific embodiments.

[0074] Example A: Based on relaxation noise modeling of , including the following steps: 1) Time-dependent Hamiltonian construction: Transmon model is used to describe superconducting qubits, considering inter-qubit coupling and controlled-Z gate operations achieved through frequency modulation. In the Schrödinger representation, the continuous time-dependent Hamiltonian is discretized into a time-dependent Hamiltonian sequence according to the physical parameters of the superconducting qubits of the quantum system and the types of gate operations , where each corresponds to the Hamiltonian value of a time segment. After evolution, a virtual RZ operation is performed for phase correction to eliminate dynamic phase errors.

[0075] 2) Noise modeling: When the quantum bits have relaxation times When considering parameters, a relaxation noise operator is constructed for each qubit. For the ... The relaxation noise operator for a quantum bit is: in, It is the first An annihilation operator for 10 qubits.

[0076] 3) Numerical evolution: in each time slice In this system, the system follows the Lindblad master equation: in, The equation is solved using numerical integration methods (such as the Runge-Kutta method), and the density matrix state is updated.

[0077] 4) Circuit Integration and Fidelity Calculation: Single-bit gates are generated from pulse waveforms, and double-bit controlled Z-gates are generated from frequency modulation trajectories. If a noise operator exists, the Lindblad master equation is solved using the density matrix; otherwise, the Schrödinger equation is solved using state vectors. After evolution, phase is corrected through phase backfilling, and state fidelity is calculated. That is, comparing the similarity between a quantum state under noise and an ideal noise-free quantum state.

[0078] Example B: Pure decoherence and The mapping process includes the following steps: 1) Construction of time-dependent Hamiltonians: Similar to Example A, a sequence of time-dependent Hamiltonians is constructed under the Schrödinger representation, and the Hamiltonians are discretized based on the physical parameters of the superconducting qubits and the gate operation type.

[0079] 2) Noise modeling: Based on the pure decoherence time of the qubit Parameters are used to construct a pure decoherence noise operator. The relationship between the pure decoherence time, relaxation time, and decoherence time is as follows: For a two-level system, the first The pure dephase noise operator for 1 qubit is: in, It is the Pauli-Z operator. For multi-level systems, the pure dephase noise operator is: in, It is a number operator.

[0080] 3) Numerical evolution: Introducing the pure dephase noise operator into the Lindblad master equation: The noisy quantum state is obtained by numerical solution.

[0081] 4) Fidelity calculation: After the evolution is completed, calculate the state fidelity and evaluate the impact of pure decoherent noise on the quantum state.

[0082] Example C: Ambient temperature noise calculation, including the following steps: 1) Construction of time-dependent Hamiltonians: Similarly, construct time-dependent Hamiltonian sequences under the Schrödinger representation, based on the physical parameters and gate operation types of superconducting qubits.

[0083] 2) Noise modeling: based on ambient temperature and quantum bit frequency Calculate the heat occupancy number: in, It is the reduced Planck constant. It is the Boltzmann constant. Then, for the first... A single quantum bit is used to construct an ambient temperature noise operator, including a lower transition operator and an upper transition operator: in, It is the decay rate parameter, usually related to... Related, defined as .

[0084] 3) Numerical Evolution: Introducing the ambient temperature noise operator into the Lindblad master equation: The noisy quantum state is obtained by numerical solution.

[0085] 4) Fidelity calculation: After the evolution is completed, the state fidelity is calculated to assess the overall impact of ambient temperature noise on the quantum state.

[0086] In all embodiments, state fidelity is calculated by comparing density matrices. With the ideal target state To achieve this, the formula is: Alternatively, a generalized fidelity formula can be used for general cases. This method ensures that simulation results accurately reflect the behavior of real quantum systems, providing a reliable basis for quantum chip design, gate operation optimization, and algorithm evaluation.

[0087] The technical terms appearing in this application are explained as follows: 1) Superconducting Qubit: A type of qubit that utilizes a Josephson junction in a superconducting circuit. A common type is Transmon.

[0088] 2) CZ gate (Controlled-ZGate): A two-qubit quantum logic gate, used when both qubits are in the state of... When the state is in a certain state, add a phase to the whole.

[0089] 3) Schrödinger representation: one of the ways of describing quantum mechanics, which treats quantum states as objects that evolve over time.

[0090] 4) Hamiltonian The mathematical operator of system energy determines the dynamic behavior of a quantum system.

[0091] 5) Density matrix A tool for describing the state of a quantum system, capable of representing pure states and noisy mixtures.

[0092] 6) Lindblad master equation: a standard form for describing the evolution of noisy quantum systems. This represents the noise channel.

[0093] 7) Time: Quantum bits from excited state Decay to ground state The average time.

[0094] 8) Time: The average time it takes for a quantum bit to maintain coherence, affected by... Both phase noise and other limitations.

[0095] 9) Time: Pure decoherence time, the loss of coherence caused only by phase fluctuations.

[0096] 10) Annihilation operator The operator that lowers the energy level of a quantum state can be intuitively understood as: bringing the quantum bitra back to a lower energy level.

[0097] 11) Number Operators : An operator used to count the number of quantum bit excitations.

[0098] 12) Oppose easy operators : A commonly used mathematical operator, used in Lindblad equations to represent the dissipative component.

[0099] 13) Virtual RZ: A type of Z-axis rotation implemented in software, which is equivalent to adding phase to the calculation results without requiring additional physical operations.

[0100] Although the steps have been numbered in the above embodiments, they are only specific embodiments given by the present invention. Those skilled in the art can adjust the execution order of the steps according to the actual situation, which is also within the protection scope of the present invention. It can be understood that some embodiments may include some or all of the above embodiments.

[0101] like Figure 2 As shown, a superconducting quantum bit physics-level simulation and circuit simulation system 200 with noise modeling according to an embodiment of the present invention includes a construction module 201, a noise operator construction module 202, and an evolution module 203. The construction module 201 is used to: under the Schrödinger representation, construct the time-dependent Hamiltonian sequence corresponding to the quantum system based on the physical parameters and gate operation type of the superconducting qubit of the quantum system; The noise operator construction module 202 is used to: construct the noise operator corresponding to each superconducting qubit based on the noise parameters of each superconducting qubit in the quantum system; The evolution module 203 is used to: introduce the time-dependent Hamiltonian sequence and all noise operators into the Lindblad master equation, evolve the density matrix of the quantum system, and obtain the quantum state of the quantum system under the influence of noise.

[0102] Optionally, in the above technical solution, the construction module 201 is specifically used for: Under the Schrödinger representation, based on the frequency modulation trajectory of the controlled Z-gate operation of the quantum system, and according to the physical parameters of the superconducting qubits of the quantum system and the gate operation type, the continuous time-dependent Hamiltonian of the quantum system is discretized into a time-dependent Hamiltonian sequence.

[0103] Optionally, the above technical solution also includes a state fidelity calculation module, which is used for: The state fidelity of the quantum state of a quantum system under noise influence is calculated by comparing the quantum state of the quantum system under ideal noise-free conditions.

[0104] Optionally, in the above technical solution, the noise operator corresponding to each superconducting quantum bit includes: a relaxation noise operator, a pure dephase noise operator, and an ambient temperature noise operator.

[0105] It should be noted that the beneficial effects of the superconducting quantum bit physics-level simulation and circuit simulation system 200 with noise modeling provided in the above embodiments are the same as those of the superconducting quantum bit physics-level simulation and circuit simulation method with noise modeling described above, and will not be repeated here. Furthermore, the system provided in the above embodiments is only illustrated by the division of the above functional modules. In practical applications, the above functions can be assigned to different functional modules as needed, that is, the system can be divided into different functional modules according to the actual situation to complete all or part of the functions described above. In addition, the system and method embodiments provided in the above embodiments belong to the same concept, and their specific implementation process is detailed in the method embodiments, and will not be repeated here.

[0106] The superconducting quantum bit physical-level simulation and circuit simulation system with noise modeling of the present invention can be a computer program (including program code) running on a computer device. For example, the superconducting quantum bit physical-level simulation and circuit simulation system with noise modeling of the present invention is an application software that can be used to execute the corresponding steps in the superconducting quantum bit physical-level simulation and circuit simulation method with noise modeling of the present invention.

[0107] In some embodiments, the superconducting quantum bit physical-level simulation and circuit simulation system with noise modeling of the present invention can be implemented in a combination of hardware and software. As an example, the superconducting quantum bit physical-level simulation and circuit simulation system with noise modeling of the present invention can be a processor in the form of a hardware decoding processor, which is programmed to execute the superconducting quantum bit physical-level simulation and circuit simulation method with noise modeling of the present invention. For example, the processor in the form of a hardware decoding processor can be one or more application-specific integrated circuits (ASICs), DSPs, programmable logic devices (PLDs), complex programmable logic devices (CPLDs), field-programmable gate arrays (FPGAs), or other electronic components.

[0108] The modules described in the embodiments of this invention can be implemented in software or hardware. The names of the modules are not, in some cases, limiting the scope of the module itself.

[0109] An electronic device according to an embodiment of the present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements any of the above-mentioned methods for physical-level simulation and circuit simulation of superconducting quantum bits with noise modeling. That is, an electronic device according to an embodiment of the present invention may include, but is not limited to: a processor and a memory; the memory is used to store the computer program; the processor is used to execute the method for physical-level simulation and circuit simulation of superconducting quantum bits with noise modeling shown in any embodiment of the present invention by calling the computer program.

[0110] In one alternative embodiment, an electronic device is provided, such as Figure 3 As shown, Figure 3 The illustrated electronic device 4000 includes a processor 4001 and a memory 4003. The processor 4001 and the memory 4003 are connected, for example, via a bus 4002. Optionally, the electronic device 4000 may further include a transceiver 4004, which can be used for data interaction between the electronic device and other electronic devices, such as sending and / or receiving data. It should be noted that in practical applications, the transceiver 4004 is not limited to one type, and the structure of the electronic device 4000 does not constitute a limitation on the embodiments of the present invention.

[0111] Processor 4001 may be a CPU (Central Processing Unit), a general-purpose processor, a DSP (Digital Signal Processor), an ASIC (Application Specific Integrated Circuit), an FPGA (Field Programmable Gate Array), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. It can implement or execute the various exemplary logic blocks, modules, and circuits described in conjunction with the disclosure of this invention. Processor 4001 may also be a combination that implements computational functions, such as including one or more microprocessor combinations, a combination of a DSP and a microprocessor, etc.

[0112] Bus 4002 may include a path for transmitting information between the aforementioned components. Bus 4002 may be a PCI (Peripheral Component Interconnect) bus or an EISA (Extended Industry Standard Architecture) bus, etc. Bus 4002 can be divided into address bus, data bus, control bus, etc. For ease of representation, Figure 3The bus 4002 is represented by only one thick line, but this does not mean that there is only one bus or one type of bus.

[0113] The memory 4003 may be ROM (Read Only Memory) or other types of static storage devices capable of storing static information and instructions, RAM (Random Access Memory) or other types of dynamic storage devices capable of storing information and instructions, or EEPROM (Electrically Erasable Programmable Read Only Memory), CD-ROM (Compact Disc Read Only Memory) or other optical disc storage, optical disc storage (including compressed optical discs, laser discs, optical discs, digital universal optical discs, Blu-ray discs, etc.), magnetic disk storage media or other magnetic storage devices, or any other medium capable of carrying or storing desired program code in the form of instructions or data structures and accessible by a computer, but not limited thereto.

[0114] The memory 4003 stores application code (computer program) for executing the present invention, and its execution is controlled by the processor 4001. The processor 4001 executes the application code stored in the memory 4003 to implement the content shown in the foregoing method embodiments.

[0115] Among them, electronic devices can also be terminal devices, which can be any device that can install applications, including at least one of smartphones, tablets, laptops, desktop computers, smart speakers, smartwatches, smart TVs, and smart in-vehicle devices.

[0116] It should be noted that, Figure 3 The electronic device shown is merely an example and should not be construed as limiting the functionality and scope of use of the embodiments of the present invention.

[0117] An embodiment of the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements any of the above-mentioned methods for physical-level simulation and circuit simulation of superconducting quantum bits with noise modeling.

[0118] Alternatively, the computer-readable storage medium may be a read-only memory (ROM), a random access memory (RAM), a compact disc read-only memory (CD-ROM), magnetic tape, a floppy disk, and an optical data storage device, etc.

[0119] In an exemplary embodiment, a computer program product or computer program is also provided, which includes computer instructions stored in a computer-readable storage medium. A processor of an electronic device reads the computer instructions from the computer-readable storage medium and executes the computer instructions, causing the electronic device to perform any of the above-described methods for physical-level simulation and circuit simulation of superconducting quantum bits with noise modeling.

[0120] Computer program code for performing the operations of this invention can be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, and C++, and conventional procedural programming languages ​​such as C or similar languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0121] It should be understood that the flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of methods and computer program products according to various embodiments of the present invention. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, may be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0122] The computer-readable storage medium provided in this invention can be, but is not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of a computer-readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EEPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this invention, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0123] The aforementioned computer-readable storage medium carries one or more programs, which, when executed by the electronic device, cause the electronic device to perform the method shown in the above embodiments.

[0124] The above description is merely a preferred embodiment of the present invention and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of disclosure in this invention is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the above-disclosed concept. For example, technical solutions formed by substituting the above features with (but not limited to) technical features with similar functions disclosed in this invention.

[0125] It should be noted that the terms "first," "second," etc., used in the specification and claims of this application are used to distinguish similar objects and represent a limitation on a specific order or sequence. Where appropriate, the order of use for similar objects can be interchanged so that the embodiments of this application described herein can be implemented in an order other than that shown or described.

[0126] Those skilled in the art will recognize that this invention can be implemented as a system, method, or computer program product. Therefore, this invention can be specifically implemented in the following forms: it can be entirely hardware, entirely software (including firmware, resident software, microcode, etc.), or a combination of hardware and software, generally referred to herein as a "circuit," "module," or "system." Furthermore, in some embodiments, this invention can also be implemented as a computer program product contained in one or more computer-readable media, which includes computer-readable program code.

[0127] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for physical-level simulation and circuit simulation of superconducting quantum bits with noise modeling, characterized in that, The method comprises the following steps: under the Schrödinger representation, constructing a time-dependent Hamiltonian sequence corresponding to the quantum system according to physical parameters of superconducting qubits of the quantum system and types of gate operations; constructing a noise operator corresponding to each superconducting qubit according to noise parameters of each superconducting qubit in the quantum system; introducing the time-dependent Hamiltonian sequence and all noise operators into a Lindblad master equation to evolve a density matrix of the quantum system, so as to obtain a quantum state of the quantum system under the influence of noise.

2. The method of claim 1, wherein the method further comprises: The method comprises the following steps: under the Schrödinger representation, constructing a time-dependent Hamiltonian sequence corresponding to the quantum system according to physical parameters of superconducting qubits of the quantum system and types of gate operations, which comprises the following steps:

3. The superconducting qubit physical level simulation and circuit simulation method with noise modeling according to claim 1 or 2, characterized in that, under the Schrödinger representation, discretizing a continuous time-dependent Hamiltonian of the quantum system into a time-dependent Hamiltonian sequence according to a frequency modulation trajectory of a controlled Z gate operation of the quantum system and according to physical parameters of superconducting qubits of the quantum system and types of gate operations. The method further comprises the following steps:

4. The superconducting qubit physical level simulation and circuit simulation method with noise modeling according to claim 1 or 2, characterized in that, comparing the quantum state of the quantum system under the influence of noise with a quantum state of the quantum system in an ideal noise-free case, and calculating a state fidelity of the quantum state of the quantum system under the influence of noise.

5. A physical-level simulation and circuit simulation system for superconducting quantum bits with noise modeling, characterized in that, The noise operator corresponding to each superconducting qubit comprises a relaxation noise operator, a pure dephasing noise operator and an environmental temperature noise operator. The method comprises a construction module, a noise operator construction module and an evolution module. The construction module is configured to construct, under the Schrödinger representation, a time-dependent Hamiltonian sequence corresponding to the quantum system according to physical parameters of superconducting qubits of the quantum system and types of gate operations. The noise operator construction module is configured to construct a noise operator corresponding to each superconducting qubit according to noise parameters of each superconducting qubit in the quantum system.

6. The superconducting qubit physical level simulation and circuit level modeling system with noise modeling of claim 5, wherein, The evolution module is configured to introduce the time-dependent Hamiltonian sequence and all noise operators into a Lindblad master equation to evolve a density matrix of the quantum system, so as to obtain a quantum state of the quantum system under the influence of noise. The construction module is specifically configured to:

7. The superconducting qubit physical level simulation and circuit simulation system with noise modeling according to claim 5 or 6, characterized in that, under the Schrödinger representation, discretizing a continuous time-dependent Hamiltonian of the quantum system into a time-dependent Hamiltonian sequence according to a frequency modulation trajectory of a controlled Z gate operation of the quantum system and according to physical parameters of superconducting qubits of the quantum system and types of gate operations. The method further comprises a state fidelity calculation module, which is configured to:

8. The superconducting qubit physical level simulation and circuit simulation system with noise modeling of claim 5 or 6, wherein, compare the quantum state of the quantum system under the influence of noise with a quantum state of the quantum system in an ideal noise-free case, and calculate a state fidelity of the quantum state of the quantum system under the influence of noise.

9. An electronic device, comprising: The noise operator corresponding to each superconducting qubit comprises a relaxation noise operator, a pure dephasing noise operator and an environmental temperature noise operator. The computer program is stored in the memory and can be run on the processor, and the processor implements the method for physically simulating and circuit simulating superconducting qubits with noise modeling according to any one of claims 1 to 4 when executing the computer program.

10. A computer-readable storage medium, characterized in that, The computer readable storage medium stores a computer program, and the computer program is executed by the processor to implement the superconducting quantum bit physical level simulation and circuit simulation method with noise modeling in any one of claims 1 to 4.

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