Method, device, equipment and storage medium for determining characteristic information of quantum system

Abstract

The present disclosure provides a method, device, equipment and storage medium for determining characteristic information of a quantum system, which relates to the field of data processing, and in particular to the field of quantum computing. The specific implementation scheme is: obtaining the decomposition information of the total Hamiltonian of the target quantum system, wherein the decomposition information is represented as: #imgabs0##imgabs1#H represents the total Hamiltonian, h k is the sub-Hamiltonian of the target quantum system, and m is a natural number greater than or equal to 2; for the sub-Hamiltonian h in the decomposition information k Perform imaginary time evolution to obtain system characteristic information of the target quantum system, wherein the system characteristic information includes at least one of the following: ground state, ground state energy. In this way, characteristic information of the target quantum system, such as ground state or ground state energy, is effectively extracted, thus providing support for studying the properties of the target quantum system.

Description

Technical Field

[0001] The present disclosure relates to the field of data processing technology, and in particular to the field of quantum computing. Background Art

[0002] In physics and chemistry, a very important issue is to find the ground state of physical systems such as molecules, atoms, and crystals. Therefore, how to extract the ground state energy of physical systems has become a research hotspot. Summary of the invention

[0003] The present disclosure provides a method, device, equipment and storage medium for determining characteristic information of a quantum system.

[0004] According to one aspect of the present disclosure, a method for determining characteristic information of a quantum system is provided, comprising:

[0005] Obtain decomposition information of the total Hamiltonian of the target quantum system, wherein the decomposition information is expressed as: H represents the total Hamiltonian, h k is the sub-Hamiltonian of the target quantum system, and m is a natural number greater than or equal to 2;

[0006] For the sub-Hamiltonian h in the decomposition information k Perform imaginary time evolution to obtain system characteristic information of the target quantum system, wherein the system characteristic information includes at least one of the following: ground state and ground state energy.

[0007] According to another aspect of the present disclosure, a device for determining characteristic information of a quantum system is provided, comprising:

[0008] An acquisition unit is used to acquire decomposition information of the total Hamiltonian of the target quantum system, wherein the decomposition information is expressed as: H represents the total Hamiltonian, h k is the sub-Hamiltonian of the target quantum system, and m is a natural number greater than or equal to 2;

[0009] An imaginary time evolution unit, used for the sub-Hamiltonian h in the decomposition information k Perform imaginary time evolution to obtain system characteristic information of the target quantum system, wherein the system characteristic information includes at least one of the following: ground state and ground state energy.

[0010] According to another aspect of the present disclosure, there is provided a classical electronic device, comprising:

[0011] at least one processor; and

[0012] a memory communicatively connected to the at least one processor; wherein,

[0013] The memory stores instructions that can be executed by the at least one processor. The instructions are executed by the at least one processor so that the at least one processor can perform the above-mentioned method.

[0014] According to another aspect of the present disclosure, there is provided a quantum computing device, comprising:

[0015] at least one quantum processing unit;

[0016] a memory coupled to at least one QPU and configured to store executable instructions,

[0017] The instructions are executed by the at least one quantum processing unit to enable the at least one quantum processing unit to perform the method described above.

[0018] According to yet another aspect of the present disclosure, a non-transitory computer-readable storage medium storing computer instructions is provided, wherein when at least one quantum processing unit executes the computer instructions, the computer instructions cause the at least one quantum processing unit to perform the above method.

[0019] According to yet another aspect of the present disclosure, a non-transitory computer-readable storage medium storing computer instructions is provided, wherein the computer instructions are used to enable the computer to execute the above method.

[0020] According to another aspect of the present disclosure, a computer program product is provided, comprising a computer program, wherein the computer program implements the above method when executed by at least one quantum processing unit; or,

[0021] The computer program implements the above-mentioned method when executed by a processor.

[0022] In this way, characteristic information of the target quantum system, such as the ground state or ground state energy, is effectively extracted, thus providing support for studying the properties of the target quantum system.

[0023] It should be understood that the content described in this section is not intended to identify the key or important features of the embodiments of the present disclosure, nor is it intended to limit the scope of the present disclosure. Other features of the present disclosure will become easily understood through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] The accompanying drawings are used to better understand the present solution and do not constitute a limitation of the present disclosure.

[0025] Figure 1 The following is a schematic diagram of the implementation process of the method for determining characteristic information of a quantum system according to an embodiment of the present disclosure. Figure 1 ;

[0026] Figure 2 The following is a schematic diagram of the implementation process of the method for determining characteristic information of a quantum system according to an embodiment of the present disclosure. Figure 2 ;

[0027] Figure 3 is a schematic diagram of a method for determining characteristic information of a quantum system in an embodiment of the disclosed solution in a specific example;

[0028] Figure 4 The structure of the device for determining characteristic information of a quantum system according to an embodiment of the present disclosure is shown in FIG. Figure 1 ;

[0029] Figure 5 The structure of the device for determining characteristic information of a quantum system according to an embodiment of the present disclosure is shown in FIG. Figure 2 ;

[0030] Figure 6 It is a block diagram of an electronic device used to implement the method for determining characteristic information of a quantum system according to an embodiment of the present disclosure. DETAILED DESCRIPTION

[0031] The following is a description of exemplary embodiments of the present disclosure in conjunction with the accompanying drawings, including various details of the embodiments of the present disclosure to facilitate understanding, which should be considered as merely exemplary. Therefore, it should be recognized by those of ordinary skill in the art that various changes and modifications may be made to the embodiments described herein without departing from the scope and spirit of the present disclosure. Similarly, for the sake of clarity and conciseness, descriptions of well-known functions and structures are omitted in the following description.

[0032] It should be noted that the ground state refers to the quantum state with the lowest energy of a physical system. In theory, the ground state of a physical system is determined by the Hamiltonian of the physical system. The Hamiltonian is a physical quantity related to the total energy of a physical system, generally denoted as H, which can be expressed mathematically by a Hermitian matrix, that is, a conjugate symmetric complex matrix. Taking a quantum system as an example, if the quantum system includes n quantum bits (Qubit) (also called n qubits, each qubit corresponds to a quantum bit), then the Hamiltonian H of the quantum system can be expressed by a 2 n ×2 n Correspondingly, the ground state energy of the quantum system is the minimum eigenvalue of the Hamiltonian H of the quantum system, and the ground state of the quantum system is the eigenvector corresponding to the minimum eigenvalue. Therefore, solving the problem of the ground state energy and ground state of a physical system, such as a quantum system, is transformed into solving the problem of solving the minimum eigenvalue and corresponding eigenvector of the matrix H.

[0033] It is understandable that the ground state of a physical system determines most of the properties of the system at low temperatures, such as the stable structure of molecules and crystals, chemical reaction rates, conductivity, magnetism, etc. Therefore, solving the ground state has very important applications in cutting-edge fields such as condensed matter physics and quantum chemistry. Moreover, many combinatorial optimization problems can also be transformed into problems of solving the ground state of the Hamiltonian, and solving the ground state also has important applications in classical optimization problems.

[0034] Although the solution to the ground state problem can be achieved through solutions such as the Variational Quantum Eigensolver (VQE), existing solutions have limitations in solving the ground state problem of large-scale physical systems (such as quantum systems containing more than 15 quantum bits). For example, they cannot overcome the barren plateau phenomenon and increase the computational cost of the algorithm, reducing its effectiveness.

[0035] Here, we briefly introduce the barren plateau phenomenon. Specifically, when the scale of the physical system increases, more quantum bits are required. For some common parameterized quantum circuits and loss functions, the gradient of the loss function with respect to most parameter points will increase exponentially with the increase in the number of quantum bits and approach zero. This will cause the parameter points to be trapped on the optimization surface resembling a plateau during the optimization process, resulting in the inability of the classical optimizer to effectively update the parameters, and thus unable to obtain the true ground state of the physical system. This is the barren plateau phenomenon (BP). This phenomenon is the main reason why conventional VQE algorithms fail for large-scale systems (e.g., more than 15 quantum bits). Therefore, there is a need for a solution that can solve or improve the barren plateau phenomenon in conventional VQE.

[0036] Based on this, the disclosed solution provides a solution for determining the characteristic information of a quantum system. On the one hand, the disclosed solution designs a suitable optimization strategy and loss function, so as to adapt to large-scale systems and be more effective; on the other hand, the disclosed solution can flexibly adjust the resources to be consumed according to the actual computing conditions. Therefore, the disclosed solution has better practicality in solving the ground state energy of larger-scale physical systems on recent quantum computing devices.

[0037] Specifically, the disclosed solution provides a method for determining characteristic information of a quantum system, such as Figure 1 As shown, including:

[0038] Step S101: Obtain decomposition information of the total Hamiltonian of the target quantum system, wherein the decomposition information is expressed as: H represents the total Hamiltonian, h kis the sub-Hamiltonian of the target quantum system, and m is a natural number greater than or equal to 2.

[0039] Step S102: Decomposing the sub-Hamiltonian h in the decomposition information k Perform imaginary time evolution to obtain system characteristic information of the target quantum system, wherein the system characteristic information includes at least one of the following: ground state and ground state energy.

[0040] In this way, characteristic information of the target quantum system, such as the ground state or ground state energy, is effectively extracted, thus providing support for studying the properties of the target quantum system.

[0041] In a specific example of the disclosed solution, the above-mentioned sub-Hamiltonian h in the decomposition information k Perform imaginary time evolution to obtain system characteristic information of the target quantum system, including:

[0042] For the sub-Hamiltonian h in the decomposition information k Perform imaginary time evolution for the imaginary time step Δτ to obtain the sub-Hamiltonian h k The k-th imaginary time evolution quantum state

[0043] Based on the sub-Hamiltonian h k The k-th imaginary time evolution quantum state Obtaining the Nth total imaginary time evolution quantum state |ψ(NΔτ)> of the total Hamiltonian, where N is a natural number greater than or equal to 1;

[0044] When it is determined that the Nth total imaginary time evolving quantum state |ψ(NΔτ)> converges, the system characteristic information of the target quantum system is obtained based on the Nth total imaginary time evolving quantum state |ψ(NΔτ)>.

[0045] Specifically, Figure 2 The following is a schematic diagram of the implementation process of the method for determining characteristic information of a quantum system according to an embodiment of the present disclosure. Figure 2 ;like Figure 2 As shown, the method for determining characteristic information of the quantum system includes:

[0046] Step S201: Obtain decomposition information of the total Hamiltonian of the target quantum system, wherein the decomposition information is expressed as: H represents the total Hamiltonian, h k is the sub-Hamiltonian of the target quantum system, and m is a natural number greater than or equal to 2.

[0047] Step S202: Decomposing the sub-Hamiltonian h in the decomposition information kPerform imaginary time evolution for the imaginary time step Δτ to obtain the sub-Hamiltonian h k The k-th imaginary time evolution quantum state

[0048] For example, when k=1, the sub-Hamiltonian h1 in the decomposition information is subjected to imaginary time evolution for an imaginary time step length Δτ, and the first imaginary time evolution quantum state is obtained:

[0049] When k=2, the sub-Hamiltonian h2 in the decomposition information is subjected to imaginary time evolution with respect to the imaginary time step length Δτ, and a second imaginary time evolution quantum state is obtained.

[0050] Until k=m, the sub-Hamiltonian h in the decomposition information m Perform imaginary time evolution for the imaginary time step Δτ and obtain the mth imaginary time evolution quantum state

[0051] Step S203: Based on the sub-Hamiltonian h k The k-th imaginary time evolution quantum state The Nth total imaginary time evolution quantum state of the total Hamiltonian |ψ(NΔτ)> is obtained, where N is a natural number greater than or equal to 1. That is, the disclosed solution can utilize the sub-Hamiltonian h k ’s imaginary-time evolution to realize the imaginary-time evolution of the total Hamiltonian.

[0052] It can be understood that, in a specific example, the sub-Hamiltonians h can be determined one by one. k The k-th imaginary time evolution quantum state Then based on the imaginary time evolution quantum state of all sub-Hamiltonians, that is, the kth imaginary time evolution quantum state k takes values ​​from 1 to m, and the Nth total imaginary time evolution quantum state |ψ(NΔτ)> of the target total Hamiltonian is obtained.

[0053] It can be understood that the m is related to the decomposition method of the total Hamiltonian, and the present disclosure does not limit this.

[0054] Step S204: when it is determined that the Nth total imaginary time evolving quantum state |ψ(NΔτ)> converges, system characteristic information of the target quantum system is obtained based on the Nth total imaginary time evolving quantum state |ψ(NΔτ)>.

[0055] It can be understood that the total Hamiltonian H acts on all quantum bits of the entire quantum system (that is, the entire target quantum system) (it can also be understood that the total Hamiltonian represents the total energy of all quantum bits of the entire target quantum system). For example, the target quantum system includes n quantum bits, where n is a natural number greater than or equal to 2; in this case, the total Hamiltonian H acts on the n quantum bits of the entire target quantum system; and the operators (that is, sub-Hamiltonians) that constitute the total Hamiltonian H are It only acts on some of the qubits of the entire target quantum system (it can also be understood that the sub-Hamiltonian represents the energy contributed by the interaction of some qubits in the entire quantum system). For example, the sub-Hamiltonian h k Acting on 1 qubit, or 2 qubits, or 3 qubits, or 4 qubits in the target quantum system, etc. Therefore, in the imaginary time evolution step of the sub-Hamiltonian, that is, for a single operator As far as the sub-Hamiltonian is concerned, within a certain error limit, we only need to pay attention to the sub-Hamiltonian h k The corresponding (i.e., acted upon) quantum bit and its adjacent quantum bits are sufficient. In this way, in one optimization process, that is, for the sub-Hamiltonian h k The optimization process significantly reduces the number of quantum bits required for processing, which in turn facilitates the processing of large-scale quantum systems.

[0056] In this way, the disclosed solution can utilize the sub-Hamiltonian h k , to realize the imaginary time evolution of the total Hamiltonian. In this way, the entire total Hamiltonian is split into several, that is, m sub-Hamiltonians, so as to reduce the sub-Hamiltonian h k The number of quantum bits involved in the imaginary time evolution steps is reduced, thus effectively avoiding the barren plateau phenomenon that is common when dealing with large-scale systems.

[0057] In a specific example of the disclosed solution, the ground state and / or ground state energy of the target quantum system can be obtained in the following manner, that is, when the Nth total imaginary time evolution quantum state |ψ(NΔτ)> is determined to converge, the system characteristic information of the target quantum system is obtained based on the Nth total imaginary time evolution quantum state |ψ(NΔτ)>, specifically including:

[0058] When it is determined that the Nth total imaginary time evolving quantum state |ψ(NΔτ)> converges, taking the Nth total imaginary time evolving quantum state |ψ(NΔτ)> as the ground state of the target quantum system; and / or,

[0059] When it is determined that the Nth total imaginary time evolving quantum state |ψ(NΔτ)> converges, the ground state energy <ψ(NΔτ)|H|ψ(NΔτ)> of the target quantum system is obtained based on the Nth total imaginary time evolving quantum state |ψ(NΔτ)>.

[0060] That is to say, when the Nth total imaginary time evolving quantum state |ψ(NΔτ)> converges, the ground state and ground state energy of the target quantum system can be directly obtained based on the Nth total imaginary time evolving quantum state |ψ(NΔτ)>. For example, the Nth total imaginary time evolving quantum state |ψ(NΔτ)> is directly used as the ground state of the target quantum system, and <ψ(NΔτ)|H|ψ(NΔτ)> is used as the ground state energy of the target quantum system.

[0061] In this way, by utilizing the characteristics of the imaginary time evolving quantum state (i.e., the imaginary time evolving quantum state will approach the ground state at an exponential rate as the imaginary time parameter increases), the ground state of the target quantum system is obtained, and then the ground state energy of the target quantum state is obtained. Compared with the existing schemes, the disclosed scheme can efficiently obtain the characteristic information of the target quantum system, and is more effective in solving the ground state problem of large-scale physical systems. Moreover, it can effectively avoid the barren plateau phenomenon that is common when dealing with large-scale systems.

[0062] In a specific example of the disclosed solution, the Nth total imaginary time evolution quantum state |ψ(NΔτ)> of the total Hamiltonian can be obtained in the following manner; specifically,

[0063] The above-mentioned sub-Hamiltonian h k The k-th imaginary time evolution quantum state Obtaining the Nth total imaginary time evolution quantum state |ψ(NΔτ)> of the total Hamiltonian, specifically comprising:

[0064] Based on the sub-Hamiltonian h k The k-th imaginary time evolution quantum state Obtain the first total imaginary time evolution quantum state |ψ of the total Hamiltonian for the imaginary time step Δτ H (Δτ)>

[0065] Based on the first total imaginary time evolution quantum state |ψ H (Δτ)>, and obtain the Nth total imaginary time evolving quantum state |ψ(NΔτ)>, wherein the Nth total imaginary time evolving quantum state |ψ(NΔτ)> represents the imaginary time evolving quantum state obtained after the total Hamiltonian undergoes imaginary time evolution of N imaginary time steps Δτ.

[0066] That is to say, in this example, firstly based on the sub-Hamiltonian h k The k-th imaginary time evolution quantum state To realize the imaginary time evolution of the total Hamiltonian for a single imaginary time step Δτ, that is, to obtain the first total imaginary time evolution quantum state |ψ of the total Hamiltonian for a single Δτ H (Δτ)>, then, in the first total imaginary time, the evolving quantum state |ψ H (Δτ)>, the imaginary time evolution is continued to obtain the second total imaginary time evolution quantum state |ψ of the total Hamiltonian for 2Δτ H (2Δτ)>, and so on, until the Nth total imaginary time evolution quantum state |ψ(NΔτ)> of the total Hamiltonian for NΔτ is obtained.

[0067] It is understandable that in practical applications, when the first total imaginary time evolution quantum state |ψ H (Δτ)>, the second total imaginary time evolution quantum state |ψ H (2Δτ)>, until the N-1th total imaginary time evolution quantum state |ψ((N-1)Δτ)> and the N-th total imaginary time evolution quantum state |ψ(NΔτ)>, the energy difference between the N-1th total imaginary time evolution quantum state |ψ(NΔτ)> and the N-1th total imaginary time evolution quantum state |ψ((N-1)Δτ)>, that is, the energy difference between two adjacent total imaginary time evolution quantum states, and determine whether the energy difference between the two meets the accuracy requirement; after determining the energy difference between the two When the energy difference between the Nth total imaginary time evolution quantum state |ψ(NΔτ)> meets the precision requirement, it can be determined that the Nth total imaginary time evolution quantum state |ψ(NΔτ)> converges; otherwise, continue to iterate to obtain the N+1th total imaginary time evolution quantum state |ψ((N+1)Δτ)>, and calculate the energy difference between the energy values ​​of the N+1th total imaginary time evolution quantum state |ψ((N+1)Δτ)> and the Nth total imaginary time evolution quantum state |ψ(NΔτ)>, and determine whether the precision requirement is met, until the precision requirement is met. Here, it can also be understood that the precision requirement can be set based on actual needs, and the disclosed solution does not limit this.

[0068] In a specific example, after obtaining the Nth total imaginary time evolving quantum state |ψ(NΔτ)> and determining that the Nth total imaginary time evolving quantum state |ψ(NΔτ)> converges, the Nth total imaginary time evolving quantum state |ψ(NΔτ)> can also be directly used as the ground state of the target quantum system, and <ψ(NΔτ)|H|ψ(NΔτ)> can be used as the ground state energy of the target quantum system.

[0069] In this way, the disclosed solution can utilize the sub-Hamiltonian h k The imaginary time evolution of the total Hamiltonian is realized by using the imaginary time evolution of the total Hamiltonian, that is, the first total imaginary time evolution quantum state of the total Hamiltonian for an imaginary time step Δτ is obtained. And evolve the quantum state when getting the first total virtual On the basis of, iteration is performed to realize the imaginary time evolution of the total Hamiltonian for N imaginary time steps Δτ, and the Nth total imaginary time evolution quantum state |ψ(NΔτ)> of the total Hamiltonian for N imaginary time steps Δτ is obtained; in this way, the ground state of the target quantum system is obtained by utilizing the characteristics of the imaginary time evolution quantum state (that is, the imaginary time evolution quantum state will approach the ground state at an exponential rate as the imaginary time parameter increases), and then the ground state energy of the target quantum state is obtained. Compared with the existing schemes, the disclosed scheme can efficiently obtain the characteristic information of the target quantum system, and is more effective in solving the ground state problem of large-scale physical systems, and can effectively avoid the barren plateau phenomenon that is common when dealing with large-scale systems.

[0070] At the same time, since the disclosed solution can split the entire Hamiltonian into several, that is, m sub-Hamiltonians, in this way, the sub-Hamiltonians h k The number of quantum bits involved in the imaginary time evolution steps is reduced, thus effectively avoiding the barren plateau phenomenon that is common when dealing with large-scale systems.

[0071] In a specific example of the disclosed solution, the following method can be used to perform the sub-Hamiltonian h k Specifically, the above-mentioned sub-Hamiltonian h in the decomposition information k Perform imaginary time evolution for the imaginary time step Δτ to obtain the sub-Hamiltonian h k The k-th imaginary time evolution quantum state Specifically include:

[0072] Determine the sub-Hamiltonian h k The exploratory quantum state The energy information, as well as the sub-Hamiltonian h k Imaginary time evolution quantum state for imaginary time step Δτ energy information, where U(θ) is the target parameterized quantum circuit acting on the target quantum system, and θ is an adjustable parameter that can be represented by a vector; that is, for the sub-Hamiltonian h k For example, it is necessary to evolve the quantum state at the k-1th imaginary time Based on this, we construct the sub-Hamiltonian h k The test quantum state and imaginary time evolution quantum state, so that the subsequent sub-Hamiltonian h k The imaginary time evolution of the total Hamiltonian is realized by the imaginary time evolution of the total Hamiltonian. Here, it can be understood that the quantum state is tested. The energy information is when the adjustable parameter is a fixed value The energy value represented by The energy information is when the adjustable parameter is a fixed value Here, the value of the adjustable parameter θ may be an initial value, or a value obtained after optimization by a preset classical optimization algorithm.

[0073] Further, at least based on the test quantum state Energy information and imaginary time evolution quantum state The energy information of the loss function is used to obtain the loss value of the loss function, wherein the loss function represents the test quantum state and virtual time evolution quantum state For example, based on the test quantum state and virtual time evolution quantum state The fidelity between them is used as the loss function C(θ), that is:

[0074]

[0075] In practical applications, we can Perform a power series expansion and retain it to the first order, so that the loss function C(θ) becomes:

[0076]

[0077] in, and It can be obtained through quantum computing equipment; it can also be obtained through SWAP testing:

[0078] |〈ψ0|U(θ)|ψ0>| and

[0079] In this way, the loss value of the loss function is obtained.

[0080] Further, when it is determined that the loss value of the loss function satisfies the preset condition, the target trial quantum state obtained when the loss value of the loss function satisfies the preset condition is The sub-Hamiltonian h is obtained k The k-th imaginary time evolution quantum state The U(θ * ) * It is the parameter value of the adjustable parameter when the loss value of the loss function meets the preset condition.

[0081] Here, in a specific example, a test quantum state can be constructed in a quantum computing device And the imaginary time evolution quantum state At this point, the classical computing device only needs to obtain the constructed test quantum state and virtual time evolution quantum state The energy information, that is, the energy value, can be obtained by obtaining the loss value of the loss function in the classical computing device. In this way, the adjustable parameter θ is adjusted based on the preset classical optimization algorithm, and the parameter value of the adjusted adjustable parameter θ is sent to the quantum computing device to obtain the constructed test quantum state after the parameter adjustment in the quantum computing device. and virtual time evolution quantum state The energy value of . This cycle continues until the loss value of the loss function meets the preset conditions.

[0082] In this way, the imaginary time evolution quantum state is approximated by constructing a trial quantum state, and then the sub-Hamiltonian h is completed. k The imaginary time evolution of the variable quantum eigenvalue is realized, that is, the disclosed solution combines the idea of ​​imaginary time evolution with the idea of ​​variational quantum eigensolver, and at the same time, reconstructs the loss function to complete the sub-Hamiltonian h k Compared with the standard quantum imaginary time evolution algorithm, the scheme disclosed in the present invention can flexibly adjust the number of variational parameters (that is, adjustable parameters θ), the structure and depth of the target parameterized quantum circuit, etc. according to the needs of specific problems. Moreover, there is no need to perform quantum tomography to consume exponential resources. Therefore, the scheme disclosed in the present invention is more practical on recent quantum computing devices. In other words, the scheme disclosed in the present invention has both practicality and flexibility.

[0083] Here, the adjustable parameter θ can be represented by a vector. In this case, the number of variational parameters (that is, the adjustable parameter θ) is the dimension of the vector.

[0084] In a specific example of the disclosed solution, the test quantum state and virtual time evolution quantum state The distance between the two is based on the test quantum state and virtual time evolution quantum state Fidelity between.

[0085] That is to say, the disclosed scheme uses the fidelity between the trial quantum state and the imaginary time evolved quantum state to measure the distance between the two, thereby constructing the loss function and also obtaining the energy that converges to the ground state, thus laying the foundation for effectively avoiding the barren plateau phenomenon that is common when dealing with large-scale systems.

[0086] In a specific example of the disclosed solution, the sub-Hamiltonian h can also be obtained in the following manner: k The k-th imaginary time evolution quantum state Specifically,

[0087] Determine X target parameterized quantum circuits U(θ); wherein X is a natural number greater than or equal to 1;

[0088] At this time, the target test quantum state obtained when the loss value based on the loss function described above meets the preset condition The sub-Hamiltonian h is obtained k The k-th imaginary time evolution quantum state Specifically include:

[0089] Determine the target test quantum state corresponding to the target parameterized quantum circuit U(θ) in the X target parameterized quantum circuits U(θ) when the loss value of the loss function satisfies the preset condition That is, each target parameterized quantum circuit U(θ) corresponds to a target test quantum state That is, there are X targets to test quantum states

[0090] From the X target parameterized quantum circuits U(θ), ​​the target test quantum state corresponding to the target parameterized quantum circuit U(θ) is In the above example, the minimum target quantum state is selected as the sub-Hamiltonian h k The k-th imaginary time evolution quantum state Here, the

[0091] It is understandable that when X = 1, there is only one target to test the quantum state At this point, the target can be directly tested for quantum state As a minimum target to test the quantum state.

[0092] In this way, by designing X target parameterized quantum circuits U(θ) to meet the requirements of different precisions in actual needs, and since there are X target parameterized quantum circuits U(θ) designed, it is further convenient to flexibly adjust the number of variational parameters (that is, adjustable parameters θ), the structure and depth of the target parameterized quantum circuit according to specific problems, while effectively reducing the sub-Hamiltonian h k The flexibility of the disclosed scheme is further enhanced by reducing the number of quantum bits involved in the imaginary time evolution step and effectively avoiding the barren plateau phenomenon commonly seen when processing large-scale systems.

[0093] In a specific example of the disclosed solution, the quantum bits in the target quantum system acted upon by U(θ) at least include the sub-Hamiltonian h k Here, in one example, the sub-Hamiltonian h k The corresponding quantum bits include: sub-Hamiltonian h k The quantum bit and the sub-Hamiltonian h k The neighboring quantum bits of the quantum bit being acted on.

[0094] In this way, the sub-Hamiltonian h is reduced k The number of quantum bits involved in the imaginary time evolution steps is reduced, thus effectively avoiding the barren plateau phenomenon that is common when dealing with large-scale systems.

[0095] In a specific example of the disclosed solution, when k=1, The ψ0 is the initial state obtained by initializing the target quantum system. k This reduces the number of quantum bits involved in the imaginary time evolution steps, thereby effectively avoiding the barren plateau phenomenon that is common when dealing with large-scale systems.

[0096] It can be understood that the disclosed solution can be executed in a quantum computing device, or in a classical computing device, or some steps are executed in a quantum computing device and other steps are executed in a classical device. For example, the part involving classical algorithm optimization is executed in a classical device, and the part involving quantum state processing is executed in a quantum device. The disclosed solution does not limit this.

[0097] In this way, the disclosed solution uses the distance between the trial quantum state and the imaginary time evolving quantum state as the loss function and performs iterative optimization, making the solution more effective for large-scale systems.

[0098] Moreover, the number of measurements required for a single optimization update of the disclosed scheme is only O(M) (here, M refers to the number of adjustable parameters in the selected target parameterized quantum circuit, that is, the number of variational parameters). Therefore, for a single optimization update, the disclosed scheme is more efficient and has lower cost.

[0099] Furthermore, the disclosed solution uses a classical optimizer and does not require quantum tomography. The trial quantum state can be flexibly adjusted according to the conditions of the equipment. Therefore, compared with the solution using the quantum tomography method, it is more flexible and practical.

[0100] The following is a further detailed description of the disclosed solution in conjunction with specific examples. Specifically, the disclosed solution provides an Adaptive Quantum Imaginary Time Evolution (AQITE) solution, the main idea of ​​which is:

[0101] On the one hand, the distance between the constructed trial quantum state and the imaginary time evolution quantum state is used as the loss function to update the trial quantum state until the energy converges to obtain a trial quantum state similar to the imaginary time evolution quantum state. Specifically, the disclosed scheme starts from the idea of ​​imaginary time evolution (also known as imaginary time evolution) (Imaginary Time Evolution, ITE), uses a loss function different from the conventional VQE algorithm, and at the same time, does not directly use the energy expectation value as the loss function, but reconstructs the loss function, that is, the distance between the constructed trial quantum state and the imaginary time evolution quantum state is used as the loss function for iterative optimization to obtain a trial quantum state similar to the imaginary time evolution quantum state, and then, the characteristics of the imaginary time evolution quantum state are used to solve the ground state and ground state energy of the system.

[0102] On the other hand, through Trotter decomposition, the number of quantum bits involved in a single iterative optimization is reduced, thereby avoiding the barren plateau phenomenon encountered by conventional VQE algorithms when dealing with large-scale systems.

[0103] Therefore, this solution is more suitable for processing large-scale physical systems. Moreover, the disclosed solution, under the selection of an appropriate initial state, in the case of fewer quantum bits, that is, in the solution for solving the ground state and ground state energy of a quantum system containing fewer quantum bits, can also have a convergence speed that exceeds that of a conventional VQE algorithm.

[0104] It should be noted that the virtual time evolution described in the disclosed solution can be understood as, given a Hamiltonian H, constructing a quantum state |ψ(τ)>=e -Hτ |ψ0>, the quantum state |ψ(τ)> starts from the initial state |ψ0>, as the parameter called imaginary time or imaginary time (abbreviated as imaginary time parameter) τ changes; at this time, the quantum state |ψ(τ)> can be called the imaginary time evolving quantum state or the imaginary time evolving state. A characteristic of the imaginary time evolving quantum state is that as long as the initial state |ψ0> is not orthogonal to the ground state of the Hamiltonian H, the imaginary time evolving quantum state |ψ(τ)> will approach the ground state at an exponential rate as the imaginary time parameter τ increases. The disclosed scheme uses this characteristic to design a quantum algorithm to solve the ground state.

[0105] It should also be noted that Trotter decomposition refers to a decomposition that converts the sum of operators on the exponent into the product of the operator exponentiation. For the disclosed solution, the Trotter decomposition is in the following form: If the Hamiltonian H of the quantum system can be written as a series of operators The sum of Then the operator e -HΔτ The Trotter decomposition is:

[0106]

[0107] Therefore, using Trotter decomposition, the disclosed solution can split the virtual time evolution of the entire Hamiltonian H into m successive small blocks: Here, for the sake of distinction, the disclosed solution refers to the system Hamiltonian of the quantum system as the total Hamiltonian H, and the decomposed small blocks h k , called the sub-Hamiltonian h k .

[0108] It can be understood that the total Hamiltonian H acts on all the qubits of the entire quantum system (it can also be understood that the total Hamiltonian represents the total energy of all the qubits of the entire quantum system). For example, the quantum system includes n qubits. At this time, the total Hamiltonian H acts on the n qubits of the entire quantum system; and the operators (i.e., sub-Hamiltonians) that make up the total Hamiltonian H are It only acts on some of the quantum bits in the entire quantum system (it can also be understood that the sub-Hamiltonian represents the energy contributed by the interaction of some quantum bits in the entire quantum system). For example, h k Acting on 1 qubit, or 2 qubits, or 3 qubits, or 4 qubits in the quantum system, etc. Therefore, for a single operator As far as the sub-Hamiltonian is concerned, within a certain error limit, we only need to pay attention to the sub-Hamiltonian h k The corresponding (i.e., acted upon) quantum bit and its adjacent quantum bits are sufficient. In this way, in one optimization process, that is, for the sub-Hamiltonian h k The optimization process significantly reduces the number of quantum bits required for processing, which in turn facilitates the processing of large-scale quantum systems.

[0109] Based on this, the core principles of the disclosed solution can be summarized as follows:

[0110] First, imaginary time evolution. Due to the imaginary time evolution quantum state e -Hτ |ψ0> will approach the ground state of the quantum system at an exponential rate as the imaginary time parameter τ increases. Therefore, the constructed test quantum state (such as the test quantum state U(θ)|ψ0>) and the imaginary time evolving quantum state (such as the imaginary time evolving quantum state e -Hτ |ψ0>) as the loss function, that is, the loss function C(θ) is:

[0111] C(θ)=-|<ψ0|e -HΔτ U(θ)|ψ0>| 2 ;

[0112] In this way, by training the parameterized quantum circuit U(θ), ​​the constructed trial quantum state U(θ)|ψ0> can be made approximately equivalent to a short period of imaginary time evolution (i.e., Δτ) starting from the initial state |ψ0>, that is, by adjusting the adjustable parameter θ of the parameterized quantum circuit U(θ), ​​the constructed trial quantum state U(θ)|ψ0> can be made equivalent to the imaginary time evolution quantum state e -HΔτ |ψ0>. In this way, through iterative training, the effect of the total Hamiltonian evolution in a long period (such as NΔτ) of imaginary time can be approximated by the cumulative multiplication of a series of parameterized quantum circuits U(θ), ​​thereby obtaining the ground state of the total Hamiltonian H. In actual operation, for ease of processing, e -HΔτ Perform a power series expansion and retain it to the first order, so that the loss function C(θ) becomes:

[0113]

[0114] Understandably, -HΔτ The processing method retained to the first order is only an exemplary description. In practical applications, processing can also be performed based on actual needs, and the present disclosure does not limit this.

[0115] Second, Trotter decomposition. In order to further avoid the barren plateau phenomenon encountered in VQE, the disclosed solution also performs Trotter decomposition. Here, it can be noted that the barren plateau phenomenon is related to the number of quantum bits involved. For example, when the number of quantum bits involved in a training is large enough (for example, more than 15 quantum bits), a barren plateau phenomenon may occur. Therefore, after Trotter decomposition, although the number of quantum bits n contained in the entire quantum system remains unchanged, the number of quantum bits involved in a single virtual time evolution, that is, for h k The number of quantum bits involved in the imaginary time evolution will be greatly reduced. For example, k The number of the quantum bits acted on and their adjacent quantum bits is, for example, slightly greater than 4.

[0116] Here, for a single training, the loss function C(θ) is:

[0117]

[0118] The quantum bits that U(θ) acts on in the quantum system include at least h k The quantum bit affected and the h k The adjacent quantum bits of the quantum bits being acted on effectively reduce the number of quantum bits involved in a single training and avoid the barren plateau phenomenon to the greatest extent.

[0119] The following combination Figure 3 The disclosed solution is further described, and the specific steps include:

[0120] Step 1: In the classical computing device, determine the decomposition information of the total Hamiltonian H of the target quantum system to be solved, that is, h k represents the sub-Hamiltonian of the target quantum system, the target quantum system includes n quantum bits, n is a natural number greater than or equal to 2, and m is a natural number greater than or equal to 2. The target quantum system is initialized to obtain an initial state |ψ0>; for example, after the initialization process, the initial state is obtained Among them, |0> indicates that all quantum bits in the target quantum system are in the same fully polarized state, represents the initialization parameterized quantum circuit used to obtain the initial state, represents the parameter vector of the initial setting, which is a fixed value. In other words, the initial state |ψ0> is the initialization parameterized quantum circuit The quantum state obtained after acting on a target quantum system in which all quantum bits are in the same fully polarized state.

[0121] It can be understood that this initialization process is only a specific example. In actual applications, other initialization methods can also be sampled to obtain the initial state |ψ0>, and the present disclosure does not limit this.

[0122] Step 2: In the quantum computing device, determine X target parameterized quantum circuits U(θ), ​​where X is a natural number greater than or equal to 1, forming a list Among them, for any target parameterized quantum circuit U(θ=0)=I, where I represents the unit matrix and θ represents the adjustable parameter vector contained in the target parameterized quantum circuit U.

[0123] In this way, since U(θ=0)=I, the stability of convergence can be effectively ensured.

[0124] It can be understood that the adjustable parameter δ in the initialization parameterized quantum circuit V used in step 1 and the adjustable parameter θ in the target parameterized quantum circuit U are the same, or different, or partially the same and partially different, and the disclosed solution is not limited to this.

[0125] Step 3: In the classical computing device, set the imaginary time step size for the imaginary time parameter τ to Δτ.

[0126] Step 4: In a classical computing device, traverse the total Hamiltonian Each item in h k ; Traverse the list The target parameterized quantum circuit in the total Hamiltonian Each item in h k, and the list Each target parameterized quantum circuit U(θ) in performs the following operations; thus, the sub-Hamiltonian h k The corresponding target probe quantum state.

[0127] It can be understood that for the sub-Hamiltonian h1, using each target parameterized quantum circuit U(θ), ​​a target test quantum state U(θ) can be obtained. * )|ψ0>, in other words, the sub-Hamiltonian is the target test quantum state U(θ * )|ψ0> is the same as the number of target parameterized quantum circuits.

[0128] Specifically, in a classical computing device, for the sub-Hamiltonian h1, for each target parameterized quantum circuit, the adjustable parameter θ of the current target parameterized quantum circuit is initialized to a zero vector (i.e., θ=0, where 0 represents a zero vector), and a trial quantum state U(θ)|ψ0> is constructed, and, in a quantum computing device, a virtual time evolution quantum state for the sub-Hamiltonian h1 is constructed. And in classical computing devices, based on the test quantum state U(θ)|ψ0> and the imaginary time evolution quantum state The distance between them is used to construct a loss function; for example, based on the test quantum state U(θ)|ψ0> and the imaginary time evolution quantum state The fidelity between them is used as the loss function C(θ), that is:

[0129]

[0130] Here, for the convenience of calculation, in the classical computing device, Perform a power series expansion and retain it to the first order, so that the loss function C(θ) becomes:

[0131]

[0132] Among them, |ψ0> and U(θ)|ψ0> can be prepared by quantum computing equipment, such as quantum computers; obtained by SWAP testing:

[0133] |〈ψ0|U(θ)|ψ0>| and

[0134] In this way, in the classical computing device, the loss value of the loss function C(θ) is obtained when the adjustable parameter θ is a zero vector. Further, in the classical computing device, the adjustable parameter θ is adjusted using a classical optimization algorithm (such as stochastic gradient descent, etc.) to minimize the loss function, or to converge the loss function; at the same time, the adjusted parameter value of the adjustable parameter is sent to the quantum computing device, and the loss value of the loss function under the adjusted parameter value of the adjustable parameter is remeasured, and this cycle is repeated until the target trial quantum state U(θ) corresponding to the current target parameterized quantum circuit is obtained after the loss function is minimized or the loss function converges. * )|ψ0>, the target test quantum state is the imaginary time evolution quantum state The approximate quantum state of .

[0135] Loop like this to traverse the completion list For each target parameterized quantum circuit in the , the target test quantum state corresponding to each target parameterized quantum circuit is obtained.

[0136] Step 5: In the classical computing device, select the minimum target test quantum state from the target test quantum states corresponding to each target parameterized quantum circuit as the first imaginary time evolution quantum state for the sub-Hamiltonian h1 that completes one imaginary time evolution of Δτ, denoted as and Among them, U1 is the target parameterized quantum circuit corresponding to the minimum target trial quantum state of the sub-Hamiltonian h1, That is, it is the parameter value corresponding to the minimum target trial quantum state of the sub-Hamiltonian h1, which can also be called the optimal parameter value.

[0137] Here, it can be understood that the first imaginary time evolution quantum state It is: the system quantum state of the target quantum system under an imaginary time evolution of Δτ when the quantum bit corresponding to (or acted upon by) the sub-Hamiltonian h1 is in the ground state.

[0138] Step 6: In the classical computing device, traverse the decomposition information of the total Hamiltonian Each term in , until the imaginary time evolution quantum state of each term that completes the imaginary time evolution of Δτ is obtained;

[0139] Specifically, according to the method of steps 4 and 5, a second imaginary-time evolved quantum state is obtained for the sub-Hamiltonian h2, which completes an imaginary-time evolution of Δτ; similarly, the second imaginary-time evolved quantum state is: under an imaginary-time evolution of Δτ, the quantum bit corresponding to (or called the acted upon) the sub-Hamiltonian h1 is in the ground state, and the quantum bit corresponding to (or called the acted upon) the sub-Hamiltonian h2 is in the ground state, the system quantum state of the target quantum system.

[0140] Specifically, using the first imaginary time evolution quantum state Substitute the initial state |ψ0> in step 4, use the sub-Hamiltonian h2 to replace the sub-Hamiltonian h1 in step 4, and adopt the method of steps 4 and 5 to obtain the second imaginary time evolution quantum state for the sub-Hamiltonian h2, which completes the imaginary time evolution for Δτ, and is recorded as and Similarly, U2 is the target parameterized quantum circuit corresponding to the minimum target test quantum state of the sub-Hamiltonian h2. That is, it is the parameter value corresponding to the minimum target trial quantum state of the sub-Hamiltonian h2, which can also be called the optimal parameter value.

[0141] By analogy, we can get the sub-Hamiltonian h k The kth imaginary time evolution quantum state that completes the imaginary time evolution of Δτ is denoted as And the for:

[0142]

[0143] Among them, U k That is, for the sub-Hamiltonian h k The target parameterized quantum circuit corresponding to the minimum target trial quantum state, That is, for the sub-Hamiltonian h k The parameter value corresponding to the minimum target trial quantum state can also be called the optimal parameter value.

[0144] In this way, the target parameterized quantum circuit corresponding to the quantum state is continuously multiplied until the sub-Hamiltonian h is obtained. m The mth imaginary time evolution quantum state that completes an imaginary time evolution of Δτ

[0145]

[0146] At this point, a Δτ imaginary time evolution is completed for the total Hamiltonian H, and the first total imaginary time evolution quantum state |ψ of the total Hamiltonian H that completes a Δτ imaginary time evolution is obtained. H (Δτ)>, and

[0147] Here, in order to conveniently express the imaginary time evolution of Δτ, the following record can be made:

[0148] Will Recorded as

[0149] And, Recorded as

[0150] At this time, the first total imaginary time evolution quantum state of the total Hamiltonian H is:

[0151]

[0152] Step 7: In the classical computing device, accumulate Δτ to obtain |ψ(2Δτ)> until |ψ(NΔτ)> is obtained. At this time, the energy expectation value of the test quantum state converges; specifically,

[0153] Use |ψ H (Δτ)> replaces |ψ0> in step 4, and executes steps 4 to 6 to complete the imaginary time evolution for 2Δτ, and obtains the second total imaginary time evolution quantum state |ψ H (2Δτ)>:

[0154]

[0155] By analogy, |ψ(2Δτ)> is used instead of |ψ(Δτ)>, and steps 4 to 6 are performed to complete the imaginary time evolution for 3Δτ, and the third total imaginary time evolution quantum state |ψ H (3Δτ)>, until the converged Nth total imaginary time evolution quantum state |ψ H (NΔτ)>

[0156] At this time, the converged Nth total imaginary time evolution quantum state |ψ(NΔτ)> is the total target trial quantum state |ψ H >:

[0157]

[0158] Here, N is a natural number greater than or equal to 1; when N=1, ψ H (0)=|ψ0>.

[0159] Step 8: In a classical computing device, output the total target test quantum state |ψ H >, the total target test quantum state is the ground state of the target quantum system estimated by the disclosed solution, and the ground state energy E=<ψ H |H|ψ H >.

[0160] It can be understood that, in practical applications, the input of the disclosed solution is the decomposition information (i.e., the decomposition formula) of the total Hamiltonian of the target quantum system to be solved, i.e. The output of the disclosed solution is the ground state of the target quantum system |ψ H > and its corresponding ground state energy E=<ψ H |H|ψ H >.

[0161] Thus, the disclosed solution has the following beneficial effects:

[0162] First, the disclosed solution is more effective in solving the ground state problem of large-scale physical systems. This is because the disclosed solution uses a loss function that is completely different from the conventional VQE algorithm, and also obtains the ability to converge to the ground state, and can reduce the number of quantum bits involved in a single training through Trotter decomposition, thereby improving the barren plateau phenomenon commonly seen in conventional VQE algorithms when dealing with large-scale systems, and can converge to the ground state more effectively.

[0163] Second, the disclosed solution has good practicality and flexibility on recent quantum computing devices. Compared with the standard quantum imaginary time evolution algorithm, the disclosed solution can flexibly adjust the number of variational parameters (i.e., adjustable parameters θ), the structure and depth of the target parameterized quantum circuit, etc. according to the needs of specific problems, and does not require quantum tomography to consume exponential resources. Therefore, the disclosed solution is more practical on recent quantum computing devices.

[0164] Third, the disclosed solution has good expansibility. Imaginary time evolution is closely related to the preparation of the Gibbs state of the physical system. Therefore, the disclosed solution can further inspire the problem of solving the Gibbs state of the physical system.

[0165] The disclosed solution also provides a device for determining characteristic information of a quantum system, such as Figure 4 As shown, including:

[0166] The acquisition unit 401 is used to acquire decomposition information of the total Hamiltonian of the target quantum system, wherein the decomposition information is expressed as: H represents the total Hamiltonian, h k is the sub-Hamiltonian of the target quantum system, and m is a natural number greater than or equal to 2;

[0167] The imaginary time evolution unit 402 is used to transform the sub-Hamiltonian h in the decomposition information. k Perform imaginary time evolution to obtain system characteristic information of the target quantum system, wherein the system characteristic information includes at least one of the following: ground state and ground state energy.

[0168] In a specific example of the disclosed solution, the virtual time evolution unit is specifically used to:

[0169] For the sub-Hamiltonian h in the decomposition information k Perform imaginary time evolution for the imaginary time step Δτ to obtain the sub-Hamiltonian h k The k-th imaginary time evolution quantum state

[0170] Based on the sub-Hamiltonian h k The k-th imaginary time evolution quantum state Obtaining the Nth total imaginary time evolution quantum state |ψ(NΔτ)> of the total Hamiltonian, where N is a natural number greater than or equal to 1;

[0171] When it is determined that the Nth total imaginary time evolving quantum state |ψ(NΔτ)> converges, the system characteristic information of the target quantum system is obtained based on the Nth total imaginary time evolving quantum state |ψ(NΔτ)>.

[0172] In a specific example of the disclosed solution, the virtual time evolution unit is specifically used to:

[0173] When it is determined that the Nth total imaginary time evolving quantum state |ψ(NΔτ)> converges, taking the Nth total imaginary time evolving quantum state |ψ(NΔτ)> as the ground state of the target quantum system; and / or,

[0174] When it is determined that the Nth total imaginary time evolving quantum state |ψ(NΔτ)> converges, the ground state energy <ψ(NΔτ)|H|ψ(NΔτ)> of the target quantum system is obtained based on the Nth total imaginary time evolving quantum state |ψ(NΔτ)>.

[0175] In a specific example of the disclosed solution, the virtual time evolution unit is specifically used to:

[0176] Based on the sub-Hamiltonian h k The k-th imaginary time evolution quantum state The first total imaginary time evolution quantum state |ψ of the total Hamiltonian for the imaginary time step Δτ is obtained. H (Δτ)>

[0177] Based on the first total imaginary time evolution quantum state |ψ H (Δτ)>, and obtain the Nth total imaginary time evolving quantum state |ψ(NΔτ)>, wherein the Nth total imaginary time evolving quantum state |ψ(NΔτ)> represents the imaginary time evolving quantum state obtained after the total Hamiltonian undergoes imaginary time evolution of N imaginary time steps Δτ.

[0178] In a specific example of the disclosed solution, the virtual time evolution unit is specifically used to:

[0179] Determine the sub-Hamiltonian h k The exploratory quantum state The energy information, as well as the sub-Hamiltonian h k Imaginary time evolution quantum state for imaginary time step Δτ energy information, wherein U(θ) is a target parameterized quantum circuit acting on the target quantum system, and θ is an adjustable parameter;

[0180] At least based on the test quantum state Energy information and imaginary time evolution quantum state The energy information of the loss function is used to obtain the loss value of the loss function, wherein the loss function represents the test quantum state and virtual time evolution quantum state The distance between

[0181] In the case where it is determined that the loss value of the loss function satisfies a preset condition, a target trial quantum state obtained when the loss value of the loss function satisfies the preset condition is The sub-Hamiltonian h is obtained k The k-th imaginary time evolution quantum state The U(θ * ) * It is the parameter value of the adjustable parameter when the loss value of the loss function meets the preset condition.

[0182] In a specific example of the disclosed solution, the test quantum state and virtual time evolution quantum state The distance between the two is based on the test quantum state and virtual time evolution quantum state Fidelity between.

[0183] In a specific example of the present disclosure, Figure 5 As shown, it also includes: a circuit determination unit 501; wherein,

[0184] The circuit determination unit 501 is used to determine X target parameterized quantum circuits U(θ); X is a natural number greater than or equal to 1;

[0185] The imaginary time evolution unit 401 is specifically used to determine the target test quantum state corresponding to the target parameterized quantum circuit U(θ) in the X target parameterized quantum circuits U(θ) when the loss value of the loss function meets the preset condition. From the X target parameterized quantum circuits U(θ), ​​the target test quantum state corresponding to the target parameterized quantum circuit U(θ) is In the above example, the minimum target quantum state is selected as the sub-Hamiltonian h k The k-th imaginary time evolution quantum state

[0186] In a specific example of the disclosed solution, the quantum bits in the target quantum system acted upon by U(θ) at least include the sub-Hamiltonian h k The corresponding quantum bit.

[0187] In a specific example of the disclosed solution, when k=1, The ψ0 is the initial state obtained by initializing the target quantum system.

[0188] Each unit in the above-mentioned device for determining the characteristic information of the quantum system can be implemented by a classical computing device or a quantum computing device, or some units can be implemented in a classical device and other units can be implemented in a quantum computing device. The present disclosure does not impose any restrictions on this.

[0189] It is understandable that the specific functions of each unit in the above-mentioned device for determining characteristic information of a quantum system can be described with reference to the above-mentioned method, and will not be repeated here.

[0190] The disclosed solution also provides a non-transitory computer-readable storage medium storing computer instructions, which, when executed by at least one quantum processing unit, causes the at least one quantum processing unit to execute the above method of applying the quantum computing device.

[0191] The disclosed solution also provides a computer program product, including a computer program, which, when executed by a processor, implements the method described above for application to a classical computing device;

[0192] Alternatively, the computer program, when executed by at least one quantum processing unit, implements the method described for application to a quantum computing device.

[0193] The disclosed solution also provides a quantum computing device, the quantum computing device comprising:

[0194] at least one quantum processing unit;

[0195] a memory coupled to the at least one QPU and configured to store executable instructions,

[0196] The instructions are executed by the at least one quantum processing unit to enable the at least one quantum processing unit to perform the method described for application to a quantum computing device.

[0197] It can be understood that the quantum processing unit (QPU) used in the disclosed solution, which may also be called a quantum processor or a quantum chip, may involve a physical chip including a plurality of quantum bits interconnected in a specific manner.

[0198] Moreover, it is understood that the quantum bit described in the present disclosure may refer to the basic information unit of a quantum computing device. The quantum bit is contained in the QPU and generalizes the concept of the classical digital bit.

[0199] According to an embodiment of the present disclosure, the present disclosure also provides a classic computing device (hereinafter, the classic computing device is specifically an electronic device as an example for explanation), a readable storage medium and a computer program product.

[0200] Figure 6 A schematic block diagram of an example electronic device 600 that can be used to implement an embodiment of the present disclosure is shown. The electronic device is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device can also represent various forms of mobile devices, such as personal digital processing, cellular phones, smart phones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the present disclosure described and / or required herein.

[0201] like Figure 6 As shown, the device 600 includes a computing unit 601, which can perform various appropriate actions and processes according to a computer program stored in a read-only memory (ROM) 602 or a computer program loaded from a storage unit 608 into a random access memory (RAM) 603. In the RAM 603, various programs and data required for the operation of the device 600 can also be stored. The computing unit 601, the ROM 602, and the RAM 603 are connected to each other via a bus 604. An input / output (I / O) interface 605 is also connected to the bus 604.

[0202] A number of components in the device 600 are connected to the I / O interface 605, including: an input unit 606, such as a keyboard, a mouse, etc.; an output unit 607, such as various types of displays, speakers, etc.; a storage unit 608, such as a disk, an optical disk, etc.; and a communication unit 609, such as a network card, a modem, a wireless communication transceiver, etc. The communication unit 609 allows the device 600 to exchange information / data with other devices through a computer network such as the Internet and / or various telecommunication networks.

[0203] The computing unit 601 may be a variety of general and / or special processing components with processing and computing capabilities. Some examples of the computing unit 601 include, but are not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various dedicated artificial intelligence (AI) computing chips, various computing units running machine learning model algorithms, digital signal processors (DSPs), and any appropriate processors, controllers, microcontrollers, etc. The computing unit 601 performs the various methods and processes described above, such as a method for determining characteristic information of a quantum system. For example, in some embodiments, the method for determining characteristic information of a quantum system may be implemented as a computer software program, which is tangibly contained in a machine-readable medium, such as a storage unit 608. In some embodiments, part or all of the computer program may be loaded and / or installed on the device 600 via the ROM 602 and / or the communication unit 609. When the computer program is loaded into the RAM 603 and executed by the computing unit 601, one or more steps of the method for determining characteristic information of the quantum system described above may be performed. Alternatively, in other embodiments, the computing unit 601 may be configured to perform a method for determining characteristic information of a quantum system in any other appropriate manner (e.g., by means of firmware).

[0204] Various implementations of the systems and techniques described above herein can be implemented in digital electronic circuit systems, integrated circuit systems, field programmable gate arrays (FPGAs), application specific integrated circuits (ASICs), application specific standard products (ASSPs), systems on chips (SOCs), load programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various implementations can include: being implemented in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which can be a special purpose or general purpose programmable processor that can receive data and instructions from a storage system, at least one input device, and at least one output device, and transmit data and instructions to the storage system, the at least one input device, and the at least one output device.

[0205] The program code for implementing the method of the present disclosure may be written in any combination of one or more programming languages. These program codes may be provided to a processor or controller of a general-purpose computer, a special-purpose computer, or other programmable data processing device, so that the program code, when executed by the processor or controller, enables the functions / operations specified in the flow chart and / or block diagram to be implemented. The program code may be executed entirely on the machine, partially on the machine, partially on the machine and partially on a remote machine as a stand-alone software package, or entirely on a remote machine or server.

[0206] In the context of the present disclosure, a machine-readable medium may be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, device, or equipment. A machine-readable medium may be a machine-readable signal medium or a machine-readable storage medium. A machine-readable medium may include, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, device, or equipment, or any suitable combination of the foregoing. A more specific example of a machine-readable storage medium may include an electrical connection based on one or more lines, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

[0207] To provide interaction with a user, the systems and techniques described herein can be implemented on a computer having: a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to the user; and a keyboard and pointing device (e.g., a mouse or trackball) through which the user can provide input to the computer. Other types of devices can also be used to provide interaction with the user; for example, the feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including acoustic input, voice input, or tactile input).

[0208] The systems and techniques described herein may be implemented in a computing system that includes back-end components (e.g., as a data server), or a computing system that includes middleware components (e.g., an application server), or a computing system that includes front-end components (e.g., a user computer with a graphical user interface or a web browser through which a user can interact with implementations of the systems and techniques described herein), or a computing system that includes any combination of such back-end components, middleware components, or front-end components. The components of the system may be interconnected by any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include: a local area network (LAN), a wide area network (WAN), and the Internet.

[0209] A computer system may include a client and a server. The client and the server are generally remote from each other and usually interact through a communication network. The relationship of client and server is generated by computer programs running on respective computers and having a client-server relationship with each other. The server may be a cloud server, a server of a distributed system, or a server combined with a blockchain.

[0210] It should be understood that the various forms of processes shown above can be used to reorder, add or delete steps. For example, the steps recorded in this disclosure can be executed in parallel, sequentially or in different orders, as long as the desired results of the technical solutions disclosed in this disclosure can be achieved, and this document does not limit this.

[0211] The above specific implementations do not constitute a limitation on the protection scope of the present disclosure. It should be understood by those skilled in the art that various modifications, combinations, sub-combinations and substitutions can be made according to design requirements and other factors. Any modification, equivalent substitution and improvement made within the spirit and principle of the present disclosure shall be included in the protection scope of the present disclosure.

Claims

1. A method for determining characteristic information of a quantum system, comprising: Obtain decomposition information of the total Hamiltonian of the target quantum system, wherein the decomposition information is expressed as: H represents the total Hamiltonian, h k is the sub-Hamiltonian of the target quantum system, and m is a natural number greater than or equal to 2; For the sub-Hamiltonian h in the decomposition information k Performing imaginary time evolution to obtain system characteristic information of the target quantum system, wherein the system characteristic information includes at least one of the following: ground state, ground state energy; Wherein, the sub-Hamiltonian h in the decomposition information k Perform imaginary time evolution to obtain system characteristic information of the target quantum system, including: For the sub-Hamiltonian h in the decomposition information k Perform imaginary time evolution for the imaginary time step Δτ to obtain the sub-Hamiltonian h k The k-th imaginary time evolution quantum state Based on the sub-Hamiltonian h k The k-th imaginary time evolution quantum state Obtaining the Nth total imaginary time evolution quantum state |ψ(NΔτ)) of the total Hamiltonian, where N is a natural number greater than or equal to 1; When it is determined that the Nth total imaginary time evolving quantum state |ψ(NΔτ)> converges, the system characteristic information of the target quantum system is obtained based on the Nth total imaginary time evolving quantum state |ψ(NΔτ)>.

2. The method according to claim 1, wherein: The method of obtaining the system characteristic information of the target quantum system based on the Nth total imaginary time evolution quantum state |ψ(NΔτ)> when it is determined that the Nth total imaginary time evolution quantum state |ψ(NΔτ)> converges includes: When it is determined that the Nth total imaginary time evolving quantum state |ψ(NΔτ)> converges, taking the Nth total imaginary time evolving quantum state |ψ(NΔτ)> as the ground state of the target quantum system; and / or, When it is determined that the Nth total imaginary time evolving quantum state |ψ(NΔτ)> converges, the ground state energy <ψ(NΔτ)|H|ψ(NΔτ)> of the target quantum system is obtained based on the Nth total imaginary time evolving quantum state |ψ(NΔτ)>.

3. The method according to claim 1, wherein: Based on the sub-Hamiltonian h k The k-th imaginary time evolution quantum state Obtaining the Nth total imaginary time evolution quantum state |ψ(NΔτ)> of the total Hamiltonian, including: Based on the sub-Hamiltonian h k The k-th imaginary time evolution quantum state Obtain the first total imaginary time evolution quantum state |ψ of the total Hamiltonian for the imaginary time step Δτ H (Δτ)> Based on the first total imaginary time evolution quantum state |ψ H (Δτ)>, and obtain the Nth total imaginary time evolving quantum state |ψ(NΔτ)>, wherein the Nth total imaginary time evolving quantum state |ψ(NΔτ)> represents the imaginary time evolving quantum state obtained after the total Hamiltonian undergoes imaginary time evolution of N imaginary time steps Δτ.

4. The method according to any one of claims 1 to 3, wherein: The sub-Hamiltonian h in the decomposition information k Perform imaginary time evolution for the imaginary time step Δτ to obtain the sub-Hamiltonian h k The k-th imaginary time evolution quantum state include: Determine the sub-Hamiltonian h k The exploratory quantum state The energy information, and the sub-Hamiltonian h k Imaginary time evolution quantum state for imaginary time step Δτ Energy information, wherein U(θ) is a target parameterized quantum circuit acting on the target quantum system, and θ is an adjustable parameter; At least based on the test quantum state Energy information and imaginary time evolution quantum state The energy information of the loss function is used to obtain the loss value of the loss function, wherein the loss function represents the test quantum state and virtual time evolution quantum state The distance between In the case where it is determined that the loss value of the loss function satisfies a preset condition, a target trial quantum state obtained when the loss value of the loss function satisfies the preset condition is The sub-Hamiltonian h is obtained k The k-th imaginary time evolution quantum state The U(θ * ) * It is the parameter value of the adjustable parameter when the loss value of the loss function meets the preset condition.

5. The method according to claim 4, wherein: The test quantum state and virtual time evolution quantum state The distance between the two is based on the test quantum state and virtual time evolution quantum state Fidelity between.

6. The method according to claim 4, further comprising: Determine X target parameterized quantum circuits U(θ); wherein X is a natural number greater than or equal to 1; Wherein, the target test quantum state obtained when the loss value based on the loss function satisfies the preset condition The sub-Hamiltonian h is obtained k The k-th imaginary time evolution quantum state include: Determine the target test quantum state corresponding to the target parameterized quantum circuit U(θ) in the X target parameterized quantum circuits U(θ) when the loss value of the loss function satisfies the preset condition From the X target parameterized quantum circuits U(θ), ​​the target test quantum state corresponding to the target parameterized quantum circuit U(θ) is In the above example, the minimum target quantum state is selected as the sub-Hamiltonian h k The k-th imaginary time evolution quantum state 7. The method according to claim 4, wherein: The quantum bits in the target quantum system acted upon by U(θ) include at least the sub-Hamiltonian h k The corresponding quantum bit.

8. The method according to claim 4, wherein: When k=1, The ψ0 is the initial state obtained by initializing the target quantum system.

9. A device for determining characteristic information of a quantum system, comprising: An acquisition unit is used to acquire decomposition information of the total Hamiltonian of the target quantum system, wherein the decomposition information is expressed as: H represents the total Hamiltonian, h k is the sub-Hamiltonian of the target quantum system, and m is a natural number greater than or equal to 2; An imaginary time evolution unit, used for the sub-Hamiltonian h in the decomposition information k Performing imaginary time evolution to obtain system characteristic information of the target quantum system, wherein the system characteristic information includes at least one of the following: ground state, ground state energy; Wherein, the virtual time evolution unit is specifically used for: For the sub-Hamiltonian h in the decomposition information k Perform imaginary time evolution for the imaginary time step Δτ to obtain the sub-Hamiltonian h k The k-th imaginary time evolution quantum state Based on the sub-Hamiltonian h k The k-th imaginary time evolution quantum state Obtaining the Nth total imaginary time evolution quantum state |ψ(NΔτ)> of the total Hamiltonian, where N is a natural number greater than or equal to 1; When it is determined that the Nth total imaginary time evolving quantum state |ψ(NΔτ)> converges, the system characteristic information of the target quantum system is obtained based on the Nth total imaginary time evolving quantum state |ψ(NΔτ)>.

10. The device according to claim 9, wherein: The virtual time evolution unit is specifically used for: When it is determined that the Nth total imaginary time evolution quantum state |ψ(NΔτ)> converges, taking the Nth total imaginary time evolution quantum state |ψ(NΔτ)> as the ground state of the target quantum system; and / or, When it is determined that the Nth total imaginary time evolving quantum state |ψ(NΔτ)> converges, the ground state energy (ψ(NΔτ)|H|ψ(NΔτ)> of the target quantum system is obtained based on the Nth total imaginary time evolving quantum state |ψ(NΔτ)>.

11. The device according to claim 9, wherein: The virtual time evolution unit is specifically used for: Based on the sub-Hamiltonian h k The k-th imaginary time evolution quantum state Obtain the first total imaginary time evolution quantum state |ψ of the total Hamiltonian for the imaginary time step Δτ H (Δτ)> Based on the first total imaginary time evolution quantum state |ψ H (Δτ)>, and obtain the Nth total imaginary time evolving quantum state |ψ(NΔτ)>, wherein the Nth total imaginary time evolving quantum state |ψ(NΔτ)> represents the imaginary time evolving quantum state obtained after the total Hamiltonian undergoes imaginary time evolution of N imaginary time steps Δτ.

12. The device according to any one of claims 9 to 11, wherein: The virtual time evolution unit is specifically used for: Determine the sub-Hamiltonian h k The exploratory quantum state The energy information, and the sub-Hamiltonian h k Imaginary time evolution quantum state for imaginary time step Δτ energy information, wherein U(θ) is a target parameterized quantum circuit acting on the target quantum system, and θ is an adjustable parameter; At least based on the test quantum state Energy information and imaginary time evolution quantum state The energy information of the loss function is used to obtain the loss value of the loss function, wherein the loss function represents the test quantum state and virtual time evolution quantum state The distance between In the case where it is determined that the loss value of the loss function satisfies a preset condition, a target trial quantum state obtained when the loss value of the loss function satisfies the preset condition is The sub-Hamiltonian h is obtained k The k-th imaginary time evolution quantum state The U(θ * ) * It is the parameter value of the adjustable parameter when the loss value of the loss function meets the preset condition.

13. The device according to claim 12, wherein: The test quantum state and virtual time evolution quantum state The distance between the two is based on the test quantum state and virtual time evolution quantum state Fidelity between.

14. The apparatus according to claim 12, further comprising: A circuit determining unit; wherein, The circuit determination unit is used to determine X target parameterized quantum circuits U(θ); X is a natural number greater than or equal to 1; The imaginary time evolution unit is specifically used to determine the target test quantum state corresponding to the target parameterized quantum circuit U(θ) in the X target parameterized quantum circuits U(θ) when the loss value of the loss function satisfies the preset condition. From the X target parameterized quantum circuits U(θ), ​​the target test quantum state corresponding to the target parameterized quantum circuit U(θ) is In the above example, the minimum target quantum state is selected as the sub-Hamiltonian h k The k-th imaginary time evolution quantum state 15. The device according to claim 12, wherein: The quantum bits in the target quantum system acted upon by U(θ) include at least the sub-Hamiltonian h k The corresponding quantum bit.

16. The device according to claim 12, wherein: When k=1, The ψ0 is the initial state obtained by initializing the target quantum system.

17. A classical electronic device, comprising: at least one processor; as well as a memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to perform the method according to any one of claims 1 to 8.

18. A quantum computing device comprising: at least one quantum processing unit; a memory coupled to at least one QPU and configured to store executable instructions, The instructions are executed by the at least one quantum processing unit to enable the at least one quantum processing unit to perform the method of any one of claims 1 to 8.

19. A non-transitory computer-readable storage medium storing computer instructions, characterized in that: When executed by at least one quantum processing unit, the computer instructions cause the at least one quantum processing unit to perform the method according to any one of claims 1 to 8.

20. A non-transitory computer-readable storage medium storing computer instructions, wherein: The computer instructions are used to cause the computer to execute the method according to any one of claims 1 to 8.

21. A computer program product comprising a computer program which, when executed by at least one quantum processing unit, implements the method according to any one of claims 1 to 8; or The computer program implements the method according to any one of claims 1 to 8 when executed by a processor.

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