Random simulation method and device for open quantum system

Abstract

The invention provides a stochastic simulation method and device for an open quantum system, and the method comprises the steps: decomposing the total Hamiltonian of a new system into a linear term combination of a Fouli operator, and constructing a combination of quantum gates through the coefficient of the linear term combination. And then, operating a classical sampling method taking a Fouli operator as a sampling sample, constructing a quantum circuit by using the combination of quantum gates, and finally obtaining a mean value of the target observed quantity in the open quantum system according to an operation result of the quantum circuit. According to the method, a large-scale actual quantum system dynamics problem is simulated by utilizing a shallow quantum circuit, limitation of quantum chip resources is relieved, an error relieving technology is utilized, the circuit depth is reduced, a part of calculation processes are allocated to a classic computer, and processes related to observed quantity are only operated on the quantum computer, so that the calculation efficiency is improved. And the calculation results of the two parts are integrated on a classic computer, so that quantum hardware resources are saved.

Description

Technical Field

[0001] One or more embodiments of the present specification relate to the field of quantum computers, and in particular, to a random simulation method and device for an open quantum system. Background Art

[0002] The calculation of observed quantities in existing quantum systems is all based on the corresponding closed quantum system. In the closed system, the evolution of the quantum state is unitary, periodic, and oscillatory, which can be described by the Schrödinger equation. During the evolution, the quantum state is always pure. However, open quantum systems are inevitably affected by environmental noise, so that the pure state becomes a mixed state. This process is non-unitary, non-periodic, oscillatory or continuously decaying. Usually, under the assumption of weak coupling with the environment and that the environment is Markov, this process can be described by the Lindblad master equation.

[0003] When the scale of an open quantum system is large, the amount of computation required for the Lindblad master equation increases exponentially with the scale of the system. Classical dynamics simulation methods are often limited by accuracy, memory, and simulation speed, making it difficult to effectively simulate open quantum systems. In this case, quantum algorithms have become a promising alternative that may reduce the exponential growth of costs. However, when high-order accuracy is required, quantum algorithms may require many auxiliary quantum bits, complex quantum control logic, or involve additional quantum state amplitude amplification processes. Therefore, compared with closed quantum system simulation algorithms, the implementation of these algorithms is much more complicated, making the simulation of open quantum systems difficult to implement in quantum computers. Summary of the invention

[0004] This application describes a random simulation method and device for an open quantum system, which can solve the above technical problems.

[0005] According to a first aspect, a random simulation method for an open quantum system is provided, the method comprising:

[0006] The Lindblad master equation is bridged by stochastic differential equations to approximately transform the open quantum system into a new closed system, and the total Hamiltonian of the new closed system is derived as the newly constructed total Hamiltonian, wherein the newly constructed total Hamiltonian incorporates the system Hamiltonian of the open quantum system and the dissipative term of the interaction between the system and the environment, and the dimension of the new closed system is higher than that of the open quantum system;

[0007] Decomposing the newly constructed time evolution operator of the total Hamiltonian into a linear term combination of Pauli operators, constructing a combination of quantum gates using coefficients of the linear term combination, and using the combination of quantum gates to calculate a target observable in an open quantum system;

[0008] A classical sampling method using Pauli operators as sampling samples is run to obtain sampled Pauli operators, the sampled Pauli operators are mapped to the combination of quantum gates, a quantum circuit is constructed using the combination of quantum gates, and a mean value of a target observed quantity in the open quantum system is obtained according to the operation result of the quantum circuit.

[0009] In some embodiments, decomposing the newly constructed time evolution operator of the total Hamiltonian into a linear combination of Pauli operators, and constructing a combination of quantum gates using coefficients of the combination of linear terms, specifically includes:

[0010] Using Lee-Trotter iterative decomposition and Richardson extrapolation method, the time evolution operator of the newly constructed total Hamiltonian is decomposed into a linear superposition of the product of the correction operator and the Lee-Trotter formula;

[0011] Constructing the correction operator through the unit matrix and the local truncation error;

[0012] The linear term in the local truncation error is decomposed into a linear term combination of Pauli operators, and the coefficients in the linear term combination are used to construct the combination of quantum gates.

[0013] In some more specific embodiments, the Li-Trotter iterative decomposition and Richardson extrapolation method are used to decompose the time evolution operator of the newly constructed total Hamiltonian into a linear superposition of the product of the correction operator and the Li-Trotter formula, and the correction operator is represented by a unit matrix and a local truncation error, specifically including:

[0014] According to the derived , combining the principal term rotation method and the Richardson extrapolation method to design the classical sampling algorithm and the corresponding quantum Monte Carlo circuit to find any observable The mean of

[0015] The principle of quantum simulation is based on:

[0016]

[0017]

[0018] and Is the construction The middle term of

[0019] Among them, the 2m-order Lie-Trotter-Suzuki product formula Iterate the calculation according to the following formula:

[0020]

[0021] in, ,

[0022] ,

[0023] In the above formula, Main item It means The low-order terms of are also local truncation errors, and , is the remainder The higher-order terms of is the identity matrix, is the identity matrix, is a parameter related to the order, is the order, is the correction operator, where yes The conjugate transpose of is the total Hamiltonian Unitary time evolution operator at time t, m is an integer.

[0024] In some embodiments, decomposing the linear term in the local phase error into a linear combination of Pauli operators and constructing a combination of quantum gates using coefficients in the linear combination specifically includes:

[0025] The local truncation error Pauli Operator Linear combination of ,in is the first coefficient in the linear combination;

[0026] Calculate the absolute value and the absolute value of the first coefficient in the linear combination ;

[0027] By the absolute value and Determine the rotation angle , ;

[0028] By the first coefficient and the rotation angle , determine the second coefficient , ;

[0029] Using the first coefficient The second coefficient and the Pauli operator , constructing a combination of quantum gates , is the Pauli operator The quantum gate, is the first coefficient The sign of determines the rotation direction of the quantum gate.

[0030] In some embodiments, the running of the classical sampling method using the Pauli operator as a sampling sample to obtain the sampled Pauli operator, mapping the sampled Pauli operator to the combination of the quantum gates, constructing a quantum circuit using the combination of the quantum gates, and obtaining the mean of the target observation in the open quantum system according to the running result of the quantum circuit, specifically includes:

[0031] Run a classical sampling method using Pauli operators as sampling samples on a classical computer to obtain sampled Pauli operators, map the sampled Pauli operators to a combination of quantum gates, and obtain a quantum circuit;

[0032] Execute the quantum circuit on a quantum computer to obtain an expected value of the target observation;

[0033] The above operation is repeatedly performed, and the mean value of the target observed quantity in the open quantum system is determined according to the expected value obtained during the multiple operation processes.

[0034] In some embodiments, the method of using the stochastic differential equation as a bridge to approximately map the newly constructed total Hamiltonian in the open quantum system by using the Lindblad master equation as a bridge specifically includes:

[0035] The Lindblad master equation is randomly approximated and converted into a stochastic differential equation.

[0036] Based on the stochastic differential equation, a newly constructed total Hamiltonian in the open quantum system is derived .

[0037] According to a second aspect, there is provided a random simulation device for an open quantum system, the device comprising:

[0038] A first processing module is used to approximately map a newly constructed total Hamiltonian in an open quantum system using a stochastic differential equation as a bridge to the Lindblad master equation, wherein the newly constructed total Hamiltonian incorporates a system Hamiltonian of the open quantum system and a dissipative term of the interaction between the system and the environment;

[0039] The second processing module is used to convert the open quantum system into a new closed system approximately by using the stochastic differential equation as a bridge of the Lindblad master equation, and derive the total Hamiltonian of the new closed system as the newly constructed total Hamiltonian, wherein the newly constructed total Hamiltonian integrates the system Hamiltonian of the open quantum system and the dissipative term of the interaction between the system and the environment, and the dimension of the new closed system is higher than that of the open quantum system;

[0040] The third processing module is used to run a classical sampling method using Pauli operators as sampling samples to obtain sampled Pauli operators, map the sampled Pauli operators to a combination of the quantum gates, construct a quantum circuit using the combination of the quantum gates, and obtain a mean value of a target observed quantity in the open quantum system according to an operation result of the quantum circuit.

[0041] In some embodiments, the second processing module is specifically used to decompose the time evolution operator of the newly constructed total Hamiltonian into a linear superposition of the product of the correction operator and the Lee-Trotter formula by using Lee-Trotter iterative decomposition and Richardson extrapolation method, and represent the correction operator by a unit matrix and a local truncation error;

[0042] The local truncation error is decomposed into a linear term combination of Pauli operators, and the coefficients in the linear term combination are used to construct the combination of quantum gates.

[0043] In some more specific embodiments, the second processing module is specifically configured to generate a total Hamiltonian according to the newly constructed , combining the principal term rotation method and the Richardson extrapolation method to design the classical sampling algorithm and the corresponding quantum Monte Carlo circuit to find the mean of any observed quantity;

[0044] The principle of quantum simulation is based on:

[0045]

[0046]

[0047] and Is the construction The middle term of

[0048] Among them, the 2m-order Lie-Trotter-Suzuki product formula Iterate the calculation according to the following formula:

[0049]

[0050] in, ,

[0051] ,

[0052] In the above formula, Main item It means The low-order terms of are also local truncation errors, and , is the remainder The higher-order terms of is the identity matrix, is the identity matrix, is a parameter related to the order, is the order, is the correction operator, where yes The conjugate transpose of is the total Hamiltonian Unitary time evolution operator at time t, m is an integer.

[0053] In some more specific embodiments, the second processing module is specifically configured to convert the local truncation error Pauli Operator Linear combination of ,in is the first coefficient in the linear combination;

[0054] The absolute value and the absolute value of the first coefficient in the linear combination are calculated using the principal term rotation method. ;

[0055] By the absolute value and Determine the rotation angle , ;

[0056] By the first coefficient and the rotation angle , determine the second coefficient , ;

[0057] Using the first coefficient The second coefficient and the Pauli operator , constructing a combination of quantum gates , is the Pauli operator The quantum gate, is the first coefficient The sign of determines the rotation direction of the quantum gate.

[0058] In some embodiments, the third processing module is specifically used to run a classical sampling method using Pauli operators as sampling samples on a classical computer to obtain sampled Pauli operators, and map the sampled Pauli operators to a combination of quantum gates to obtain a quantum circuit;

[0059] Execute the quantum circuit on a quantum computer to obtain an expected value of the target observation;

[0060] The above operation is repeatedly performed, and the mean value of the target observed quantity in the open quantum system is determined according to the expected value obtained during the multiple operation processes.

[0061] In some embodiments, the first processing module is specifically used to perform randomized approximation processing on the Lindblad master equation to convert it into a stochastic differential equation;

[0062] Based on the stochastic differential equation, a newly constructed total Hamiltonian in the open quantum system is derived .

[0063] According to a third aspect, a computer storage medium is provided, on which a computer program is stored. When the computer program is executed by one or more processors, the random simulation method of an open quantum system as described in any one of the above technical solutions is implemented.

[0064] According to a fourth aspect, an electronic device is provided, comprising a memory and one or more processors, wherein a computer program is stored in the memory, and when the computer program is executed by the one or more processors, a random simulation method for an open quantum system as described in any one of the above technical solutions is implemented.

[0065] In the above-mentioned system and method provided in the embodiments of this specification, shallower quantum circuits are used to simulate large-scale actual quantum system dynamics problems, thereby alleviating the limitation of quantum chip resources. Error mitigation technology is used to reduce the circuit depth, and part of the calculation process is allocated to the classical computer, while only the process involving the observable quantity is run on the quantum computer. Finally, the two parts of the calculation results are combined, saving precious quantum hardware resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0067] Figure 1 A schematic diagram showing the direct mapping of the Lindblad master equation provided in the embodiments of this specification into a Schrödinger-like equation; Figure 2 A schematic diagram of a first block coding method provided in an embodiment of this specification is shown; Figure 3 A schematic diagram of a second block coding method provided in an embodiment of this specification is shown; Figure 4 A schematic diagram showing a flow chart of a random simulation method for a quantum system provided in an embodiment of this specification; Figure 5 A schematic diagram showing a flow chart of a random simulation method for an open quantum system provided in an embodiment of this specification; Figure 6 A schematic diagram showing a random simulation device for an open quantum system provided in an embodiment of this specification. DETAILED DESCRIPTION

[0068] The solution provided in this specification is described below in conjunction with the accompanying drawings.

[0069] In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described below in conjunction with the accompanying drawings.

[0070] In the description of the embodiments of the present application, words such as "exemplary", "for example" or "for example" are used to indicate examples, illustrations or descriptions. Any embodiment or design described as "exemplary", "for example" or "for example" in the embodiments of the present application should not be interpreted as being more preferred or more advantageous than other embodiments or designs. Specifically, the use of words such as "exemplary", "for example" or "for example" is intended to present related concepts in a concrete way.

[0071] In the description of the embodiments of the present application, the term "and / or" is merely a description of the association relationship of associated objects, indicating that three relationships may exist. For example, A and / or B may represent: A exists alone, B exists alone, and A and B exist at the same time. In addition, unless otherwise specified, the term "plurality" means two or more.

[0072] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include one or more of the features. The terms "include", "comprises", "has" and their variations all mean "including but not limited to", unless otherwise specifically emphasized.

[0073] Since the quantum noise of the environment cannot be avoided in the quantum world, the actual open quantum system is weakly coupled with the environment and the environment is Markovian. The process can be described by the Lindblad master equation. In order to simulate the open quantum system, in a scheme architecture, such as Figure 1As shown, the Lindblad master equation is directly mapped into a Schrödinger-like equation. The non-unitary process is constructed into a larger unitary process by adding appropriate auxiliary quantum bits (qubits). After running for a period of time, post-selection measurements are performed on the auxiliary system so that the remaining main system satisfies the Lindblad master equation. However, each step of evolution will inevitably lead to the loss of quantum resources with a certain probability, and the overall resources are lost at an exponential rate of the number of evolution steps n. When the system is small, the evolution time is short, the sub-circuits are shallow, and the number of evolution steps is small, the resource loss is acceptable. When the system is large or the evolution time is long, the accumulated loss is unacceptable, making the simulation unable to continue.

[0074] One current solution is to use block coding techniques to handle time-dependent Hamiltonian operators and jump operators. One such coding method is Figure 2 As shown, the Claus operator is decomposed into a unitary operator that can be approximated by a matrix exponential, where the dissipation parameters in the Lindblad master equation are given by These four matrices are encoded. This approach has been applied to the vectorized form of the Lindblad equation. However, it does not fully characterize the numerical or model errors. More importantly, this approach requires the density matrix to be input as dimensional vector, where is the dimension of the Hilbert space. Another block coding method is Figure 3 As shown, the dissipative operator Directly encode into Figure 3 The form shown here forms a large Hermitian Hamiltonian , we can build deeper quantum circuits on quantum computers and simulate the evolution of open quantum systems for a longer period of time. However, when simulating the Schrödinger equation, if we use the traditional Trotter formula to simulate directly, we will have to wait for a few seconds in each step. Accuracy, line depth must be at least , the line expenditure will be huge.

[0075] In order to solve the problem of line expenses when simulating the Schrödinger equation, the first prior art is to map the Lindblad master equation to a Schrödinger-like equation, then expand it to a high-dimensional Hermitian system by adding auxiliary qubits, and finally project and numerically post-process it through post-selection, and then convert it back to the Lindblad master equation. This type of solution requires the calculation of a relatively large matrix time-integral in the middle, which is difficult to calculate when the system is large due to the high matrix dimension. In addition, in the post-selection process, there is a probability loss and resource loss at each step, making it difficult to simulate for a long time. The second prior art is a solution based on Kraus decomposition. This type of solution is usually based on the Kraus decomposition form of the master equation, which is a non-Hermitian matrix, and then unitary expansion is performed, and finally the simulation is realized by performing post-selection measurement on the auxiliary qubit. This type of solution requires an intermediate matrix to be decomposed into eigenvalues ​​for Kraus decomposition of the master equation. The computational complexity increases exponentially with the size of the system, which is difficult to perform in practice and can only be used for very small systems. The third prior art is a solution based on a variational quantum algorithm. This type of solution usually transforms the Lindblad master equation into a non-Hermitian linear differential equation, such as through vectorization or through the stochastic Schrödinger equation, and then uses a variational quantum algorithm to realize the relevant state evolution. The main disadvantages of this type of solution include that each step requires a measurement process, which is cumbersome and may introduce additional measurement errors. When the system is large in scale, due to the increase in the number of parameters to be solved, the "barren plateau problem" that often occurs in this algorithm may occur, resulting in the inability to continue the calculation.

[0076] In order to solve the above problems, Figure 4 It is shown that the present invention maps the open quantum system simulation problem into the Hamiltonian simulation problem based on the stochastic differential equation (SDE), uses the quantum circuit Monte Carlo (QCMC) technology, combines the principal term rotation method and the Richardson extrapolation method, and combines the respective advantages of classical computers and quantum computers to design an open quantum system random simulator, which can simulate the open quantum system with high precision. The scheme of the invention mainly includes: writing the relevant Lindblad master equation according to the open quantum system to be simulated; performing randomized approximation processing on the Lindblad master equation and converting it into a stochastic differential equation, and using the stochastic differential equation to derive the Hamiltonian of the open quantum system ; According to the derived , combining the leading-order-rotation method and the Richardson extrapolation method to design the classical sampling algorithm and the corresponding quantum Monte Carlo circuit, running the classical sampling algorithm on a classical computer, and running the quantum Monte Carlo circuit on a quantum computer based on the overall samples obtained on the classical computer to determine the mean of the target observation in the open quantum system.

[0077] like Figure 5 The random simulation method of an open quantum system includes the following steps:

[0078] 110. The Lindblad master equation is bridged by stochastic differential equations to approximately transform the open quantum system into a new closed system, and the total Hamiltonian of the new closed system is derived as the newly constructed total Hamiltonian. The newly constructed total Hamiltonian integrates the system Hamiltonian of the open quantum system and the dissipative term of the interaction between the system and the environment. The dimension of the new closed system is higher than that of the open quantum system.

[0079] Specifically, the Lindblad master equation is:

[0080] The Lindblad master equation describes the time evolution of the quantum state of an open quantum system. The density matrix Contains all possible quantum state information of the open quantum system quantum state at time t, is the system Hamiltonian of an open quantum system, describing the interactions within the open quantum system. describes the evolution of an open quantum system when it has no interaction with the external environment, describes the dissipation of an open quantum system interacting with its environment, is the jth operator interacting with the environment, yes The conjugate transpose of Describes the decoherence effects caused by the interaction of an open quantum system with its environment.

[0081] The Lindblad master equation is randomly approximated and converted into a stochastic differential equation with an approximate accuracy of , stochastic differential equation:

[0082]

[0083] Utilize during conversion Processing, where The wave function represents the quantum state at time t. The open quantum system may be in a mixture of multiple pure states, each of which has a certain probability. The expectation value operator is to calculate the statistical average effect of these pure states.

[0084] Stochastic differential equations describe the evolution of open quantum systems under random conditions. represents the change of the quantum state of an open quantum system, describes the unitary evolution of an open quantum system in the absence of external perturbations, Describes the dissipative term associated with the interaction between an open quantum system and its environment, represents the deterministic evolution of an open quantum system due to the Hamiltonian and dissipative terms. represents the random evolution of the quantum state of an open quantum system due to random interactions with the environment, is the increment of the Brownian motion associated with the jth environment, which is used to simulate the influence of the environment on the open quantum system.

[0085] Write the stochastic differential equation in Kraus form and compute the Kraus operator ;

[0086]

[0087] It should be noted that the stochastic differential equation is written in Kraus form here. The equation written in Kraus form is approximate to the original stochastic differential equation, but no Kraus decomposition is performed.

[0088] By adding quantum bit A, we can find the evolution operator of the open quantum system: , and the state of the open quantum system is obtained:

[0089]

[0090] The above formula describes the open quantum system after interacting with the environment, iteratively updating the density matrix through unitary evolution and partial trace operation. ,in is a unitary evolution operator, which represents the open quantum system in time The positive process of evolution, represents the reverse process of the evolution of an open quantum system at time ∆t, and the projection operator Indicates that the auxiliary quantum bit is in the ground state, m indicates the number of auxiliary quantum bits, and TrA indicates a partial trace operation on subsystem A.

[0091] The above equation is derived to obtain the newly constructed total Hamiltonian of the open quantum system: , the newly constructed total Hamiltonian of the open quantum system It includes the system Hamiltonian H of the open quantum system, the Hamiltonian of the environment, and the interaction Hamiltonian between the open quantum system and the environment.

[0092] In this embodiment, the above method is used to avoid the problem of mapping the Lindblad master equation into an F matrix during the process of solving the Lindblad master equation. Since the F matrix has a very high dimension, it is difficult to implement on a classical computer.

[0093] 120. The time evolution operator of the newly constructed total Hamiltonian is decomposed into a linear combination of Pauli operators. The coefficients of the linear combination are used to construct a combination of quantum gates. The combination of quantum gates is used to calculate the target observable in the open quantum system.

[0094] Specifically, the time evolution operator of the newly constructed total Hamiltonian is decomposed into a linear superposition of the product of the correction operator and the Lee-Trotter formula by using the Lee-Trotter iterative decomposition and Richardson extrapolation method, and the correction operator is represented by a unit matrix and a local truncation error.

[0095] Specifically, according to the newly constructed total Hamiltonian , combining the principal term rotation method and the Richardson extrapolation method to design the classical sampling algorithm and the corresponding quantum Monte Carlo circuit to find the mean of any observed quantity;

[0096] The principle of quantum simulation is based on:

[0097]

[0098]

[0099] and Is the construction The middle term of

[0100] Among them, the 2m-order Lie-Trotter-Suzuki product formula Iterate the calculation according to the following formula:

[0101]

[0102] in, ,

[0103] ,

[0104] In the above formula, Main item It means The low-order terms of are also local truncation errors, and , is the remainder The higher-order terms of is the identity matrix, is the identity matrix, is a parameter related to the order, is the order, is the correction operator, where yes The conjugate transpose of is the total Hamiltonian Unitary time evolution operator at time t, m is an integer.

[0105] Specifically, is the identity matrix, which is used to represent the part of the open quantum system that does not change during the evolution process. The local truncation error represents the approximate unitary evolution operator The difference with the time evolution operator of the total Hamiltonian, including the linear term and higher-order terms .

[0106] Using Richardson extrapolation, the local truncation error The exponential order of is increased to a preset value.

[0107] yes The low-order terms of can be calculated explicitly, , is the remainder The higher-order terms of .

[0108] Specifically, the local phase error is decomposed into a linear combination of Pauli operators, and the coefficients in the linear term combination are used to construct a combination of quantum gates, including:

[0109] The local truncation error Pauli Operator Linear combination of ,in is the corresponding Pauli operator The first coefficient of

[0110] The linear term of the local truncation error Pauli Operator Linear combination of ,in is the first coefficient in the linear combination;

[0111] Computes the absolute value and sum of the first coefficients in a linear combination ;

[0112] By the absolute value and Determine the rotation angle , ;

[0113] Through the first coefficient and rotation angle , determine the second coefficient , ;

[0114] Using the first coefficient The second coefficient and the Pauli operator , constructing a combination of quantum gates ,in is the Pauli operator The quantum gate, is the first coefficient The sign of determines the rotation direction of the quantum gate.

[0115] 130. Run the classical sampling method with Pauli operators as sampling samples to obtain the sampled Pauli operators, map the sampled Pauli operators to the combination of quantum gates, use the combination of quantum gates to construct quantum circuits, and obtain the mean of the target observation in the open quantum system based on the operation results of the quantum circuits.

[0116] Specifically, a classical sampling method using Pauli operators as sampling samples is run on a classical computer to obtain sampled Pauli operators, and the sampled Pauli operators are mapped to a combination of quantum gates to obtain a quantum circuit;

[0117] Execute the quantum circuit on the quantum computer to obtain the expected value of the target observation;

[0118] The above operations are performed repeatedly, and the mean value of the target observed quantity in the open quantum system is determined based on the expected values ​​obtained during multiple operations.

[0119] Specifically, the observable can be a physical quantity, such as magnetic field intensity or energy intensity. In the field of quantum chemistry, the random simulation method of open quantum systems can be applied to simulate chemical molecular structures, chemical reactions, etc., to achieve more efficient and lower energy consumption chemical design. When applied to chemical reactions, the Lindblad master equation is bridged by stochastic differential equations to approximately transform the chemical reaction as an open quantum system into a new closed system, and the total Hamiltonian of the new closed system is derived as the newly constructed total Hamiltonian, where the newly constructed total Hamiltonian incorporates the system Hamiltonian of the open quantum system and the dissipative term of the interaction between the system and the environment. The dimension of the new closed system is higher than that of the open quantum system, and the dissipative term is the interaction of the environment with the chemical reaction. Finally, by simulating chemical reactions, the physical and chemical data of the products of the chemical reactions can be obtained.

[0120] Simulating molecular structures and electronic states, which are computationally intensive on conventional computers. VQE works by initializing the quantum computer to a default state, then converting it to some desired (non-parameterized) reference state, selecting a parameterized quantum circuit (ansatz) to prepare the trial wave function, and iteratively adjusting the circuit parameters to minimize the expectation value of the Hamiltonian. This approach effectively approximates the ground state energy of molecules in quantum chemistry simulations.

[0121] In this embodiment, the above method is used to simulate large-scale actual quantum system dynamics problems using shallower quantum circuits, thereby alleviating the limitation of quantum chip resources. Error mitigation technology is used to reduce circuit depth, and part of the calculation process is allocated to the classical computer, while only the process involving the observable quantity is run on the quantum computer. Finally, the two parts of the calculation results are combined, saving precious quantum hardware resources.

[0122] like Figure 5 A random simulation device of an open quantum system is shown, comprising:

[0123] The first processing module is used to convert the open quantum system into a new closed system approximately by using the stochastic differential equation as a bridge of the Lindblad master equation, and derive the total Hamiltonian of the new closed system as a newly constructed total Hamiltonian, wherein the newly constructed total Hamiltonian integrates the system Hamiltonian of the open quantum system and the dissipative term of the interaction between the system and the environment, and the dimension of the new closed system is higher than that of the open quantum system;

[0124] A second processing module is used to decompose the time evolution operator of the newly constructed total Hamiltonian into a linear term combination of Pauli operators, and construct a combination of quantum gates using coefficients of the linear term combination, wherein the combination of quantum gates is used to calculate a target observable in an open quantum system;

[0125] The third processing module is used to run a classical sampling method using Pauli operators as sampling samples to obtain sampled Pauli operators, map the sampled Pauli operators to a combination of the quantum gates, construct a quantum circuit using the combination of the quantum gates, and obtain a mean value of a target observed quantity in the open quantum system according to an operation result of the quantum circuit.

[0126] In some embodiments, the second processing module is specifically used to decompose the time evolution operator of the newly constructed total Hamiltonian into a linear superposition of the product of the correction operator and the Lee-Trotter formula by using Lee-Trotter iterative decomposition and Richardson extrapolation method, and represent the correction operator by a unit matrix and a local truncation error;

[0127] The local truncation error is decomposed into a linear term combination of Pauli operators, and the coefficients in the linear term combination are used to construct the combination of quantum gates.

[0128] In some more specific embodiments, the second processing module is specifically configured to generate a total Hamiltonian according to the newly constructed , combining the principal term rotation method and the Richardson extrapolation method to design the classical sampling algorithm and the corresponding quantum Monte Carlo circuit to find the mean of any observed quantity;

[0129] The principle of quantum simulation is based on:

[0130]

[0131]

[0132] and Is the construction The middle term of

[0133] Among them, the 2m-order Lie-Trotter-Suzuki product formula Iterate the calculation according to the following formula:

[0134]

[0135] in, ,

[0136] ,

[0137] In the above formula, Main item It means The low-order terms of are also local truncation errors, and , is the remainder The higher-order terms of is the identity matrix, is the identity matrix, is a parameter related to the order, is the order, is the deviation correction operator. yes The conjugate transpose of is the total Hamiltonian Unitary time evolution operator at time t, m is an integer.

[0138] In some more specific embodiments, the second processing module is specifically configured to convert the local truncation error Pauli Operator Linear combination of ,in is the first coefficient in the linear combination;

[0139] The absolute value and the absolute value of the first coefficient in the linear combination are calculated using the principal term rotation method. ;

[0140] By the absolute value and Determine the rotation angle , ;

[0141] By the first coefficient and the rotation angle , determine the second coefficient , ;

[0142] Using the first coefficient The second coefficient and the Pauli operator , constructing a combination of quantum gates , is the Pauli operator The quantum gate, is the first coefficient The sign of determines the rotation direction of the quantum gate.

[0143] In some embodiments, the third processing module is specifically used to run a classical sampling method using Pauli operators as sampling samples on a classical computer to obtain sampled Pauli operators, and map the sampled Pauli operators to a combination of quantum gates to obtain a quantum circuit;

[0144] Execute the quantum circuit on a quantum computer to obtain an expected value of the target observation;

[0145] The above operation is repeatedly performed, and the mean value of the target observed quantity in the open quantum system is determined according to the expected value obtained during the multiple operation processes.

[0146] In some embodiments, the first processing module is specifically used to perform randomized approximation processing on the Lindblad master equation to convert it into a stochastic differential equation;

[0147] Based on the stochastic differential equation, a newly constructed total Hamiltonian in the open quantum system is derived .

[0148] The present invention also provides a computer storage medium, on which a computer program is stored. When the computer program is executed by one or more processors, the random simulation method for an open quantum system as described in any one of the above technical solutions is implemented.

[0149] The present invention also provides an electronic device, comprising a memory and one or more processors, wherein the memory stores a computer program, and when the computer program is executed by the one or more processors, the random simulation method for an open quantum system as described in any one of the above technical solutions is implemented.

[0150] The specific implementation methods described above further illustrate the purpose, technical solutions and beneficial effects of the present application in detail. It should be understood that the above description is only the specific implementation methods of the present application and is not intended to limit the scope of protection of the present application. Any modifications, equivalent substitutions, improvements, etc. made on the basis of the technical solutions of the present application should be included in the scope of protection of the present application.

Claims

1. A random simulation method for an open quantum system, characterized in that: The method comprises: The Lindblad master equation is bridged by stochastic differential equations to approximately transform the open quantum system into a new closed system, and the total Hamiltonian of the new closed system is derived as the newly constructed total Hamiltonian, wherein the newly constructed total Hamiltonian incorporates the system Hamiltonian of the open quantum system and the dissipative term of the interaction between the system and the environment, and the dimension of the new closed system is higher than that of the open quantum system; Decomposing the newly constructed time evolution operator of the total Hamiltonian into a linear term combination of Pauli operators, constructing a combination of quantum gates using coefficients of the linear term combination, and using the combination of quantum gates to calculate a target observable in an open quantum system; A classical sampling method using Pauli operators as sampling samples is run to obtain sampled Pauli operators, the sampled Pauli operators are mapped to the combination of quantum gates, a quantum circuit is constructed using the combination of quantum gates, and a mean value of a target observed quantity in the open quantum system is obtained according to the operation result of the quantum circuit.

2. The method according to claim 1, characterized in that Decomposing the newly constructed total Hamiltonian time evolution operator into a linear combination of Pauli operators, and constructing a combination of quantum gates using coefficients of the linear term combination, specifically includes: By using Lee-Trotter iterative decomposition and Richardson extrapolation method, the time evolution operator of the newly constructed total Hamiltonian is decomposed into a linear superposition of the product of a correction operator and a Lee-Trotter formula, and the correction operator is represented by a unit matrix and a local truncation error; The local truncation error is decomposed into a linear term combination of Pauli operators, and the coefficients in the linear term combination are used to construct the combination of quantum gates.

3. The method according to claim 2, characterized in that The method uses Lee-Trotter iterative decomposition and Richardson extrapolation to decompose the newly constructed time evolution operator of the total Hamiltonian into a linear superposition of the product of the correction operator and the Lee-Trotter formula, and represents the correction operator by a unit matrix and a local truncation error, specifically including: According to the newly constructed total Hamiltonian , combining the principal term rotation method and the Richardson extrapolation method to design the classical sampling algorithm and the corresponding quantum Monte Carlo circuit to find the mean of any observed quantity; The principle of quantum simulation is based on: and Is the construction The middle term of Among them, the 2m-order Lie-Trotter-Suzuki product formula Iterate the calculation according to the following formula: in, , ， In the above formula, Main item It means The low-order terms of are also local truncation errors, and , is the remainder The higher-order terms of is the identity matrix, is a parameter related to the order, is the order, is the correction operator, where yes The conjugate transpose of is the total Hamiltonian Unitary time evolution operator at time t, m is an integer.

4. The method according to claim 3, characterized in that Decomposing the local phase error into a linear combination of Pauli operators and constructing a combination of quantum gates using coefficients in the linear term combination specifically includes: The local truncation error Pauli Operator Linear combination of ,in is the first coefficient in the linear combination; Calculate the absolute value and the absolute value of the first coefficient in the linear combination ; By the absolute value and Determine the rotation angle , ; By the first coefficient and the rotation angle , determine the second coefficient , ; Using the first coefficient The second coefficient and the Pauli operator , constructing a combination of quantum gates ,in is the Pauli operator The quantum gate, is the first coefficient The sign of determines the rotation direction of the quantum gate.

5. The method according to claim 1, characterized in that The method of running a classical sampling method using Pauli operators as sampling samples to obtain sampled Pauli operators, mapping the sampled Pauli operators to a combination of quantum gates, constructing a quantum circuit using the combination of quantum gates, and obtaining a mean value of a target observed quantity in the open quantum system according to the operation result of the quantum circuit, specifically includes: Run a classical sampling method using Pauli operators as sampling samples on a classical computer to obtain sampled Pauli operators, map the sampled Pauli operators to a combination of quantum gates, and obtain a quantum circuit; Execute the quantum circuit on a quantum computer to obtain an expected value of the target observation; The above operation is repeatedly performed, and the mean value of the target observed quantity in the open quantum system is determined according to the expected value obtained during the multiple operation processes.

6. The method according to claim 1, characterized in that The Lindblad master equation is bridged by stochastic differential equations to approximately transform the open quantum system into a new closed system, and the total Hamiltonian of the new closed system is derived as the newly constructed total Hamiltonian, specifically including: The Lindblad master equation is randomly approximated and converted into a stochastic differential equation. By adding auxiliary bits, the open system is approximately transformed into a new closed system; Derive the total Hamiltonian of the new closed system .

7. A random simulation device for an open quantum system, characterized in that: The device comprises: The first processing module is used to convert the open quantum system into a new closed system approximately by using the stochastic differential equation as a bridge of the Lindblad master equation, and derive the total Hamiltonian of the new closed system as a newly constructed total Hamiltonian, wherein the newly constructed total Hamiltonian integrates the system Hamiltonian of the open quantum system and the dissipative term of the interaction between the system and the environment, and the dimension of the new closed system is higher than that of the open quantum system; A second processing module is used to decompose the time evolution operator of the newly constructed total Hamiltonian into a linear term combination of Pauli operators, and construct a combination of quantum gates using coefficients of the linear term combination, wherein the combination of quantum gates is used to calculate a target observable in an open quantum system; The third processing module is used to run a classical sampling method using Pauli operators as sampling samples to obtain sampled Pauli operators, map the sampled Pauli operators to a combination of the quantum gates, construct a quantum circuit using the combination of the quantum gates, and obtain a mean value of a target observed quantity in the open quantum system according to an operation result of the quantum circuit.

8. The device according to claim 7, characterized in that The second processing module is specifically used to decompose the time evolution operator of the newly constructed total Hamiltonian into a linear superposition of the product of the correction operator and the Lee-Trotter formula by using Lee-Trotter iterative decomposition and Richardson extrapolation method, and represent the correction operator by a unit matrix and a local truncation error; The local truncation error is decomposed into a linear term combination of Pauli operators, and the coefficients in the linear term combination are used to construct the combination of quantum gates.

9. A computer storage medium, characterized in that The computer-readable storage medium stores a computer program, and when the computer program is executed by one or more processors, the random simulation method of an open quantum system as claimed in any one of claims 1 to 6 is implemented.

10. An electronic device, characterized in that: The method comprises a memory and one or more processors, wherein a computer program is stored in the memory, and when the computer program is executed by the one or more processors, the random simulation method of the open quantum system according to any one of claims 1 to 6 is implemented.

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