Superconducting quantum bit physical level simulation and circuit simulation method with noise modeling

Abstract

This invention discloses a method for physical-level simulation and circuit simulation of superconducting qubits with noise modeling, relating to the fields of quantum computing and quantum simulation technology. The method includes: constructing a time-varying Hamiltonian sequence corresponding to the quantum system under the Schrödinger representation, based on the physical parameters of the superconducting qubits and the gate operation type; constructing a noise operator corresponding to each superconducting qubit based on the noise parameters of each superconducting qubit in the quantum system; and incorporating the time-varying Hamiltonian sequence and all noise operators into the Linblad master equation to evolve the density matrix of the quantum system, obtaining the quantum state of the quantum system under noise influence. In this invention, the noisy quantum state obtained provides an accurate basis for evaluating the performance of quantum circuits, effectively guiding the design optimization of superconducting quantum chips, the improvement of gate operation control strategies, and the performance prediction of quantum algorithms on actual hardware.

Description

Technical Field

[0001] This invention relates to the fields of quantum computing and quantum simulation technology, and in particular to a method for physical-level simulation and circuit simulation of superconducting qubits with noise modeling. Background Technology

[0002] In the field of superconducting quantum computing, reliable simulation of quantum circuits is crucial for algorithm verification and hardware design. However, existing mainstream quantum circuit simulators face significant challenges in accurately predicting the behavior of real quantum devices. Most of these simulators are based on idealized quantum gate models, which fail to fully reflect the various physical noises and error propagation effects present in the operation of real superconducting quantum devices. As the scale of quantum processors and the complexity of circuits increase, the gap between this ideal model and the actual physical system becomes increasingly prominent, severely limiting the guiding value of simulation results for experiments.

[0003] To address the aforementioned issues, existing technical solutions mainly fall into two categories. One category directly employs ideal quantum gate models for circuit-level simulation. This method boasts high computational efficiency but completely ignores the details of physical implementation. The other, more advanced approach attempts to perform physical-level simulations under the Schrödinger representation. By introducing Transmon physical parameters and frequency-tuned controlled Z-gates, noise-free physical-level simulations are achieved. This category also proposes phase correction and gate fidelity evaluation methods under the interaction representation, bridging the gap between ideal models and physical reality to some extent, and providing an important foundation for more accurate quantum simulations.

[0004] However, these existing solutions still have significant shortcomings. 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 physics-level simulation schemes primarily focus on gate operation implementation under ideal conditions, neglecting the unavoidable noise effects in real quantum systems. Furthermore, some schemes attempt to add a noise approximation after the ideal gate operation. This "gate first, noise later" approach differs significantly from the real physical process and cannot accurately describe the dynamic impact and cumulative effect of noise during the gate operation.

[0005] Therefore, there is an urgent need in this field for a novel 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 the ideal evolution and noise effects of quantum systems within 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 applications. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to address the shortcomings of the prior art, and the following technical solution is provided:

[0007] 1) In a first aspect, the present invention provides a method for physical-level simulation and circuit simulation of superconducting quantum bits with noise modeling, the specific technical solution of which is as follows:

[0008] Under the Schrödinger representation, based on the physical parameters of the superconducting qubits of the quantum system and the gate operation type, a time-dependent Hamiltonian sequence corresponding to the quantum system is constructed.

[0009] Based on the noise parameters of each superconducting qubit in the quantum system, construct the noise operator corresponding to each superconducting qubit;

[0010] By incorporating the time-dependent Hamiltonian sequence and all noise operators into the Lindblad master equation, the density matrix of the quantum system is evolved, yielding the quantum state of the quantum system under the influence of noise.

[0011] The beneficial effects of the noise modeling-based physical-level simulation and circuit simulation method for superconducting quantum bits provided by this invention are as follows:

[0012] By incorporating time-dependent Hamiltonian sequences and noise operators into the Lindblad master equation for density matrix evolution, integrated modeling is achieved, fundamentally avoiding the artificial segmentation problem of gate-first, noise-later approaches in existing technologies. This makes the simulation process closer to the actual physical evolution of superconducting qubits. The method can construct corresponding noise operators based on the noise parameters of each superconducting qubit, including relaxation noise operators, pure decoherence noise operators, and ambient temperature noise operators. This incorporates key noise parameters such as temperature, relaxation time, and decoherence time into the simulation framework, improving the realism and reliability of the simulation results. Furthermore, this method constructs time-dependent Hamiltonian sequences under the Schrödinger representation, ensuring the accuracy of the physics-level simulation. Simultaneously, density matrix evolution fully describes the mixed-state characteristics of quantum states under noise influence. The resulting noisy quantum states (quantum states of quantum systems under noise influence) provide accurate basis for the performance evaluation of quantum circuits, effectively guiding the design optimization of superconducting quantum chips, the improvement of gate operation control strategies, and the performance prediction of quantum algorithms on practical hardware. This powerfully promotes the transformation of quantum computing from theoretical research to engineering applications.

[0013] Based on the above scheme, the physical-level simulation and circuit simulation method of superconducting quantum bits with noise modeling of the present invention can be further improved as follows.

[0014] Furthermore, under the Schrödinger representation, based on the physical parameters and gate operation types of the superconducting qubits of the quantum system, a time-dependent Hamiltonian sequence corresponding to the quantum system is constructed, including:

[0015] 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.

[0016] The beneficial effects of adopting the above-mentioned further scheme are as follows: By discretizing the continuous time-dependent Hamiltonian of the quantum system into a sequence of time-dependent Hamiltonians, accurate numerical realization of physical-level simulation is achieved. Based on the frequency-modulated trajectory of the controlled Z-gate operation of the quantum system and the physical parameters and gate operation type of the superconducting qubit, this method can accurately describe the dynamic evolution during the gate operation process. By transforming the continuous-time evolution into a discrete sequence through time-slicing technology, the authenticity of the physical process is preserved while providing feasibility for numerical calculation. This discretization process allows the evolution of complex quantum systems to be solved step by step through iteration, ensuring the numerical stability and computational accuracy of the simulation process. At the same time, this method establishes an accurate dynamic foundation for the subsequent introduction of noise operators and the evolution of the density matrix, enabling the entire simulation process to truly reflect the actual physical behavior of the superconducting qubit during the gate operation process, providing reliable technical support for evaluating quantum gate performance and optimizing control parameters.

[0017] Furthermore, it also includes:

[0018] 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.

[0019] The beneficial effects of adopting the above-mentioned further scheme are as follows: By calculating the state fidelity of quantum states under noise influence, an objective and effective evaluation basis is provided for assessing the impact of noise on quantum systems. By accurately comparing noisy quantum states with those in an ideal noise-free state, the cumulative degree of noise effects during quantum state evolution can be quantified. This state fidelity-based evaluation method can accurately reflect the impact of different noise sources on quantum gate operations and quantum circuit performance, providing a reliable performance metric for the physical-level simulation of superconducting qubits. The calculation of state fidelity provides direct guidance for quantum chip design optimization, helps identify noise-sensitive key components, and also provides a unified evaluation standard for comparing and improving quantum gate operation schemes. This technical feature gives the simulation results clear physical meaning and practical reference value, effectively supporting the performance evaluation and optimization of quantum computing systems.

[0020] Furthermore, the noise operators corresponding to each superconducting quantum bit include: relaxation noise operator, pure dephase noise operator, and ambient temperature noise operator.

[0021] The advantages of adopting the above-mentioned further scheme are as follows: By constructing relaxation noise operators, pure dephase noise operators, and ambient temperature noise operators, a systematic coverage of the main noise mechanisms of superconducting qubits is achieved. This comprehensive noise modeling can accurately describe the various physical effects faced by qubits in actual operation, including energy relaxation processes, phase coherence decay, and thermal excitation effects. By simultaneously considering three types of noise operators, the simulation process can comprehensively reflect the combined effects of multiple noise sources in real quantum devices, improving the realism and accuracy of physics-level simulations. This modular noise operator design facilitates the flexible configuration of different noise parameters and supports adjustments to the noise operators according to specific experimental conditions, thus providing a more reliable simulation basis for the performance evaluation and optimization of superconducting quantum computing systems.

[0022] 2) In a second aspect, the present invention also provides a physical-level simulation and circuit simulation system for superconducting quantum bits with noise modeling, the specific technical solution of which is as follows:

[0023] It includes a construction module, a noise operator construction module, and an evolution module;

[0024] The construction module 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 qubits of the quantum system;

[0025] The noise operator construction module 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.

[0026] 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.

[0027] Based on the above scheme, the physical-level simulation and circuit simulation system for superconducting quantum bits with noise modeling of the present invention can be further improved as follows.

[0028] Furthermore, the construction module is specifically used for:

[0029] 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.

[0030] Furthermore, it also includes a state fidelity calculation module, which is used for:

[0031] 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.

[0032] Furthermore, the noise operators corresponding to each superconducting quantum bit include: relaxation noise operator, pure dephase noise operator, and ambient temperature noise operator.

[0033] 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.

[0034] 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.

[0035] 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

[0036] 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:

[0037] 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.

[0038] 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.

[0039] Figure 3 This is a schematic diagram of the structure of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0040] 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.

[0041] 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.

[0042] 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:

[0043] S1. Under the Schrödinger representation, based on the physical parameters and gate operation types of the superconducting qubits of the quantum system, construct the time-varying sequence of the time-dependent Hamiltonians corresponding to the quantum system. Specifically, under the Schrödinger representation, based on the frequency modulation trajectory of the controlled Z-gate operation of the quantum system, and based on the physical parameters and gate operation types of the superconducting qubits of the quantum system, discretize the continuous time-dependent Hamiltonians of the quantum system into a time-dependent Hamiltonian sequence. This includes the following steps:

[0044] S10. Based on the physical parameters of the superconducting qubits and the gate operation type of the quantum system, determine the basic Hamiltonian structure of the quantum system. Specifically, it is necessary to analyze in detail the physical parameters of the superconducting qubits of the quantum system. These parameters include the energy level spacing of each qubit, the nonlinear characteristics of the Josephson junction, and the coupling strength between qubits. The energy level spacing determines the intrinsic energy level structure of the qubit, the nonlinear characteristics of the Josephson junction ensure the resolvable energy levels of the qubit, and the coupling strength describes the degree of interaction between qubits. Simultaneously, the specific form of the Hamiltonian is determined according to the gate operation type. For single-qubit gate operations, corresponding driving control terms need to be added to the Hamiltonian. These driving control terms describe the interaction between the external microwave field and the qubit. For two-qubit gate operations, especially controlled Z-gate operations, in addition to considering the single-qubit terms, coupling interaction terms also need to be added to the Hamiltonian. These coupling terms reflect the energy exchange mechanism between the two qubits. The finally determined basic Hamiltonian structure includes the intrinsic energy terms, driving control terms, and coupling interaction terms of the qubit, providing a complete theoretical framework and mathematical model foundation for the subsequent construction of time-dependent Hamiltonian sequences.

[0045] S11. For controlled Z-gate operations, the time dependence of the Hamiltonian needs to be defined based on its frequency modulation trajectory. The frequency modulation trajectory describes the precise path of the qubit frequency change over time when implementing a controlled Z-gate. This trajectory is typically designed based on the fast near-adiabatic principle. In practice, based on the energy level structure characteristics of the quantum system, especially the cross-crossing characteristic of the qubit energy levels, a frequency change curve that maximizes the gate operation fidelity while minimizing leakage error needs to be calculated. This frequency modulation trajectory must ensure that the qubit system can accumulate a precise π phase difference at the end of the gate operation, while avoiding excitation to non-computational energy levels. The design of the frequency modulation trajectory directly determines the time evolution of relevant parameters in the Hamiltonian and is a key factor in ensuring the accuracy and high fidelity of controlled Z-gate operations, requiring rigorous numerical optimization and physical verification.

[0046] S12. Based on physical parameters and frequency modulation trajectories, construct the continuous-time-dependent Hamiltonian of the quantum system. This continuous-time-dependent Hamiltonian introduces a complete mathematical description with time dependence on the basic Hamiltonian structure. For Transmon-type superconducting qubits, the intrinsic energy term is described using a nonlinear harmonic oscillator model, accurately reflecting the energy level structure of the qubit; the driving control term corresponds to the interaction of external control signals, and its specific form depends on the gate operation type 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 moment to the end of the gate operation, where the form of the Hamiltonian at each time point is jointly determined by the physical parameters, gate operation state, and instantaneous value of the frequency modulation trajectory at that time, ensuring accurate simulation of the real physical evolution process.

[0047] S13. To perform numerical simulations, the continuous time-dependent Hamiltonian needs to be discretized into a sequence of time-dependent Hamiltonians. The discretization process is achieved by dividing the total gate operation time into multiple small time intervals, typically hundreds to thousands of small time steps. During this division, a suitable time step needs to be determined based on the system's dynamic characteristics to ensure accurate capture of the fastest dynamic process. Within each time step, it is assumed that the system's Hamiltonian remains constant, and its value is taken as the continuous time-dependent Hamiltonian value corresponding to the midpoint of that time interval. The accuracy of discretization needs to be controlled by adjusting the time step. Typically, the time step needs to be much smaller than the system's fastest dynamic timescale, while also considering the balance between computational efficiency and numerical stability to ensure that the discretized sequence accurately reflects the dynamic characteristics of the original continuous Hamiltonian.

[0048] S14. The generated time-dependent Hamiltonian sequence will serve as the basis for quantum state evolution. This sequence is arranged in chronological order, with each element corresponding to the system's Hamiltonian value for a specific time interval. The first element in the sequence corresponds to the Hamiltonian at the initial moment, and the last element corresponds to the Hamiltonian at the end of the gate operation. The intermediate elements are arranged sequentially according to time progression. This sequence fully describes the evolution of the system's Hamiltonian during the gate operation, including all interaction terms and the influence of the external control field. In numerical simulations, this time-dependent Hamiltonian sequence will be directly input into the numerical solver to progressively advance the quantum state evolution calculation. The sequence's storage format needs to be specially optimized to support efficient large-scale numerical computation and fast data access, providing an accurate and reliable physical basis for subsequent density matrix evolution, noise modeling, and fidelity calculations.

[0049] The frequency modulation trajectory of controlled Z-gate operation refers to the path taken by adjusting the frequency of a superconducting qubit over time when implementing a controlled Z-gate. This trajectory is typically designed based on the fast near-adiabatic principle, controlling the frequency of the qubits to evolve along a specific curve to induce effective energy level crossings or avoid crossings between two superconducting qubits, thereby generating the phase change required for the controlled Z-gate. The frequency modulation trajectory ensures the accuracy and high fidelity of the gate operation while minimizing unnecessary energy level excitations and errors.

[0050] The physical parameters of a superconducting quantum bit include numerical values ​​describing its fundamental characteristics, such as its intrinsic frequency, energy level spacing, Josephson junction energy, charging energy, relaxation time, decoherence time, and pure decoherence time. These parameters determine the quantum bit's energy level structure, dynamic behavior, and the strength of its interaction with the environment, and form the basis for constructing Hamiltonian and noise models.

[0051] In this context, the gate operation type of a superconducting qubit refers to the various quantum logic gates executed in a quantum circuit, such as single-qubit gates and two-qubit gates. Single-qubit gates include X-gates, Y-gates, and Z-gates, which are typically implemented using external microwave pulses; two-qubit gates, such as controlled Z-gates, are implemented through frequency modulation or coupling modulation. Each gate operation type corresponds to a specific Hamiltonian form and control sequence, used to accurately describe the transformation of quantum states in simulations.

[0052] The continuous-time Hamiltonian is a mathematical object describing the continuous change of the energy operator of a quantum system over time. It encompasses all interaction terms of the system and the influence of external control fields, such as the driving, coupling, and frequency-modulating terms of the qubit. Under the Schrödinger representation, the continuous-time Hamiltonian determines the continuous evolution dynamics of the quantum state and is a core element in simulating the time-dependent behavior of quantum systems.

[0053] The time-dependent Hamiltonian sequence is a series of Hamiltonian values ​​obtained by discretizing continuous time-dependent Hamiltonians in the time domain. Each sequence element corresponds to an approximate constant Hamiltonian within a specific time interval, used for numerically solving the evolution equations. This discretization transforms complex continuous-time problems into computable discrete steps, facilitating the gradual progression of quantum state evolution in simulations.

[0054] S2. Based on the noise parameters of each superconducting qubit in the quantum system, construct the noise operator corresponding to each superconducting qubit;

[0055] The noise operators corresponding to each superconducting quantum bit include: relaxation noise operator, pure dephase noise operator, and ambient temperature noise operator.

[0056] Among them, the noise parameters of superconducting qubits are a set of key physical quantities used to quantify the coherence loss and state errors caused by their interaction with the environment, mainly including relaxation time. Decoherence time and pure retrieval coherence time .in, Characterizing superconducting qubits from excited state Spontaneous transition to the ground state The energy relaxation process, reciprocal It reflects the rate of energy dissipation; This describes the overall decay of the phase coherence of superconducting qubits, the value of which is affected by... Energy relaxation and Common constraints of pure phase noise, relaxation time Decoherence time and pure retrieval coherence time Satisfy physical relationship: In addition, ambient temperature With the main frequency of superconducting qubits Together, they determine the thermal occupation number of the excitation and relaxation processes in the thermal environment. These noise parameters together constitute the basic input for constructing various superconducting noise operators and performing physical-level noise simulations.

[0057] The specific implementation process for calculating the relaxation noise operator corresponding to each superconducting qubit is as follows:

[0058] Reading the relaxation time of each superconducting qubit Relaxation time It describes the quantum bit from the excited state. Spontaneously decays to the ground state The average time of energy relaxation is a physical quantity and a key indicator characterizing the energy relaxation process. This is applied to the first quantum quantum system... The relaxation time of a superconducting quantum bit is denoted as . .Will By directly substituting into the standard mathematical expression of the relaxation noise operator, we obtain the first... Relaxation noise operator corresponding to each superconducting quantum bit : This operation is performed one by one for all superconducting qubits participating in the simulation to ensure that the noise effect of each superconducting qubit is modeled independently and accurately, thereby obtaining the relaxation noise operator corresponding to each superconducting qubit.

[0059] in, It is the first An annihilation operator for a superconducting qubit. An annihilation operator is a fundamental concept in quantum mechanics; its function is to lower the energy level of a qubit by one order, for example, by annihilating an excited state. Transition to ground state This physically corresponds precisely to the microscopic behavior of a qubit losing one energy quantum during energy relaxation. The calculation first involves calculating... reciprocal of the parameter This value represents the relaxation rate of the superconducting qubit. Subsequently, taking the square root of this relaxation rate yields the coefficients of the relaxation noise operator. Finally, With the Annihilation operator of 1 qubit Perform scalar multiplication to ultimately construct a formula for describing the first... Relaxation noise operator for the energy relaxation effect of a superconducting quantum bit .

[0060] The calculated relaxation noise operators are integrated and stored. The relaxation noise operator generated for each superconducting qubit is added to a unified noise operator set. This set will be invoked later when constructing the Lindblad master equation, participating as part of the noise term in the dynamical evolution of the entire quantum system. During storage, each relaxation noise operator is associated with its corresponding superconducting qubit index. Associative binding is performed to ensure that the corresponding superconducting qubits can be correctly and accurately acted upon during the evolution process.

[0061] The specific implementation process for calculating the pure dephase noise operator corresponding to each superconducting quantum bit is as follows:

[0062] Reading the pure decoherence time of each superconducting qubit Pure decoherence time It is a physical quantity that specifically describes the loss of coherence of superconducting qubits caused by random phase fluctuations; it is independent of the energy relaxation process. The first... The decoherence time of one qubit is denoted as According to the first Whether a quantum bit is a two-level or multi-level system, the appropriate mathematical expression is chosen to calculate the pure dephase noise operator. Specifically:

[0063] 1) For a two-level system, its pure dephase noise operator is given by the formula The calculation is obtained. In this formula, It acts on the first Pauli Z operators on superconducting qubits. The Pauli Z operator is a diagonal matrix in the computational basis; its essential effect is to introduce an energy-level-dependent phase into the quantum state, thereby accurately simulating the random diffusion of phase information. Indicates: the The pure dephase noise operator corresponding to each qubit.

[0064] 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.

[0065] 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.

[0066] 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.

[0067] The specific implementation process for calculating the ambient temperature noise operator for each superconducting quantum bit is as follows:

[0068] 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 .

[0069] Calculate the first Hot occupation number of superconducting qubits Specifically, the Bose-Einstein distribution formula is used to calculate:

[0070]

[0071] in, It is the reduced Planck constant. This is Boltzmann's constant. When making calculations, it is necessary to ensure that the units of all physical quantities are consistent with the International System of Units (SI). It is the first The dominant frequency of a superconducting quantum bit is specifically calculated by first calculating the exponent term. Then calculate the value of the natural exponential function, subtract 1, and take the reciprocal to obtain the final value. Hot occupation number of superconducting qubits The heat occupation number represents the temperature at which heat is generated. In a thermal equilibrium environment, the main frequency is The average excitation quantum number of the quantum mode quantizes the excitation intensity of the superconducting quantum bit by the ambient thermal fluctuations.

[0072] Then, based on the calculated heat occupancy number An ambient temperature noise operator is constructed. The ambient temperature noise operator consists of two parts: a lower transition operator and an upper transition operator. The lower transition operator... The relaxation process of a qubit from a high energy level to a low energy level in a thermal environment is simulated using the following formula:

[0073]

[0074] Up-transition operator The transition process of a qubit from a low energy level to a high energy level caused by environmental thermal excitation is calculated using the following formula:

[0075]

[0076] in, It is the first An annihilation operator for a superconducting quantum bit This refers to the corresponding generation operator. The coefficients of both operators need to be calculated separately, with the coefficient of the down-transition operator being... The coefficients of the up-transition operator are Then, these coefficients are multiplied by their corresponding operators.

[0077] The above operation is performed one by one for all superconducting qubits that require modeling of the ambient temperature noise operator, and the ambient temperature noise operator corresponding to each superconducting qubit is calculated.

[0078] Subsequently, the calculated ambient temperature noise operators are integrated and stored. Down-transition operators are generated for each superconducting qubit. and the transition operator They will be added as a noise pair to a unified set of noise operators. During storage, these two operators will be associated with their corresponding superconducting qubit indices. Clearly define the associations and label them as ambient temperature noise types to ensure they can be correctly invoked together when constructing the Lindblad master equations later.

[0079] S3. Introduce the time-dependent Hamiltonian sequence and all noise operators 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. Specifically:

[0080] S30. The initial state of the quantum system needs to be initialized. Depending on the simulation requirements, the density matrix of the quantum system is set to a specific initial state, typically starting from a pure state such as the ground state, or, depending on the circuit requirements, to other specific quantum states. This initial density matrix will serve as the starting point for the evolution process.

[0081] S31. Using the time-slicing method, the evolution of the quantum system is progressively advanced according to the time order defined in the time-dependent Hamiltonian sequence. For each time slice in the sequence, the corresponding Hamiltonian and all constructed noise operators within that time segment are obtained. Then, the complete Lindblad master equation is constructed:

[0082]

[0083] Among them, dissipation terms The specific form is as follows:

[0084]

[0085] Here, ρ represents the density matrix of the quantum system. It is the core mathematical quantity describing the quantum states of the system, and its special characteristic is that it can simultaneously represent pure states and mixed states. In noisy open quantum systems, due to entanglement between the system and its environment, a single state vector is insufficient to fully describe the system's state, and the density matrix must be used. The diagonal elements of the density matrix represent the probability distribution of the system in each ground state, while the off-diagonal elements characterize the coherence between different quantum states. This represents the Hamiltonian operator corresponding to the k-th time segment in a discrete-time series. It originates from the time-dependent Hamiltonian sequence generated in S13. . It encapsulates all the energy information of the system within that specific time interval, including the eigenenergy of the superconducting qubits, the interactions driven by the control field, and the coupling energy between the qubits. It is the root cause driving the deterministic unitary evolution of the system. Generally refers to the k-th noise operator, also often called the Lindblad operator or jump operator. It is not a single operator, but rather represents the set of all constructed noise operators. This is the quantum jump term. It describes the noise operator. The actual effect of the physical processes represented (such as energy decay and phase reversal) on ρ is the term that causes a sudden change in the quantum state. This is the product of the adjoint operator and the original operator of the noise operator, forming a Hermitian operator. It can be understood as a "rate operator" or "noise intensity operator" associated with the noise channel, whose expected value is proportional to the probability rate at which the noise process occurs. This is a compensation or dissipation term. It must be introduced to keep the trace (total probability) of the density matrix always 1 and to return to the standard von Neumann equations in the absence of noise. Mathematically, it ensures the complete positive definiteness and trace conservation properties of the evolution process.

[0086] Within each time step, this differential equation needs to be solved numerically. Typically, numerical integration methods such as the Runge-Kutta method are used to calculate the rate of change of the density matrix under the Lindblad master equation based on the current time step's density matrix state, and then update the density matrix state for the next time step. This process requires ensuring that the time step is small enough to meet numerical stability requirements.

[0087] S32. During the evolution process, different types of noise operators need to be specially handled. For relaxation noise operators, the main effects are on the diagonal and off-diagonal elements of the density matrix; for pure dephase noise operators, the main effect is the attenuation of the off-diagonal elements of the density matrix; for ambient temperature noise operators, the combined effects of both the upper and lower transition operators need to be considered. All these noise effects are uniformly handled within the framework of the Lindblad master equation.

[0088] S33. After completing the evolution of all time segments, output the final density matrix as the quantum state of the quantum system under the influence of noise. This density matrix contains complete information on all Hamiltonian interactions and noise accumulation throughout the entire evolution process, and can be used for subsequent fidelity calculations and quantum state analysis.

[0089] The Lindblad master equation is the standard mathematical description of the dynamical evolution of open quantum systems. It can simultaneously describe the unitary evolution process and the non-unitary dissipative process of a quantum system. The equation consists of two main parts: the first part is the Hamiltonian evolution term, which describes the ideal evolution behavior of the quantum state under the action of the energy operator; the second part is the dissipative term, composed of a series of noise operators, used to model various decoherence and relaxation effects caused by the interaction between the system and its environment. The Lindblad master equation provides a rigorous and complete theoretical framework for the noisy evolution of quantum systems.

[0090] The density matrix of a quantum system is a mathematical tool for describing the state of a quantum system. It can uniformly describe both pure and mixed quantum states. Unlike state vectors, which can only describe pure quantum states, the density matrix can describe the probabilistic mixture of different quantum states. This property makes it particularly suitable for handling open quantum systems with noise and uncertainty. In simulations, the elements of the density matrix contain statistical information about all observable quantities of the system, including important physical quantities such as particle number distribution and coherence strength.

[0091] In quantum mechanics, evolution refers to the dynamic process of a quantum system's state changing over time. Within the framework of the Lindblad master equations, evolution specifically refers to the continuous change of the density matrix under the influence of Hamiltonian driving forces and noise operators. This process encompasses several aspects, including the natural evolution of the system's energy, the logical transformations of quantum gate operations, and the decoherence effects caused by environmental noise. Numerical evolution approximates this continuous change process by discretizing the time domain and employing iterative calculations, ultimately obtaining the quantum state of the quantum system at a specific moment.

[0092] Optionally, the above technical solution also includes:

[0093] S4. Compare the quantum state of the quantum system under noise with the quantum state of the quantum system under ideal noise-free conditions, and calculate the state fidelity of the quantum state of the quantum system under noise.

[0094] The process of acquiring the quantum state of a quantum system under ideal noise-free conditions is as follows:

[0095] S40. It is necessary to construct an evolutionary framework for quantum systems under ideal conditions. This process takes place under the Schrödinger representation, using the exact same initial quantum state and time-dependent Hamiltonian sequence as in noisy evolution. The key difference is that ideal evolution completely ignores the effects of all noise operators, i.e., it assumes that the quantum system is a closed system completely isolated from the external environment.

[0096] S41. The evolution of quantum states is advanced through numerical integration of the Schrödinger equation. The Schrödinger equation is of the following form:

[0097]

[0098] In practical numerical computation, time-dependent Hamiltonian sequences are used in this process. For each time segment in the sequence, the system obtains the corresponding Hamiltonian. Numerical algorithms, such as the Runge-Kutta method or a matrix exponent-based exact solver, are used to compute the evolution operator within that time step, and then this operator is applied to the current state vector. Update the state vector to the next time point. .

[0099] During the evolution process, especially for gate operations like controlled Z-gates implemented through frequency modulation, phase correction is typically required after the evolution is complete. This is because physical-level evolution can generate additional dynamic phase. The system corrects these phases by applying virtual RZ gate operations. Virtual RZ gates are a type of mathematical processing performed at the software level that directly adjusts the phase factor of the state vector to ensure that the final quantum state is perfectly 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 phase correction, the resulting state vector... This refers to the quantum state of a quantum system under ideal, noise-free conditions. This pure state will serve as a benchmark for subsequent fidelity comparisons with results containing noise.

[0100] The specific implementation process for calculating the state fidelity of a quantum system under noise is as follows:

[0101] S42. Define the input for calculating state fidelity. The input consists of two parts: the first part is the quantum state of the quantum system under noise influence, obtained through the evolution of the Lindblad master equation, which is a density matrix. The first part describes the mixed state after being affected by actual noise; the second part is the quantum state of the quantum system obtained by the above process under ideal noise-free conditions, which is a pure state. .

[0102] S43. Based on the specific manifestations of the two quantum states, select and apply the corresponding mathematical definition of state fidelity for calculation:

[0103] 1) When the density matrix containing noise is... With the ideal pure state When making comparisons, state fidelity The calculation formula is:

[0104]

[0105] This calculation is numerically equivalent to taking the density matrix. The middle corresponds to the ideal state The diagonal matrix element. Its physical meaning is: the mixed state prepared in actual experiments or simulations. What percentage of them are in the ideal target state that we expect?

[0106] 2) As a more general case, if it is necessary to analyze two density matrices... and To calculate fidelity, for example, to compare the outputs under two different noise models, the generalized fidelity formula is used:

[0107]

[0108] This calculation involves the square root of a matrix and multiplication, which needs to be performed using a linear algebra numerical library.

[0109] S44, Ideal State and the density matrix containing noise As input, a predefined fidelity calculation function is invoked. This function first determines the type of the input quantum state. After confirming that one side is a pure state and the other is a density matrix, the function selects the first formula for calculation. The calculation process involves multiplying the ideal state vector and the density matrix, then left-multiplying by the conjugate transpose of the ideal state vector, ultimately obtaining a scalar real number between 0 and 1, which is the state fidelity. . This indicates complete agreement. It indicates complete orthogonality.

[0110] S45. Output and record the state fidelity calculation result. The value, as a 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 qubit 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.

[0111] In the field of quantum chip design, a quantum system can be a multi-qubit superconducting quantum processor based on the Transmon architecture. Using the method of this invention, the physical parameters of the superconducting qubits of the system, including the energy level spacing and coupling strength of each qubit, are first determined based on the qubit arrangement and coupling structure in the chip design. Based on these parameters, a frequency-modulated trajectory of a controlled Z-gate operation is constructed, generating the corresponding time-dependent Hamiltonian sequence. Simultaneously, the noise parameters of each qubit in the chip design specifications, including relaxation time, are determined. Decoherence time and ambient temperature Corresponding relaxation noise operators, pure dephase noise operators, and ambient temperature noise operators are constructed. These Hamiltonian sequences and noise operators are then introduced into the Lindblad master equation to evolve the system density matrix, ultimately obtaining the quantum states of the chip design under noise influence. Using the obtained noisy quantum states, their state fidelity can be calculated. By comparing the quantum state fidelity indices of different chip design schemes, quantitative basis is provided for optimizing the physical layout and material selection of quantum chips, thereby guiding the manufacture of higher-performance quantum processors.

[0112] 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 this invention, for different controlled Z-gate control strategies, based on their specific frequency modulation trajectories and pulse waveforms, and combined with the physical parameters of the superconducting qubits of the quantum system, corresponding time-dependent Hamiltonian sequences are constructed. Simultaneously, a complete noise model including relaxation noise operators and pure dephase noise operators is constructed based on measured noise parameters. The output quantum states under each control scheme are obtained through the evolution of the Linblad master equation. Using these noisy quantum states, their state fidelity to the ideal target state is calculated, which can accurately quantify the noise sensitivity of different frequency modulation trajectories, thereby selecting the gate control scheme with optimal noise resistance performance and providing reliable technical guidance for experimentally realizing high-fidelity quantum gate operations.

[0113] In the field of quantum algorithm evaluation, a quantum system can be a superconducting quantum processor running a specific quantum algorithm. Using the method of this invention, a complete time-dependent Hamiltonian sequence is constructed based on the quantum gate sequence involved in the algorithm, including single-qubit and two-qubit gate operation types, combined with the specific physical parameters of the superconducting quantum bits. Simultaneously, based on the actual noise parameters of the target quantum hardware, a comprehensive noise model incorporating relaxation, decoherence, and ambient temperature effects is constructed. The noisy quantum state after algorithm execution is obtained through the evolution of the Linblad master equation. Using this quantum state, its state fidelity is calculated, which can accurately predict the execution performance of algorithms such as quantum chemical simulations or combinatorial optimizations on real hardware, providing key technical basis for algorithm parameter adjustment, hardware selection, and algorithm fault tolerance threshold analysis.

[0114] In the field of quantum error correction verification, a quantum system can be a superconducting quantum circuit integrating specific error-correcting codes. Using the method of this invention, auxiliary bits and corresponding error-correcting gates are added to a basic quantum system to construct a time-dependent Hamiltonian sequence containing error-correcting steps. Simultaneously, a noise operator is constructed based on actual noise parameters, and the error-corrected quantum state is obtained through evolution using the Lindblad master equation. Using this noisy quantum state, by comparing the state fidelity of the output quantum state after adopting different error-correction schemes, the suppression effect of each error-correcting code on specific noise modes can be objectively evaluated. This provides reliable technical guidance for selecting the most suitable error-correction scheme for hardware noise characteristics and promotes the practical development of fault-tolerant quantum computing.

[0115] The overall objective of this invention is to propose a physical-level simulation and circuit simulation method for superconducting qubits with noise modeling. Under the Schrödinger representation, based on the physical parameters of the superconducting qubits and the gate operation types, a time-varying sequence of time-dependent Hamiltonians corresponding to the quantum system is constructed. The physical parameters of the superconducting qubits include energy level spacing, coupling strength, and Josephson junction energy; the gate operation types include single-qubit and two-qubit gate operations, particularly controlled Z-gate operations. Simultaneously, based on the noise parameters of each superconducting qubit in the quantum system, a noise operator corresponding to each superconducting qubit is constructed; the noise parameters include relaxation time. Decoherence time Pure decoherence time and ambient temperature Noise operators include relaxation noise operators, pure dephase noise operators, and ambient temperature noise operators. Subsequently, 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 noise influence. The standard form of the Lindblad master equation is:

[0116]

[0117] in, This represents the noise dissipation term. Finally, the quantum states of the quantum system under noise are compared with those under ideal noise-free conditions. The state fidelity of the quantum states under noise is calculated, thus completing the evaluation of the quantum circuit performance. This method achieves integrated simulation of physical-level gate operations and noise effects, enabling more accurate prediction of the behavior of real quantum hardware.

[0118] In this invention, noise and physical gate operations are modeled in an integrated manner within the same time-evolution framework. The Lindblad master equation combines the time-dependent Hamiltonian sequence and noise operators to achieve the joint evolution of the quantum system's density matrix. This modeling approach avoids the artificial "gate-first, noise-later" separation found in traditional methods, better reflecting the physical processes of superconducting qubits in actual devices and ensuring the realism and accuracy of the simulation results. Noise modeling is integrated as an independent module into the simulation framework, based on the qubit's noise parameters (such as relaxation time). Decoherence time Pure decoherence time and ambient temperature The system automatically generates different types of noise operators, including relaxor noise operators, pure dephase noise operators, and ambient temperature noise operators. This modular design allows users to flexibly configure and extend the noise model, easily adapting to the characteristics of different quantum hardware platforms. The simulation system automatically selects the solution strategy based on the presence or absence of noise operators. When at least one noise operator is constructed, the system uses density matrix evolution to solve the Lindblad master equation; when no noise operator is constructed, the system degenerates into Schrödinger equation evolution for state vectors. This adaptive mechanism ensures the accuracy of noise simulation while also considering computational efficiency in the noise-free case.

[0119] In this invention, firstly, under the Schrödinger representation, a time-dependent Hamiltonian sequence corresponding to the quantum system is constructed based on the physical parameters of the superconducting qubits and the gate operation type. The physical parameters of the superconducting qubits include the energy level spacing of each qubit, the nonlinear characteristics of the Josephson junction, and the coupling strength between qubits. The gate operation types 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 based on its frequency modulation trajectory. The frequency modulation trajectory describes the path of the qubit frequency change over time, ensuring 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, within which the Hamiltonian is approximately constant. Secondly, based on the noise parameters of each superconducting qubit in the quantum system, a noise operator corresponding to each superconducting qubit is constructed. The noise operators include relaxation noise operators, pure dephase noise operators, and ambient 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 states of the quantum system under noise influence. Finally, the simulation results are evaluated by calculating state fidelity. Detailed explanations are provided below using specific examples.

[0120] Example A: Based on The relaxation noise modeling includes the following steps:

[0121] 1) Construction of Time-Dependent Hamiltonians: The Transmon model is used to describe superconducting qubits, considering inter-qubit coupling and controlled Z-gate operations achieved through frequency modulation. Under the Schrödinger representation, based on the physical parameters of the superconducting qubits and the gate operation type of the quantum system, the continuous time-dependent Hamiltonians are discretized into a sequence of time-dependent Hamiltonians. Each of them This corresponds to the Hamiltonian value for a given time segment. After evolution, phase correction is performed using a virtual RZ operation to eliminate dynamic phase errors.

[0122] 2) Noise modeling: When the quantum bit has a relaxation time When considering parameters, a relaxation noise operator is constructed for each qubit. For the ... The relaxation noise operator for a quantum bit is:

[0123]

[0124] in, It is the first An annihilation operator for 10 qubits.

[0125] 3) Numerical evolution: in each time slice In this system, the system follows the Lindblad master equation:

[0126]

[0127] in, The equation is solved using numerical integration methods (such as the Runge-Kutta method), and the density matrix state is updated.

[0128] 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.

[0129] Example B: Pure decoherence and The mapping process includes the following steps:

[0130] 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.

[0131] 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:

[0132]

[0133] For a two-level system, the first The pure dephase noise operator for 1 qubit is:

[0134]

[0135] in, It is the Pauli-Z operator. For multi-level systems, the pure dephase noise operator is:

[0136]

[0137] in, It is a number operator.

[0138] 3) Numerical evolution: Introducing the pure dephase noise operator into the Lindblad master equation:

[0139]

[0140] The noisy quantum state is obtained by numerical solution.

[0141] 4) Fidelity calculation: After the evolution is completed, calculate the state fidelity and evaluate the impact of pure decoherent noise on the quantum state.

[0142] Example C: Ambient temperature noise calculation, including the following steps:

[0143] 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.

[0144] 2) Noise modeling: based on ambient temperature and quantum bit frequency Calculate the heat occupancy number:

[0145]

[0146] 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:

[0147]

[0148] in, It is the decay rate parameter, usually related to... Related, defined as .

[0149] 3) Numerical Evolution: Introducing the ambient temperature noise operator into the Lindblad master equation:

[0150]

[0151] The noisy quantum state is obtained by numerical solution.

[0152] 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.

[0153] 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.

[0154] The technical terms appearing in this application are explained as follows:

[0155] 1) Superconducting Qubit: A type of qubit that utilizes a Josephson junction in a superconducting circuit. A common type is Transmon.

[0156] 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.

[0157] 3) Schrödinger representation: one of the ways of describing quantum mechanics, which treats quantum states as objects that evolve over time.

[0158] 4) Hamiltonian The mathematical operator of system energy determines the dynamic behavior of a quantum system.

[0159] 5) Density matrix A tool for describing the state of a quantum system, capable of representing pure states and noisy mixtures.

[0160] 6) Lindblad master equation: a standard form for describing the evolution of noisy quantum systems. This represents the noise channel.

[0161] 7) Time: Quantum bits from excited state Decay to ground state The average time.

[0162] 8) Time: The average time it takes for a quantum bit to maintain coherence, affected by... Both phase noise and other limitations.

[0163] 9) Time: Pure decoherence time, the loss of coherence caused only by phase fluctuations.

[0164] 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.

[0165] 11) Number Operators : An operator used to count the number of quantum bit excitations.

[0166] 12) Oppose easy operators : A commonly used mathematical operator, used in Lindblad equations to represent the dissipative component.

[0167] 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.

[0168] 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.

[0169] 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.

[0170] 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;

[0171] 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;

[0172] 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.

[0173] Optionally, in the above technical solution, the construction module 201 is specifically used for:

[0174] 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.

[0175] Optionally, the above technical solution also includes a state fidelity calculation module, which is used for:

[0176] 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.

[0177] 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.

[0178] 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.

[0179] 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.

[0180] 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.

[0181] 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.

[0182] 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.

[0183] 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.

[0184] 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.

[0185] 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 3 The 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.

[0186] 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.

[0187] 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.

[0188] 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.

[0189] 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.

[0190] 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.

[0191] 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.

[0192] 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.

[0193] 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).

[0194] 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.

[0195] 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.

[0196] 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.

[0197] 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.

[0198] 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.

[0199] 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.

[0200] 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, include: Under the Schrödinger representation, based on the physical parameters of the superconducting qubits of the quantum system and the gate operation type, a time-dependent Hamiltonian sequence corresponding to the quantum system is constructed, including: under the Schrödinger representation, based on the frequency modulation trajectory of the controlled Z-gate operation of the quantum system, and based on 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; Based on the noise parameters of each superconducting quantum bit in the quantum system, a noise operator corresponding to each superconducting quantum bit is constructed. The noise operators corresponding to each superconducting quantum bit include: relaxation noise operator, pure dephase noise operator and ambient temperature noise operator. Introducing the time-dependent Hamiltonian sequence and all noise operators into the Lindblad master equation, the density matrix of the quantum system is evolved to obtain the quantum states of the quantum system under noise influence, including: The density matrix of the quantum system is initialized to its initial state; Using a time-slicing method, the evolution of the quantum system is progressively advanced according to the time order defined in the time-dependent Hamiltonian sequence. For each time segment in the time-dependent Hamiltonian sequence, the corresponding Hamiltonian operator, the relaxation noise operator, the pure dephase noise operator, and the ambient temperature noise operator are obtained to construct the complete Lindblad master equation. ,in, , Represents the dissipation term. Represents the density matrix, This represents the Hamiltonian operator corresponding to the k-th time segment. Let k represent the k-th noise operator, which includes at least one of the relaxed noise operator, the pure dephase noise operator, and the ambient temperature noise operator. express The adjoint operator; Within each time step, the Lindblad master equation is solved numerically, and the rate of change is calculated based on the density matrix state of the current time step and updated to the density matrix state of the next time step. During the evolution process, the relaxation noise operator affects the diagonal and off-diagonal elements of the density matrix; the pure dephase noise operator causes the off-diagonal elements of the density matrix to decay; and the ambient temperature noise operator takes into account the combined effects of the upper and lower transition operators of the ambient temperature noise operator. After completing the evolution of all time segments, the final density matrix is ​​output as the quantum state of the quantum system under the influence of noise.

2. The method for physical-level simulation and circuit simulation of superconducting quantum bits with noise modeling according to claim 1, characterized in that, Also includes: The state fidelity of the quantum state under noise influence is calculated by comparing the quantum state of the quantum system under ideal noise-free conditions.

3. A physical-level simulation and circuit simulation system for superconducting quantum bits with noise modeling, characterized in that, It includes a construction module, a noise operator construction module, and an evolution module; The construction module 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, including: under the Schrödinger representation, discretizing the continuous time-dependent Hamiltonian of the quantum system into a time-dependent Hamiltonian sequence based on the frequency modulation trajectory of the controlled Z-gate operation of the quantum system and the physical parameters and gate operation type of the superconducting qubit of the quantum system; The noise operator construction module is used to: construct a noise operator corresponding to each superconducting quantum bit according to the noise parameters of each superconducting quantum bit in the quantum system. 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. 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 noise influence, including: The density matrix of the quantum system is initialized to its initial state; Using a time-slicing method, the evolution of the quantum system is progressively advanced according to the time order defined in the time-dependent Hamiltonian sequence. For each time segment in the time-dependent Hamiltonian sequence, the corresponding Hamiltonian operator, the relaxation noise operator, the pure dephase noise operator, and the ambient temperature noise operator are obtained to construct the complete Lindblad master equation. ,in, , Represents the dissipation term. Represents the density matrix, This represents the Hamiltonian operator corresponding to the k-th time segment. Let k represent the k-th noise operator, which includes at least one of the relaxed noise operator, the pure dephase noise operator, and the ambient temperature noise operator. express The adjoint operator; Within each time step, the Lindblad master equation is solved numerically, and the rate of change is calculated based on the density matrix state of the current time step and updated to the density matrix state of the next time step. During the evolution process, the relaxation noise operator affects the diagonal and off-diagonal elements of the density matrix; the pure dephase noise operator causes the off-diagonal elements of the density matrix to decay; and the ambient temperature noise operator takes into account the combined effects of the upper and lower transition operators of the ambient temperature noise operator. After completing the evolution of all time segments, the final density matrix is ​​output as the quantum state of the quantum system under the influence of noise.

4. The superconducting quantum bit physics-level simulation and circuit simulation system with noise modeling according to claim 3, characterized in that, It also includes a state fidelity calculation module, which is used for: The state fidelity of the quantum state under noise influence is calculated by comparing the quantum state of the quantum system under ideal noise-free conditions.

5. An electronic device, characterized in that, The method 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 the physical-level simulation and circuit simulation method for superconducting quantum bits with noise modeling as described in any one of claims 1 to 2.

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, which, when executed by a processor, implements the physical-level simulation and circuit simulation method for superconducting quantum bits with noise modeling as described in any one of claims 1 to 2.

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