A method and device for obtaining steady state of an open physical system

Abstract

The present invention provides a method and apparatus for obtaining the steady state of an open physical system. The method comprises: determining the target quantum mixed state based on the spectral decomposition of the density matrix of the target quantum mixed state, using the evolution of a d-dimensional quantum pure state with n qubits in a quantum circuit and the quantum state after intermediate measurements, so that the target quantum mixed state has initialized circuit parameters; constructing a corresponding loss function based on selected observables, and calculating the loss function and its gradient using quantum shadow tomography; and adjusting the circuit parameters of the target quantum mixed state using a gradient descent method until the loss function is minimized, thereby obtaining the steady state. This method significantly reduces the number of qubits required for calculation, making it easier to implement under current technical conditions and having broad application prospects.

Description

Technical Field

[0001] The present invention relates to the technical field of quantum computing, and in particular to a method and device for obtaining a steady state of an open physical system. Background Art

[0002] In the existing technology, there are two main methods to simulate the steady state of an open quantum system (assuming the dimension is d) using the variational principle. One is to convert a d-dimensional mixed state into Vectorization of quantum states using Liouville representation Then it is encoded in a d2-dimensional pure state [1]. That is, if a d-dimensional mixed state can be represented by n quantum bits (d = 2 n ), then using the above description with pure state, d 2 A d-dimensional pure state requires 2n qubits to describe. When solving for the steady state, a non-negative loss function is constructed using the open system state evolution equation - the Lindblad equation. A steady state corresponds to a loss function of zero. Therefore, after continuously optimizing the circuit parameters in the classical solver to minimize the loss function (close to zero), the final result is an approximate solution to the steady state. Another method is to use n qubits to represent the d-dimensional open system and another n qubits to represent the environment, still requiring a total of 2n qubits. A d-dimensional mixed state is generated on n qubits by partial trace [2].

[0003] Based on the above examples, existing methods for calculating the steady state of an open physical system require at least 2n qubits to describe and implement. However, qubits are an extremely precious resource in quantum computing. Therefore, a method for obtaining the steady state of an open physical system is needed that can significantly reduce the number of qubits required for calculation.

[0004] References:

[0005] [1] Yoshioka, Nobuyuki, et al. "Variational quantum algorithm for nonequilibrium steady states." Physical Review Research 2.4 (2020): 043289.

[0006] [2] Yuan, Xiao, et al. "Theory of variational quantum simulation." Quantum3 (2019): 191. Summary of the Invention

[0007] In order to solve the technical problems existing in the above-mentioned prior art, a first aspect of the present invention provides a method for obtaining a steady state of an open physical system, the method comprising:

[0008] According to the spectral decomposition form of the density matrix ρ of the target quantum mixed state of the open physical system, the quantum state |ψ after the evolution of the d-dimensional quantum pure state with n quantum bits in the quantum circuit is used. i > to determine the target quantum mixed state so that the target quantum mixed state has an initialized circuit parameter θ, wherein the spectral decomposition form is expressed as: and d = 2 n ;

[0009] Constructing a corresponding loss function based on the selected observable quantity, observing the target quantum mixed state using quantum shadow tomography and calculating the loss function and its gradient based on the observation results;

[0010] The circuit parameter θ of the target quantum mixed state is adjusted using a gradient descent method until the loss function is minimized, thereby obtaining the steady state.

[0011] Preferably, in the method for obtaining the steady state of an open physical system, the quantum state after the evolution of the d-dimensional quantum pure state with n quantum bits in the quantum circuit |ψ i >Determining the target quantum mixed state includes:

[0012] The quantum circuit is constructed as follows:

[0013] The quantum pure state of the n quantum bits Sequentially through the first unitary door and projection measurements to obtain the quantum state |i>, which jointly generates a measured probability distribution p i , its mathematical expression is:

[0014] Pass the quantum state |i> through the second unitary gate Unitary evolution to the quantum state |ψ i >, its mathematical representation is:

[0015] According to the spectral decomposition form, for i from 1 to d, when the measured probability distribution p i and the corresponding quantum state |ψ i > is determined, the density matrix ρ of the target quantum mixed state is determined, and wherein the line parameters

[0016] Preferably, in the method for obtaining the steady state of an open physical system, the projection measurement comprises performing a Z basis vector projection measurement of d quantum bits>{i}<{i}, where i is a d-bit 0-1 string,

[0017] Preferably, in the method for obtaining the steady state of an open physical system, constructing a corresponding loss function based on the selected observable comprises:

[0018] According to the open physical system, the Lindblad equation L(ρ) is adopted as the observable quantity of the system and the loss function C(θ) is constructed as a square term with the norm (Frobenius norm) of the Lindblad equation L(ρ): and among them

[0019] The loss function C(θ) should satisfy the following conditions in the steady state of the open physical system: C(θ)≥0, C(θ)=0iff.L(ρ(θ))=0.

[0020] Preferably, in the method for obtaining the steady state of an open physical system, observing the target quantum mixed state using the quantum shadow tomography technique and calculating the loss function C(θ) based on the observation results include:

[0021] Randomly select N U The third unitary gate performs N operations on the target quantum mixed state on the Z basis vector. S Measure and get the measurement results Among them, for a given k-th the third unitary gate U k , the measured quantum state |ψ i The classic shadows of > are:

[0022]

[0023] where M is the quantum channel derived from a given set of unitary gates; and

[0024] Each item after the loss function C(θ) is expanded is rewritten into the following form:

[0025]

[0026] Wherein, O1 and O2 are determined according to the expansion of the loss function C(θ).

[0027] Preferably, in the method for obtaining the steady state of an open physical system, calculating the gradient of the loss function includes calculating the gradient according to a parameter translation law, wherein the partial derivative of the s-th component of the parameter θ can be calculated by the following formula:

[0028]

[0029] where e s is the unit vector of the sth component.

[0030] Preferably, in the method for obtaining the steady state of an open physical system, the difference method is used instead of the parameter translation law to calculate the gradient.

[0031] Preferably, in the method for obtaining the steady state of an open physical system, adjusting the circuit parameter θ of the target quantum mixed state by using the gradient descent method until the loss function is minimized comprises:

[0032] providing the gradient of the loss function as input to a classical optimizer to obtain the updated line parameter θ;

[0033] Adjust the quantum state |ψ according to the updated line parameter θ i >Until the calculated loss function is minimized.

[0034] Preferably, in the method for obtaining the steady state of an open physical system, the N U Each of the third unitary gates is a randomly selected Pauli gate or Clifford gate.

[0035] A second aspect of the present invention provides an apparatus for obtaining a steady state of an open physical system, comprising:

[0036] A mixed state preparation module is configured to prepare a d-dimensional quantum pure state having n quantum bits after evolution in a quantum circuit according to the spectral decomposition form of the density matrix ρ of the target quantum mixed state of the open physical system. i >, wherein the target quantum mixed state is composed of the quantum state |ψ i > describes and has initialized line parameters θ, where the spectral decomposition form is expressed as: and d = 2 n ;

[0037] a quantum shadow tomography calculation module configured to construct a corresponding loss function based on a selected observable, observe the target quantum mixed state using quantum shadow tomography, and calculate the loss function and its gradient based on the observation results;

[0038] a classical calculation module, configured to obtain the gradient, calculate and output the updated line parameter θ using a gradient descent method;

[0039] wherein the apparatus is configured to adjust the target quantum mixed state output by the mixed state preparation module according to the updated circuit parameter θ output by the classical calculation module and iteratively optimize until the loss function is minimized; and

[0040] The classical computing module is configured to be implemented based on a classical computer, and the mixed state preparation module and the quantum shadow tomography computing module are configured to be implemented based on quantum circuits.

[0041] Preferably, in the device for obtaining a steady state of an open physical system, the mixed state preparation module includes:

[0042] Pure state generation submodule, which is used to generate and output the quantum pure state of n quantum bits

[0043] First unitary door Its input end is coupled to the pure state generation submodule;

[0044] The projection measurement module has its input coupled to the first unitary gate The output terminal;

[0045] Second unitary door Its input terminal is coupled to the output terminal of the projection measurement module, the second unitary gate The output quantum state |ψ i >used to determine the target quantum mixed state based on the spectral decomposition form;

[0046] The mixed state preparation module is configured as follows:

[0047] The quantum pure state |0> is sequentially passed through the first unitary gate The quantum state |i> is obtained by the projection measurement module, which jointly generates a measured probability distribution p i , its mathematical expression is:

[0048] The quantum state |i> is passed through the second unitary gate Unitary evolution to the quantum state |ψ i >, its mathematical representation is: as well as

[0049] According to the spectral decomposition form, for i from 1 to d, when the measured probability distribution p i and the corresponding quantum state |ψ i >is determined, the density matrix ρ of the target quantum mixed state is determined; and wherein the circuit parameters

[0050] The third aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, which can be executed by a processor to implement the steps of any method provided in the first aspect of the present invention, wherein the computer program can be used in a quantum computing module and a classical computing module.

[0051] A fourth aspect of the present invention provides an electronic device, comprising:

[0052] one or more processors;

[0053] A storage device for storing one or more programs, which, when executed by the one or more processors, enables the electronic device to implement the steps of any one of the methods provided in the first aspect of the present invention, wherein the electronic device includes a quantum computing module and a classical computing module.

[0054] The methods, apparatuses, media, or devices provided by the various aspects of this application are used to achieve the steady state of an open quantum system, which can halve the number of qubits required for computations using similar methods in the prior art. Given the preciousness of qubits in computing, this significantly reduced reliance on the number of qubits makes this method even more advantageous and suitable for widespread use in current or low-cost quantum computing devices. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] The embodiments of the present invention are further described below with reference to the accompanying drawings, in which:

[0056] Figure 1 The portion of a device for obtaining a steady state of an open physical system provided by one embodiment, which is implemented by a quantum circuit, is shown. DETAILED DESCRIPTION

[0057] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Those skilled in the art can make appropriate adjustments to the components, parameters, etc. in the embodiments of the present invention based on the concept of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without making creative work are within the scope of protection of the present invention. In other cases, well-known methods, devices, implementations or operations are not shown or described in detail to avoid blurring various aspects of the present invention.

[0058] In addition, the described features, structures or characteristics may be combined in one or more embodiments in any suitable manner. In the following description, many specific details are provided to provide a full understanding of the embodiments of the present invention. However, those skilled in the art will appreciate that the technical solutions of the present invention can be practiced without one or more of the specific details, or other methods, components, devices, steps, etc. can be adopted. In other cases, well-known methods, devices, implementations or operations are not shown or described in detail to avoid blurring various aspects of the present invention. The processes in the embodiments are merely illustrative and do not necessarily include all the content and operations / steps, nor do they necessarily have to be performed in the order described. For example, some operations / steps can also be decomposed, while some operations / steps can be merged or partially merged, so the order of actual execution may change according to actual conditions.

[0059] This application proposes a new method for obtaining the steady state of an open quantum system that significantly reduces the dependence of quantum computers on the number of quantum bits. It adopts quantum-classical hybrid computing: an algorithm that uses quantum circuits to perform calculations on the inner layer to determine observable quantities and corresponding loss functions, and uses traditional classical optimizers to adjust the parameters of the quantum circuits on the outer layer. Such quantum-classical hybrid computing can maximize the advantages of quantum computing.

[0060] First, the system architecture involved in this application is introduced and explained.

[0061] Figure 1 The figure shows the part implemented by quantum circuits in the apparatus 1 for obtaining the steady state of an open physical system provided by one embodiment of the present application. This part includes a mixed state preparation module 100 and a quantum shadow tomography calculation module 200. The apparatus 1 also includes a classical calculation module ( Figure 1 (not shown), the classical computing module is used to perform operations related to classical computing, such as using the gradient descent method to update the circuit parameters for controlling the mixed state preparation module based on the loss function C(θ) obtained from the calculation results of the quantum shadow tomography computing module, and judging whether the circuit parameters have met the preset threshold or reached the preset iteration step size during the iteration process. However, optionally, the classical computing module can also be replaced by a quantum circuit that can implement the same computing process in theory, so Figure 1 The example structures shown are not limitations of the present invention.

[0062] exist Figure 1 In the example shown, the mixed state preparation module 100 is configured to be a spectral decomposition form of the density matrix ρ of the target quantum mixed state of the open physical system. To prepare a d-dimensional quantum pure state (d=2n) with n quantum bits in the quantum circuit after the evolution of the quantum state |ψ i> is used to represent the target quantum mixed state, so that the target quantum mixed state has an initialized circuit parameter θ.

[0063] The mixed state preparation module 100 includes:

[0064] Pure state generation submodule 101, which has an output terminal for generating and outputting a quantum pure state of n quantum bits

[0065] First unitary door Its input terminal is coupled to the pure state generation submodule, and it has an output terminal;

[0066] The projection measurement module 103 has its input coupled to the first unitary gate In an exemplary embodiment, the projection measurement includes performing a Z basis vector projection measurement of d qubits>{i}<{i}, where i is a d-bit 0-1 string,

[0067] Second unitary door Its input terminal is coupled to the output terminal of the projection measurement module 103, and it has an output terminal. The output quantum state |ψ i >used to determine the target quantum mixed state based on the spectral decomposition form.

[0068] The mixed state preparation module 100 of the above structure can be implemented based on quantum circuits. It is configured to sequentially pass the quantum pure state |0> generated by the pure state generation submodule 101 through the first unitary gate The quantum state |i> is obtained by the interaction with the projection measurement module 103, thereby jointly generating a measured probability distribution p i , its mathematical expression is: Then, the quantum state |i> is passed through the second unitary gate Unitary evolution to the quantum state |ψ i >, its mathematical representation is:

[0069] According to the spectral decomposition form, the target quantum mixed state can be described by its density matrix ρ. Therefore, for i from 1 to d, by configuring the appropriate first unitary gate, projection measurement module 103 and second unitary gate, when the measured probability distribution p i and the corresponding quantum state |ψ i > is determined, the density matrix ρ of the target quantum mixed state is determined. Specifically, the above determination is achieved by operating the circuit parameter θ, which can be regarded as and The joint operation of in and The operation can be achieved through a series of specific unitary gates.

[0070] Figure 1 The quantum shadow tomography calculation module 200 shown is configured to construct a corresponding loss function based on the selected observable quantity, observe the target quantum mixed state using quantum shadow tomography technology, and calculate the loss function and its gradient based on the observation results.

[0071] In an exemplary embodiment, in order to determine a more effective loss function, the inventors chose to use the Lindblad equation L(ρ) commonly used in the art as the main equation to describe the evolution of the open system. The Lindblad equation L(ρ) can be written as follows:

[0072]

[0073] Open system steady-state requirements

[0074] L(ρ)=0

[0075] A suitable loss function C(θ) needs to satisfy

[0076] C(θ)≥0, C(θ)=0iff.L(ρ(θ))=0

[0077] In an exemplary embodiment, the inventors consider selecting the square of the Frobenius norm of L(ρ) as the loss function,

[0078]

[0079] The advantage of this choice is that the loss function value can be easily measured in the quantum circuit using shadow tomography technology.

[0080] Figure 1 The quantum shadow tomography technology used by the quantum shadow tomography computing module 200 is well known in the field of quantum computing and is only schematically described below. In an exemplary operation of the quantum shadow tomography computing module 200 described in this embodiment, it is configured to randomly select N U A unitary gate is used to perform the random measurement required for shadow tomography. The random unitary gate can be composed of either a random Pauli gate or a random Clifford gate. Finally, the entire system is measured on the Z basis vector and the measurement result is obtained. A total of N measurements Stimes. When the kth unitary gate is given, a classical shadow of the measured quantum state can be obtained:

[0081]

[0082] Where M is the quantum channel obtained by a given set of unitary gates. After sampling the unitary gates, a series of shadows are obtained, which can be used to find the quadratic function of the quantum state ρ, that is,

[0083]

[0084] Therefore, it can be seen that all terms in the expanded loss function satisfy the above form. Shadow tomography can be used to simultaneously estimate all values ​​and ultimately sum them to obtain the loss function value. Here, O1 and O2 are determined based on the expanded form of the loss function. The expansion of the loss function is also well known in the art and will not be described in detail here. Thus, the quantum shadow tomography calculation module 200 obtains the loss function.

[0085] The quantum shadow tomography calculation module 200 is further configured to calculate the gradient of the loss function C(θ) with respect to θ based on the obtained loss function calculation result.

[0086] In an exemplary embodiment, the gradient of the loss function C(θ) with respect to θ is calculated using the parameter translation rule. In the gradient calculation, the partial derivative of the sth component of the parameter θ can be calculated as follows:

[0087]

[0088] where e s is the unit vector of the sth component. However, in other embodiments according to the present invention, other gradient calculation methods known in the art may also be used for the gradient calculation described in various embodiments of this application, such as the difference method. Thus, the quantum shadow tomography calculation module 200 is configured to use the loss function value and the gradient calculation result as the output of the module.

[0089] As previously mentioned, apparatus 1 also includes a classical computing module coupled to the output of quantum shadow tomography module 200. Using the gradient information output by quantum shadow tomography module 200, various gradient descent-based algorithms developed in the field of classical optimization can be used to update the circuit parameters θ of mixed-state preparation module 100, thereby completing an optimization iteration until the loss function converges to a preset convergence threshold or the number of iterations reaches a preset number. At this point, the updated circuit parameters are considered to be the optimal parameters corresponding to the steady state of the open system. This means that the steady state of the open physical system has been achieved.

[0090] In an exemplary embodiment, the classical computing module is implemented by a classical computer.

[0091] Next, we will combine Figure 1 The system architecture shown is used to introduce and illustrate an embodiment of the method for obtaining the steady state of an open physical system in the present application.

[0092] In an exemplary embodiment, a method for obtaining a steady state of an open physical system includes the following three steps:

[0093] Step 1):

[0094] According to the spectral decomposition form of the density matrix ρ of the target quantum mixed state of the open physical system, the quantum state |ψ after the evolution of the d-dimensional quantum pure state with n quantum bits in the quantum circuit is used. i > to determine the target quantum mixed state so that the target quantum mixed state has an initialized circuit parameter θ, wherein the spectral decomposition form is expressed as: And d=2n.

[0095] Wherein, determining the target quantum mixed state by using a set of evolution results of a quantum pure state having n quantum bits in a quantum circuit includes constructing the quantum circuit as follows: i) transforming the quantum pure state of the n quantum bits into Sequentially through the first unitary door and projection measurement to obtain the quantum state |i>, which jointly generates a measured probability distribution p i , its mathematical expression is: ii) Pass the quantum state |i> through the second unitary gate The unitary evolution to the quantum state |ψ i >, its mathematical representation is: According to the spectral decomposition form, for i from 1 to d, when the measured probability distribution p i and the corresponding quantum state |ψ ￡ > is determined, the density matrix ρ of the target quantum mixed state is determined; the circuit parameters The projection measurement includes performing a Z basis vector projection measurement of d quantum bits>{i}<{i}, where i is a d-bit 0-1 string,

[0096] Step 1) is used to output a mixed state that can be adjusted by the circuit parameter θ, with the purpose of making the output mixed state gradually approach and equal to the target quantum mixed state intended to be obtained after subsequent adjustment and optimization of θ.

[0097] Step 2):

[0098] A corresponding loss function is constructed based on the selected observable quantity, and the loss function and its gradient are calculated using quantum shadow tomography. The construction of the corresponding loss function based on the selected observable quantity includes: according to the open physical system, using the Lindblad equation L(ρ) as the observable quantity of the system and constructing the loss function C(θ) as a square term having the norm of the Lindblad equation L(ρ): The calculation of the loss function C(θ) using the quantum shadow tomography technique includes: randomly selecting N U A third unitary gate (Pauli gate or Clifford gate can be randomly selected) performs N operations on the target quantum mixed state on the Z basis vector. S Measure and get the measurement results Among them, for a given k-th the third unitary gate U k , the measured quantum state |ψ i The classic shadows of > are:

[0099]

[0100] where M is the quantum channel derived from a given set of unitary gates; and

[0101] Each item after the loss function C(θ) is expanded is rewritten into the following form:

[0102]

[0103] Wherein, O1 and O2 are determined according to the expansion of the loss function.

[0104] In step 2), after determining the value of the loss function, the gradient of the loss function is calculated according to the parameter translation rule, where the partial derivative of the sth component of the parameter θ can be calculated as follows:

[0105]

[0106] where e s is the unit vector of the sth component. In an alternative embodiment, the gradient can be calculated by using a difference method instead of the parameter translation law.

[0107] The gradient value obtained by step 2) is used as the output of step 2).

[0108] Step 3):

[0109] According to the gradient value output in step 2, the circuit parameter θ of the target quantum mixed state is adjusted using the gradient descent method until the loss function is minimized, thereby obtaining the steady state. Step 3) includes: providing the gradient of the loss function as input to the classical optimizer to obtain the updated circuit parameter θ; adjusting the quantum state |ψ according to the updated circuit parameter θ i >Until the calculated loss function is minimized, that is, until the loss function no longer decreases or reaches the set number of iterations, the line parameter θ is obtained as the optimal one.

[0110] It is understandable that in the above embodiment, the loss function is determined only exemplarily according to the square of the norm of L(ρ), but other suitable forms of loss functions are theoretically possible and are not limited here.

[0111] The classical optimizer used to optimize the loss function in other embodiments of the present application may also be any suitable optimizer known in the art that can run on a classical computer or a quantum computer.

[0112] In another embodiment of the present application, a storage medium is provided in which a computer program is stored. The computer program includes a quantum computer program and a classical computer program. The computer program is configured to execute the method described in Example 1 when executed, and the computer program can be used in a quantum computing module and a classical computing module.

[0113] In other embodiments according to the present application, an electronic device is provided, comprising a memory and a processor, wherein the memory stores a computer program, and the processor is configured to run the computer program to execute the method described in Example 1, wherein the electronic device comprises a quantum computing module and a classical computing module.

[0114] Some or all of the method steps may be performed by (or using) a hardware device (e.g., a processor, a microprocessor, a programmable computer, or an electronic circuit) comprising a quantum circuit. In some embodiments, such a device may perform one or more of the most important method steps.

[0115] Depending on certain implementation requirements, embodiments of the present invention may be implemented in hardware or software. This implementation may be performed using a non-transitory storage medium (such as a digital storage medium, e.g., a floppy disk, DVD, Blu-ray, CD, ROM, PROM, and EPROM, EEPROM, or FLASH) having stored thereon electronically readable control signals that cooperate (or are capable of cooperating) with a programmable computer system to perform the corresponding method. Thus, the digital storage medium may be computer-readable.

[0116] Some embodiments of the invention comprise a data carrier having electronically readable control signals, which are capable of cooperating with a programmable computer system, such that one of the methods described herein is performed.

[0117] Generally, embodiments of the present invention can be implemented as a computer program product having a program code, which is operable to perform one of the methods when the computer program product runs on a computer. The program code can, for example, be stored on a machine-readable carrier.

[0118] Other embodiments comprise the computer program for performing one of the methods described herein, stored on a machine readable carrier.

[0119] In other words, an exemplary embodiment of the present invention is, therefore, a computer program having a program code for performing one of the methods described herein, when the computer program runs on a computer.

[0120] Therefore, a further embodiment of the present invention is a storage medium (or a data carrier or a medium readable by a quantum computer and optionally a classical computer) comprising a computer program stored thereon for performing one of the methods described herein when the computer program is executed by a processor. The data carrier, digital storage medium or recorded medium is generally tangible and / or non-transitory.

[0121] Yet another embodiment of the present invention is a device according to the present invention, comprising a processor and a storage medium.

[0122] Another embodiment of the present invention is a data stream or a signal sequence representing the computer program for performing one of the methods described herein. The data stream or the signal sequence can be configured to be transmitted via a data communication connection, such as the Internet.

[0123] A further embodiment comprises a processing means, for example a computer or a programmable logic device, configured to or adapted to perform one of the methods described herein, which may comprise quantum processing means, and optionally classical processing means.

[0124] A further embodiment comprises a computer on which is installed the computer program for performing one of the methods described herein.

[0125] Yet another embodiment of the present invention includes an apparatus or system configured to transmit (e.g., electronically or optically) a computer program for performing one of the methods described herein to a receiver. A portion of the receiver may be, for example, a computer with quantum circuits, a mobile device, a storage device, or the like. The apparatus or system may include, for example, a file server for transmitting the computer program to the receiver.

[0126] The method described in the present invention can be used to describe open quantum systems and can therefore be applied in research calculations in fields such as condensed matter physics and optics.

[0127] Although the present invention has been described through preferred embodiments, the present invention is not limited to the embodiments described herein but includes various changes and modifications that may be made without departing from the scope of the present invention.

Claims

1. A method for obtaining a steady state of an open physical system, the method comprising: According to the density matrix of the target quantum mixed state of the open physical system The spectral decomposition form of the d-dimensional quantum pure state with n quantum bits is used to represent the quantum state after evolution in the quantum circuit. To determine the target quantum mixed state so that the target quantum mixed state has initialized circuit parameters , wherein the spectrum decomposition form is expressed as: ,as well as ; Constructing a corresponding loss function based on the selected observable quantity, observing the target quantum mixed state using quantum shadow tomography and calculating the loss function and its gradient based on the observation results; and Using the gradient descent method to adjust the circuit parameters of the target quantum mixed state until the loss function is minimized, thereby obtaining the steady state; The quantum state after the evolution of the d-dimensional quantum pure state with n quantum bits in the quantum circuit is Determining the target quantum mixed state includes: The quantum circuit is constructed as follows: The quantum pure state of the n quantum bits Sequentially through the first unitary door and projection measurement to obtain quantum states , which jointly generates a measured probability distribution , its mathematical expression is: ;as well as The quantum state Through the second unitary door Unitary evolution to the quantum state , its mathematical expression is: ; According to the spectrum decomposition form, for From 1 to d, when the measured probability distribution and the corresponding quantum state When the density matrix of the target quantum mixed state is determined is determined, as well as where the line parameters .

2. The method according to claim 1, wherein the projection measurement comprises performing a Z basis vector projection measurement of n quantum bits. i is a d-bit 0-1 string, .

3. The method according to claim 1, wherein constructing a corresponding loss function based on the selected observable comprises: According to the open physical system, the Lindblad equation is used As the observable quantity of the system, the loss function is selected and Constructed with the Lindblad equation The square term of the Frobenius norm: ; as well as in The loss function The open physical system should satisfy the following in steady state: .

4. The method according to claim 3, wherein the target quantum mixed state is observed using the quantum shadow tomography technique and the loss function is calculated based on the observation results. include: Random selection A third unitary gate performs a Measure and get the measurement results , where for a given The third unitary gate , the measured quantum state The classic shades are: in The resulting quantum channel for a given set of unitary gates; and The loss function Each item after expansion is rewritten to have the following form: in, and According to the loss function The expansion of is determined.

5. The method of claim 3, wherein calculating the gradient of the loss function comprises calculating the gradient according to a parameter translation rule, wherein Parameters The partial derivative of the sth component can be calculated as follows, in is the unit vector of the sth component.

6. The method according to claim 5, wherein: The gradient is calculated by using the difference method instead of the parameter translation law.

7. The method according to claim 1, wherein The circuit parameters of the target quantum mixed state are adjusted by the gradient descent method. Until the loss function is minimized, it includes: The gradient of the loss function is fed as input to a classical optimizer to obtain updated line parameters. ; According to the updated line parameters Adjusting the quantum state Until the loss function obtained by calculation is minimized.

8. The method according to claim 4, wherein described Each of the third unitary gates is a randomly selected Pauli gate or Clifford gate.

9. A device for obtaining a steady state of an open physical system, characterized in that: A mixed state preparation module configured to generate a density matrix of a target quantum mixed state according to the open physical system The spectral decomposition form of the d-dimensional quantum pure state with n quantum bits is prepared after the evolution of the quantum state in the quantum circuit. , wherein the target quantum mixed state is composed of the quantum state Describes and has initialized line parameters , wherein the spectrum decomposition form is expressed as: ,as well as ; a quantum shadow tomography calculation module configured to construct a corresponding loss function based on a selected observable, observe the target quantum mixed state using quantum shadow tomography, and calculate the loss function and its gradient based on the observation results; A classical calculation module is configured to obtain the gradient, calculate and output the updated line parameters using the gradient descent method ; The device is configured to calculate the updated line parameters according to the output of the classical calculation module. Adjusting the target quantum mixed state output by the mixed state preparation module and iteratively optimizing until the loss function is minimized; and The classical computing module is configured to be implemented based on a classical computer, and the mixed state preparation module and the quantum shadow tomography computing module are configured to be implemented based on a quantum circuit; The mixed state preparation module includes: Pure state generation submodule, which is used to generate and output the quantum pure state of n quantum bits ; First unitary door , whose input end is coupled to the pure state generation submodule; The projection measurement module has its input coupled to the first unitary gate output terminal; and Second unitary door , whose input is coupled to the output of the projection measurement module, the second unitary gate Output quantum state for determining the target quantum mixed state based on the spectral decomposition form; The mixed state preparation module is configured as follows: The quantum pure state Sequentially through the first unitary door and projection measurement module to obtain quantum states , which jointly generates a measured probability distribution , its mathematical expression is: ;as well as The quantum state Through the second unitary door Unitary evolution to the quantum state , its mathematical expression is: ; According to the spectrum decomposition form, for From 1 to d, when the measured probability distribution and the corresponding quantum state When the density matrix of the target quantum mixed state is determined, is determined; and wherein the line parameters .

10. A computer-readable storage medium, characterized in that A computer program is stored thereon, which can be executed by a processor to implement the steps of the method according to any one of claims 1 to 8, wherein the computer program can be used in a quantum computing module and a classical computing module.

11. An electronic device, characterized in that: include: one or more processors; A storage device for storing one or more programs, which, when executed by the one or more processors, enables the electronic device to implement the steps of the method as described in any one of claims 1 to 8, wherein the electronic device includes a quantum computing module and a classical computing module.

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