WO2023103754A1 - 量子体系下的热化态制备方法、设备及存储介质 - Google Patents

量子体系下的热化态制备方法、设备及存储介质 Download PDF

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WO2023103754A1
WO2023103754A1 PCT/CN2022/132997 CN2022132997W WO2023103754A1 WO 2023103754 A1 WO2023103754 A1 WO 2023103754A1 CN 2022132997 W CN2022132997 W CN 2022132997W WO 2023103754 A1 WO2023103754 A1 WO 2023103754A1
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state
quantum
target
thermalization
qubit
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PCT/CN2022/132997
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French (fr)
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张士欣
张胜誉
姚宏
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腾讯科技（深圳）有限公司
清华大学
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Priority to JP2023538921A priority Critical patent/JP2024505345A/ja
Priority to KR1020237024872A priority patent/KR20230124666A/ko
Priority to EP22903177.8A priority patent/EP4280124A1/en
Publication of WO2023103754A1 publication Critical patent/WO2023103754A1/zh
Priority to US18/336,671 priority patent/US20230351238A1/en

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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N10/00—Quantum computing, i.e. information processing based on quantum-mechanical phenomena
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N10/00—Quantum computing, i.e. information processing based on quantum-mechanical phenomena
    • G06N10/60—Quantum algorithms, e.g. based on quantum optimisation, quantum Fourier or Hadamard transforms
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N10/00—Quantum computing, i.e. information processing based on quantum-mechanical phenomena
    • G06N10/20—Models of quantum computing, e.g. quantum circuits or universal quantum computers
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N10/00—Quantum computing, i.e. information processing based on quantum-mechanical phenomena
    • G06N10/40—Physical realisations or architectures of quantum processors or components for manipulating qubits, e.g. qubit coupling or qubit control
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/04—Architecture, e.g. interconnection topology
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/04—Architecture, e.g. interconnection topology
    • G06N3/0499—Feedforward networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/08—Learning methods
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B82—NANOTECHNOLOGY
    • B82Y—SPECIFIC USES OR APPLICATIONS OF NANOSTRUCTURES; MEASUREMENT OR ANALYSIS OF NANOSTRUCTURES; MANUFACTURE OR TREATMENT OF NANOSTRUCTURES
    • B82Y10/00—Nanotechnology for information processing, storage or transmission, e.g. quantum computing or single electron logic

Definitions

  • the embodiments of the present application relate to the field of quantum technology, and in particular to a thermal state preparation method, equipment and storage medium in a quantum system.
  • the mixed states on the system qubits are prepared by taking offsets on the auxiliary qubits.
  • the Gibbs entropy of the mixed state is a nonlinear logarithmic function of the density matrix, it cannot be directly and efficiently measured, and state tomography that consumes exponential resources is required.
  • the "exponential resource” mentioned here means that the number of measurements is exponentially related to the number of qubits in the system, resulting in excessive measurement time.
  • Embodiments of the present application provide a thermal state preparation method, device and storage medium in a quantum system. Described technical scheme is as follows:
  • a method for preparing a thermal state in a quantum system comprising:
  • each set of measurement results includes: a first measurement result corresponding to the system qubit, and a second measurement result corresponding to the auxiliary qubit, n is a positive integer;
  • variational parameters include at least one of the following: parameters of the parameterized quantum circuit, parameters of the neural network;
  • the mixed state of the target quantum system is obtained to approximately characterize the thermalization state of the target quantum system.
  • a device for preparing a thermal state in a quantum system comprising:
  • the measurement result acquisition module is used to obtain n sets of measurement results obtained by performing n measurements on the output quantum state of the parameterized quantum circuit after the input quantum state of the combined qubit is transformed by the parameterized quantum circuit; wherein , the combined qubit includes an auxiliary qubit and a system qubit of the target quantum system, and each set of measurement results includes: a first measurement result corresponding to the system qubit, and a second measurement corresponding to the auxiliary qubit As a result, n is a positive integer;
  • a weight parameter acquisition module configured to process the second measurement result through a neural network to obtain a weight parameter
  • a correlation function calculation module configured to calculate the value of the correlation function of the mixed state of the target quantum system based on the weight parameter and the first measurement result;
  • the objective function calculation module is used to calculate the expected value of the objective function based on the correlation function value of the mixed state
  • a variational parameter adjustment module configured to adjust the variational parameters with the goal of convergence of the expected value of the objective function; wherein the variational parameters include at least one of the following: parameters of the parameterized quantum circuit, the The parameters of the neural network;
  • the thermalization state obtaining module is used to obtain the mixed state of the target quantum system to approximately characterize the thermalization state of the target quantum system when the expected value of the target function satisfies the convergence condition.
  • a computer device is provided, and the computer device is used to implement the above method for preparing a thermalized state in a quantum system.
  • the computer device is a quantum computer, or a classical computer, or a mixed device execution environment of a quantum computer and a classical computer.
  • a computer-readable storage medium is provided, and a computer program is stored in the storage medium, and the computer program is loaded and executed by a processor to realize the thermal state preparation in the quantum system described above method.
  • a computer program product is provided, the computer program product or computer program includes a computer program, the computer program is stored in a computer-readable storage medium, and a processor can read from the computer The storage medium reads and executes the computer program, so as to realize the method for preparing a thermal state under the quantum system.
  • a thermal state preparation system under a quantum system includes: parameterized quantum circuits and computer equipment;
  • the parameterized quantum circuit is used to transform the input quantum state of the combined qubit to obtain the output quantum state of the parameterized quantum circuit; wherein the combined qubit includes a system of auxiliary qubits and a target quantum system qubit;
  • the computer device is configured to obtain n sets of measurement results obtained by performing n measurements on the output quantum state of the parameterized quantum circuit; wherein, each set of measurement results includes: a first measurement corresponding to the system qubit Result, and the second measurement result corresponding to the auxiliary qubit, n is a positive integer;
  • the computer device is further configured to process the second measurement result through a neural network to obtain a weight parameter; based on the weight parameter and the first measurement result, calculate and obtain the correlation of the mixed state of the target quantum system Function value; Based on the correlation function value of the mixed state, calculate the expected value of the objective function;
  • the computer device is further configured to adjust the variational parameters with the goal of convergence of the expected value of the objective function; when the expected value of the objective function satisfies the convergence condition, obtain the mixed state of the target quantum system to Approximately characterizing the thermalization state of the target quantum system; wherein the variational parameters include at least one of the following: parameters of the parameterized quantum circuit, parameters of the neural network.
  • This solution introduces the neural network output weight parameter, and uses the weight parameter to adjust the weight corresponding to different auxiliary qubit measurement results, thereby enhancing the overall expression ability of the circuit through the trainable parameters of the neural network, achieving more efficient and accurate To prepare the effect of thermalization state.
  • Fig. 1 is a schematic diagram of the thermalization state preparation framework under the quantum system provided by an embodiment of the present application
  • Fig. 2 is a flowchart of a method for preparing a thermalized state under a quantum system provided by an embodiment of the present application
  • Fig. 3 is a flowchart of a method for preparing a thermalized state under a quantum system provided by another embodiment of the present application;
  • Fig. 4 is the schematic diagram of the experimental result provided by one embodiment of the present application.
  • Fig. 5 is a schematic diagram of the experimental results provided by another embodiment of the present application.
  • Fig. 6 is a schematic diagram of the experimental results provided by another embodiment of the present application.
  • Fig. 7 is a block diagram of a thermalized state preparation device under a quantum system provided by an embodiment of the present application.
  • Fig. 8 is a schematic diagram of a computer device provided by an embodiment of the present application.
  • Quantum computing Based on quantum logic computing, the basic unit of data storage is the quantum bit (qubit).
  • Qubit The basic unit of quantum computing. Traditional computers use 0 and 1 as the basic units of binary. The difference is that quantum computing can process 0 and 1 at the same time, and the system can be in the linear superposition state of 0 and 1:
  • ⁇ > ⁇
  • 2 represent the probability of being 0 and 1, respectively.
  • Quantum circuit A representation of a quantum general-purpose computer, which represents the hardware implementation of the corresponding quantum algorithm/program under the quantum gate model. If the quantum circuit contains adjustable parameters to control the quantum gate, it is called a parameterized quantum circuit (Parameterized Quantum Circuit, referred to as PQC) or a variable quantum circuit (Variational Quantum Circuit, referred to as VQC), the two are the same concept.
  • PQC Parameterized Quantum Circuit
  • VQC Variational Quantum Circuit
  • Hamiltonian A Hermitian matrix that describes the total energy of a quantum system.
  • the Hamiltonian is a physical vocabulary and an operator that describes the total energy of a system, usually denoted by H.
  • Quantum-classical hybrid computing a calculation paradigm in which the inner layer uses quantum circuits (such as PQC) to calculate the corresponding physical quantities or loss functions, and the outer layer uses traditional classical optimizers to adjust the variational parameters of quantum circuits. Taking advantage of quantum computing is believed to be one of the important directions that has the potential to prove quantum superiority.
  • quantum circuits such as PQC
  • NISQ Noisy Intermediate-Scale Quantum
  • VQE Variational Quantum Eigensolver
  • Post-selection For the measurement results output by the quantum computer, choose to keep or discard the measurement results based on the specific value of the bit string (bitstring) corresponding to some bits, which is called post-selection. Post-selection appears in many current research hotspots, including but not limited to linear unitary matrix combination to realize LCU (linear combinations of unitary operations, linear combination of unitary operations (linear combination operator)), entanglement entropy phase change caused by measurement, etc.
  • Pauli string An item composed of the direct product of multiple Pauli matrices at different lattice points.
  • the general Hamiltonian can usually be disassembled into the sum of a group of Pauli strings.
  • the measurement of VQE is generally measured item by item according to the Pauli string decomposition.
  • Non-unitary The so-called unitary matrix is a matrix that satisfies All matrices of , and all evolution processes directly allowed by quantum mechanics, can be described by unitary matrices.
  • U is a unitary matrix (Unitary Matrix), also known as a unitary matrix, a unitary matrix, etc., is the conjugate transpose of U.
  • matrices that do not meet this condition are non-unitary, which requires auxiliary means or even exponentially more resources to be realized experimentally, but non-unitary matrices often have stronger expressive power and faster ground state projection effects .
  • the above-mentioned “exponentially many resources” means that the demand for resources increases exponentially with the increase in the number of qubits.
  • the exponentially many resources can mean that the total number of quantum circuits that need to be measured is exponentially multiple, that is, the corresponding needs Exponentially much computation time.
  • Bit string a string of numbers composed of 0 and 1.
  • the classical results obtained by each measurement of the quantum circuit can be represented by 0 and 1 respectively according to the upper and lower spin configurations on the measurement basis, so that the total measurement result corresponds to a bit string.
  • Pauli operator also known as Pauli matrix, is a set of three 2 ⁇ 2 unitary Hermitian complex matrices (also known as unitary matrices), generally represented by the Greek letter ⁇ (sigma). Among them, the Pauli X operator is The Pauli Y operator is The Pauli Z operator is
  • Gibbs thermalization state refers to the quantum mixed state that satisfies the thermal equilibrium distribution, that is, its classical probability satisfies the Boltzmann distribution Z is the partition function (normalization factor), is the reciprocal of the system temperature, and E i is the intrinsic energy spectrum of the physical system.
  • the Gibbs thermalization state using the matrix index of the Hamiltonian H, can be expressed more concisely as If the Gibbs thermalization state can be prepared efficiently, the physical properties and correlation function measurements of finite temperature thermal equilibrium systems can be realized.
  • the Gibbs thermalization state is also the mixed state ⁇ corresponding to the minimum free energy loss function with Gibbs entropy:
  • the first term Tr(H ⁇ ) of this formula is the energy term, and the second term can be reduced to S is called Gibbs entropy.
  • Gibbs entropy is a general expression of system entropy under equilibrium thermodynamic equilibrium. If the system has n energy levels, the probability of occupying the i-th energy level is p i , and the entropy of the system is Where k B is the Boltzmann constant (Boltzmann constant), this formula is called the Gibbs entropy formula.
  • Renyi (Ruili) thermalization state it is a free energy loss function that minimizes Renyi entropy (Renyi entropy, Ruili entropy), and the corresponding mixed state ⁇ :
  • Trace distance The trace distance T between two mixed states ⁇ , ⁇ is defined as:
  • Finite temperature system refers to the system with temperature greater than 0, which is opposite to the zero temperature system corresponding to the ground state.
  • the equilibrium state of the finite temperature system is not the ground state, but the mixed state represented by the Gibbs thermalization state.
  • Free energy refers to the part of the reduced internal energy of the system that can be converted into external work in a certain thermodynamic process. It measures the "useful energy” that the system can output externally in a specific thermodynamic process . Can be divided into Helmholtz (Helmholtz) free energy and Gibbs free energy.
  • the technical solution provided by this application will help to accelerate and enhance the development and practicability of quantum hardware in the NISQ period.
  • the enhancement scheme proposed in this application after the variation of the neural network fully considers the characteristics of quantum hardware in the NISQ era, and can increase the expressive ability of shallower quantum circuits through the classical neural network.
  • this scheme is perfectly compatible with other NISQ variational post-processing schemes, such as the Variational Quantum Neural network Hybrid Eigensolver (VQNHE for short) (the neural network of this application scheme acts on the auxiliary qubit , the neural network of the VQNHE scheme acts on the system qubit), which can be used in combination to further improve the mixed-state preparation, that is, the effect of finite temperature VQE.
  • VQNHE Variational Quantum Neural network Hybrid Eigensolver
  • the application scheme can be easily applied to quantum hardware evaluation, testing, scientific research and actual production in the short to medium term. Its applications include, but are not limited to, the simulation of finite temperature states of the Hamiltonian of systems from quantum many-body physics and quantum chemistry problems.
  • the thermalization state preparation method under the quantum system provided in the embodiment of the present application can be implemented by a classical computer (such as a PC (Personal Computer, personal computer)), for example, the classical computer executes a corresponding computer program to realize the method;
  • the method can be realized by a quantum computer; or it can also be executed in a mixed equipment environment of a classical computer and a quantum computer, for example, the method is realized by cooperation of a classical computer and a quantum computer.
  • a quantum computer is used to realize the processing and measurement of the quantum state in the embodiment of the present application
  • a classical computer is used to realize other steps such as neural network calculation, objective function calculation, and variational parameter optimization in the embodiment of the present application.
  • the execution subject of each step is a computer device for introduction and description.
  • the computer device may be a classical computer or a quantum computer, and may also include a mixed execution environment of the classical computer and the quantum computer, which is not limited in this embodiment of the present application.
  • the thermalized state preparation framework under the quantum system is shown in FIG. 1 , including: a parameterized quantum circuit (PQC) 10 , a neural network 20 and an optimizer 30 .
  • the parameterized quantum circuit 10 is used to transform the input quantum state of the combined qubit to obtain the corresponding output quantum state.
  • the combined qubit includes the auxiliary qubit and the system qubit of the target quantum system.
  • the output quantum state of the parameterized quantum circuit 10 is measured n times to obtain n sets of measurement results, each set of measurement results includes a first measurement result corresponding to the system qubit, and a second measurement result corresponding to the auxiliary qubit, n is a positive integer.
  • the neural network 20 is used to process the second measurement result to obtain weight parameters.
  • the value of the correlation function of the mixed state of the target quantum system is calculated, and then the expected value of the objective function is calculated based on the value of the correlation function of the mixed state.
  • the optimizer 30 is used to adjust the parameters of the target object (such as including the parameterized quantum circuit 10 and/or the neural network 20 ) with the goal of convergence of the expected value of the target function.
  • the expected value of the objective function satisfies the convergence condition, the mixed state of the target quantum system is obtained, and the obtained mixed state can approximate the thermalization state of the target quantum system.
  • Fig. 2 is a flow chart of a method for preparing a thermalized state in a quantum system provided by an embodiment of the present application. This method can be applied in the framework shown in Fig. 1 , for example, the execution body of each step can be a computer device. The method may include the following steps (210-260):
  • Step 210 obtain n sets of measurement results obtained by performing n measurements on the output quantum state of the parameterized quantum circuit after the parameterized quantum circuit transforms the input quantum state of the combined qubit; wherein the combined qubit includes auxiliary Qubits and system qubits of the target quantum system, each set of measurement results includes: a first measurement result corresponding to the system qubit, and a second measurement result corresponding to the auxiliary qubit, and n is a positive integer.
  • the target quantum system can be any quantum system that needs to be studied, and the thermalization state of the target quantum system in a finite temperature system can be approximately prepared through the technical solution provided in this embodiment.
  • the target quantum system can be any quantum physical system or quantum chemical system, and the obtained thermalization state of the target quantum system can be used to evaluate the real properties of the actual material of the system in a finite temperature state, and can also be used to Investigate the behavior of the system in a non-thermal equilibrium system.
  • the system qubit refers to the qubits contained in the target quantum system. If the target quantum system contains 5 qubits, the number of system qubits is also 5.
  • the auxiliary qubits are prepared to obtain the mixed state of the target quantum system.
  • auxiliary qubits can be the same as the number of system qubits, or it can be smaller or larger than the system qubits quantity.
  • the input of the parameterized quantum circuit includes the input quantum state of the combined qubit, that is, includes the input quantum state of the system qubit and the auxiliary qubit.
  • the input quantum state can generally be an all-0 state, a uniform superposition state or a Hartree-Fock (Hartley-Fock) state, and the input quantum state is also called a tentative state.
  • the arrangement of the system qubits and the auxiliary qubits is not limited.
  • the system qubits and auxiliary qubits can be arranged in an overlapping manner, such as the system qubits and auxiliary qubits are arranged at intervals one by one, or an auxiliary qubit is inserted every interval of several system qubits, and so on.
  • the overlapping arrangement can maximize the entanglement between the system qubit and the auxiliary qubit, so that the parameterized quantum circuit can use a shallower circuit depth and reduce complexity.
  • the parameterized quantum circuit will transform the input quantum state of the combined qubit, and output the corresponding output quantum state.
  • the first measurement result can be obtained.
  • the output quantum state corresponding to the auxiliary qubit By measuring the output quantum state corresponding to the auxiliary qubit, a second measurement result can be obtained.
  • the foregoing first measurement result may be a bit string, which is referred to as a first bit string in this application, and the first bit string is denoted by s' in FIG. 1 .
  • the above-mentioned second measurement result may also be a bit string, which is called a second bit string in this application, and the second bit string is denoted by s in FIG. 1 .
  • the input quantum state of the combined qubit is transformed through the parameterized quantum circuit, and the output quantum state of the parameterized quantum circuit is measured n times to obtain n sets of measurement results.
  • the computer device obtains the above n sets of measurement results, and executes the subsequent steps described below.
  • the output quantum state of the parameterized quantum circuit can be measured n times through the measurement circuit to obtain n sets of measurement results.
  • the specific structure of the measurement circuit is not limited, and any circuit capable of measuring the output quantum state of the parameterized quantum circuit is acceptable.
  • Step 220 process the second measurement result through the neural network to obtain weight parameters.
  • the neural network is used to process the second measurement result (such as the second bit string s) corresponding to the auxiliary qubit, and we refer to the output result of the neural network as a weight parameter.
  • the second measurement result is input into the neural network, and the weight parameters are obtained through the calculation of the neural network.
  • the structure of the neural network is not limited, and it may be a simple fully connected structure or other more complex structures, which is not limited in the present application.
  • Step 230 based on the weight parameter and the first measurement result, calculate the correlation function value of the mixed state of the target quantum system.
  • the weighted average is performed on the operation results corresponding to the n first measurement results respectively, to obtain the correlation function value of the mixed state of the target quantum system. Since the first measurement result and the second measurement result are in one-to-one correspondence, for the first measurement result and the second measurement result belonging to the same group of measurement results, the weight parameter obtained based on the second measurement result is used for the same group The operation results corresponding to the first measurement results are multiplied to obtain a product result.
  • n sets of measurement results can obtain n product results, and the n product results are added to obtain a weighted sum result, and then the correlation function value of the mixed state of the target quantum system is calculated based on the weighted sum result. For example, the weighted summation result is divided by the sum of weight parameters respectively corresponding to the n second measurement results to obtain the correlation function value of the mixed state of the target quantum system.
  • the target correlation function is used to perform calculation processing on the n first measurement results respectively, to obtain calculation results respectively corresponding to the n first measurement results.
  • the target correlation function is used to obtain the value of the correlation function of the mixed state of the target quantum system.
  • Step 240 based on the value of the correlation function of the mixed state, calculate the expected value of the objective function.
  • the objective function is used to optimize the variational parameters.
  • the expected value of the objective function is the free energy of the mixed state calculated based on the correlation function value of the mixed state.
  • Step 250 aiming at the convergence of the expected value of the objective function, adjusting the variational parameters; wherein, the variational parameters include at least one of the following: parameterized quantum circuit parameters, and neural network parameters.
  • the variational parameters include parameterized quantum circuit parameters and neural network parameters. That is, the parameters of both the parameterized quantum circuit and the neural network are optimized. Aiming at the convergence of the expected value of the objective function, the parameters of the parameterized quantum circuit and the parameters of the neural network are adjusted, and after such multiple rounds of iterative optimization, the expected value of the objective function meets the convergence condition.
  • the parameters of the parameterized quantum circuit and the parameters of the neural network can be adjusted synchronously, or can be adjusted sequentially, that is, one set of parameters is fixed to adjust the other set of parameters, which is not limited in this application.
  • only the parameters of the parameterized quantum circuit may be adjusted without adjusting the parameters of the neural network, or only the parameters of the neural network may be adjusted without adjusting the parameters of the parameterized quantum circuit.
  • the parameters are adjusted, which is not limited in this application.
  • Step 260 when the expected value of the objective function satisfies the convergence condition, obtain the mixed state of the target quantum system to approximately represent the thermalization state of the target quantum system.
  • the mixed state of the target quantum system prepared by the above method can be approximately equal to the thermalization state of the target quantum system.
  • the weight parameter is regarded as a probability value
  • the multiple sets of weight parameters are one-to-one corresponding to the multiple sets of output quantum states to obtain the mixed state of the target quantum system.
  • the mixed state obtained at this time is used to approximately represent the target quantum system. thermalized state.
  • the input quantum state of the system qubit and the auxiliary qubit is first processed through the parameterized quantum circuit, and then through The neural network processes the measurement results corresponding to the auxiliary qubits to obtain the corresponding weight parameters, and uses the weight parameters to approximate the probability in the mixed state, and then calculates the expected value of the objective function based on the correlation function of the built mixed state.
  • the expected value convergence of the objective function is the goal, and the parameters of the parameterized quantum circuit and the parameters of the neural network are optimized, so that when the expected value of the objective function meets the convergence condition, the mixed state of the target quantum system is obtained to approximately represent the thermalization of the target quantum system state.
  • This solution introduces the neural network output weight parameter, and uses the weight parameter to adjust the weight corresponding to different auxiliary qubit measurement results, thereby enhancing the overall expression ability of the circuit through the trainable parameters of the neural network, achieving more efficient and accurate To prepare the effect of thermalization state.
  • Fig. 3 is a flowchart of a method for preparing a thermalized state in a quantum system provided by another embodiment of the present application. This method can be applied in the framework shown in Fig. 1 , for example, the execution body of each step can be a computer device. The method may include the following steps (310-390):
  • Step 310 obtain n sets of measurement results obtained by performing n measurements on the output quantum state of the parameterized quantum circuit after the parameterized quantum circuit transforms the input quantum state of the combined qubit; wherein the combined qubit includes auxiliary Qubits and system qubits of the target quantum system, each set of measurement results includes: a first measurement result corresponding to the system qubit, and a second measurement result corresponding to the auxiliary qubit, and n is a positive integer.
  • the system qubits and the auxiliary qubits are arranged in an overlapping manner. Because parametric quantum circuits require a certain amount of entanglement, and the greater the entanglement created by a single layer, the fewer routing layers are required.
  • the system qubits and auxiliary qubits are arranged in an overlapping manner. Through the above arrangement, the entanglement between the system qubits and the auxiliary qubits is maximized, and the route depth required for parameterizing the quantum circuit is shallower.
  • Step 320 process the second measurement result through the neural network, and limit the value range of the output result of the neural network to obtain weight parameters within the value range.
  • the fluctuation of the weight parameter output by the neural network may be too large, which may cause the relative error of estimation to be difficult to control.
  • the weight parameter approximately represents the probability in the mixed state, which may have a serious mismatch with the probability of the second measurement result obtained by measuring the output quantum state corresponding to the auxiliary qubit, which is equivalent to the fact that the importance sampling distribution does not match the actual distribution , resulting in a relatively large error. Therefore, we can limit the value range of the output results of the neural network, so as to prevent the number of measurements required to estimate the value of the correlation function from diverging with the system size index.
  • this thermalization state preparation scheme that limits the value range of the output results of the neural network as the thermalization state preparation scheme for post-processing of the bounded neural network.
  • the above value range is set to [1/r, r], where r is a value greater than 1.
  • Setting the range of values to [1/r, r] can mathematically strictly control the number of measurements required for the preparation of thermalized states using the scheme of this application under the condition that the specified accuracy is achieved, compared with the use of ordinary VQE
  • the number of measurements required by the framework to perform eigenstate estimation only a polynomial multiple of r.
  • the thermalization state preparation framework has better expressive ability, but the error will also increase. Therefore, in order to ensure a certain expressive ability without causing excessive errors, it is found through experiments that Set the value of r to be e ⁇ 15.
  • the application does not limit the way of limiting the range of values.
  • the output of the neural network can be directly limited, so that the output of the neural network does not have a value outside the value range, and can only output a value within the value range. In this way, you can directly Use the value output by the neural network as the weight parameter.
  • the output of the neural network may not be directly restricted, the output of the neural network may be a value outside the value range, and then a numerical mapping is performed on the output of the neural network to obtain a The value within the value range is used as the final weight parameter.
  • step 330 the target correlation function is used to perform calculation processing on the n first measurement results respectively, to obtain calculation results respectively corresponding to the n first measurement results.
  • the objective correlation function is used to obtain the correlation function value of the mixed state of the target quantum system under the target Pauli string.
  • operations are performed on the first measurement results corresponding to the system qubits from a plurality of different Pauli strings to obtain operation results corresponding to different Pauli strings.
  • the value of the correlation function of the mixed state of the target quantum system under multiple different Pauli strings can be obtained.
  • the expected value of the Hamiltonian corresponding to the mixed state is calculated, and based on the expected value of the Hamiltonian corresponding to the mixed state and the entropy corresponding to the mixed state, calculate Get the expected value of the objective function.
  • the expected value of the Hamiltonian corresponding to the mixed state is calculated.
  • the objective function is constructed based on the Hamiltonian and some other parameters, so based on the expected value of the Hamiltonian corresponding to the mixed state and the entropy corresponding to the mixed state, the expected value of the objective function can be calculated.
  • the objective function please refer to the description below.
  • Step 340 based on the weight parameters corresponding to the n second measurement results, perform weighted average on the operation results corresponding to the n first measurement results respectively, to obtain the correlation function value of the mixed state of the target quantum system under the target Pauli string .
  • the correlation function value C n of the mixed state of the target quantum system under the target Pauli string is:
  • w(s) represents the weight parameter corresponding to the second measurement result (such as the second bit string s)
  • C(s') represents the operation result corresponding to the first measurement result (such as the first bit string s')
  • C() represents the target correlation function.
  • m represents the length of the first bit string s', represents the first bit string s 'The number of bits in ', m is a positive integer.
  • Step 350 obtaining the correlation function values of the mixed state under multiple different Pauli strings.
  • the correlation function values of the mixed state under multiple different Pauli strings are obtained by using different correlation functions.
  • the output quantum state corresponding to the system qubit can be measured from multiple different Pauli strings, and based on the measurement results of different Pauli strings, the mixed state can be obtained in multiple different The value of the associated function under the Pauli string.
  • Step 360 based on the correlation function values of the mixed state under multiple different Pauli strings, calculate the expected value of the Hamiltonian corresponding to the mixed state.
  • the expected value of the Hamiltonian corresponding to the mixed state is calculated.
  • Step 370 based on the expected value of the Hamiltonian corresponding to the mixed state and the entropy corresponding to the mixed state, calculate the expected value of the objective function.
  • the expected value of the objective function is calculated.
  • the above entropy corresponding to the mixed state may be Gibbs entropy or Renyi entropy corresponding to the mixed state.
  • the objective function may be expressed by a calculation formula of the free energy corresponding to the mixed state.
  • the objective function is the free energy corresponding to the thermalization state in the second form; wherein, the thermalization state in the first form and the thermalization state in the second Formal thermalization states are two different forms of thermalization states, and there is a local approximation property between the first form thermalization state and the second form thermalization state.
  • the so-called local approximation feature means that in some specific cases, the expectations of the local observations given by the above two forms of thermalization states are similar.
  • the first form of thermalized state is a Gibbs thermalized state and the second form of thermalized state is a Renyi thermalized state.
  • the Gibbs thermalization state and the Renyi thermalization state have local approximation characteristics, and the mixed state with the minimization of Renyi free energy is consistent with the Gibbs thermalization state in the local correlation in the thermodynamic limit.
  • the most direct way is to use the Gibbs free energy as the objective function, but when measured on a quantum computer, the measurement and solution of the Gibbs entropy in the Gibbs free energy are too Complex, so we use the above local approximation properties, we can use the Renyi free energy as the objective function.
  • the measurement and solution of the Renyi entropy in the Renyi free energy is simpler and more efficient than the measurement and solution of the Gibbs entropy. It should be noted that when performing numerical simulation on a classical computer, the computational complexity of Gibbs entropy and Renyi entropy is not much different.
  • H represents the Hamiltonian corresponding to the mixed state
  • the density matrix corresponding to the ⁇ mixed state ⁇ and ⁇ are temperature parameters
  • Tr represents the trace of the matrix
  • H represents the Hamiltonian corresponding to the mixed state
  • the density matrix corresponding to the ⁇ mixed state ⁇ is the temperature parameter
  • Tr represents the trace of the matrix .
  • Step 380 aiming at the convergence of the expected value of the objective function, adjusting the variational parameters; wherein, the variational parameters include at least one of the following: parameterized quantum circuit parameters, and neural network parameters.
  • the parameter optimization of parameterized quantum circuits and neural networks can adopt gradient optimization or gradient-free optimization schemes, which is consistent with other variational quantum algorithms.
  • the only thing to note is that the weighted expectation of the neural network here does not meet the conditions for parameter translation to obtain the analytical gradient, so the gradient of the quantum circuit parameter part can only be estimated in the form of finite difference.
  • Step 390 if the expected value of the objective function satisfies the convergence condition, obtain the mixed state of the target quantum system to approximately represent the thermalization state of the target quantum system.
  • the mixed state of the target quantum system prepared by the above method can be approximately equal to the thermalization state of the target quantum system.
  • the thermalization state preparation scheme of the post-processing of the bounded neural network is adopted, and the value range of the output result of the neural network is limited, so that the finally obtained weight parameters are limited within the above value range, This can avoid the problem that the relative error of the estimation may be difficult to control due to the fluctuation of the weight parameter output by the neural network may be too large, and it will help to further improve the accuracy of the final thermalization state.
  • the expected value of the Hamiltonian corresponding to the mixed state is calculated, and then based on the expected value of the Hamiltonian corresponding to the mixed state and the corresponding Entropy, the expected value of the objective function is calculated, so that the solution of the objective function comprehensively considers the information of the mixed state under multiple different Pauli strings, which improves the accuracy of the objective function, which also helps to further improve the final thermalization state precision.
  • p i has the same meaning as p(i) in the above formula.
  • this scheme has a large gap in the accuracy of approximating the thermal state.
  • the quantum circuit + neural network post-processing method provided by this application is introduced. Compared with the neural network pre-processing method + quantum circuit method provided by the above-mentioned related technology, it has advantages in expressive ability.
  • Z represents the Pauli Z operator
  • X represents the Pauli X operator
  • n is a positive integer
  • i is a positive integer less than or equal to n.
  • H i is the Hadamard gate acting on the i qubit, and its matrix is expressed as
  • the quantum circuit + neural network post-processing scheme (that is, the scheme of this application) has similar quantum resources, and the expressive ability of preparing mixed states is far superior to that of the neural network pre-processing + quantum circuit scheme (that is, the scheme two). Therefore, although Scheme 2 can efficiently calculate Gibbs entropy, it still uses the former architecture for optimization and approximation, which can make more effective use of limited quantum hardware resources.
  • the scheme 1 curve 43 performs the worst, even the lowest is lower than 0.6, and the performance of the curve 44 with bounded neural network weight is the best, followed by the weight curve 45 with neural network and the weight curve without neural network 46.
  • Figure 5 shows the converged Gibbs free energy fidelity of different temperatures, different schemes, and different times of independent optimization. It can be seen that the results without neural network post-processing fluctuate greatly, and the training is very Unstable, as shown in the figure, there is no neural network weight interval 51. In contrast, the bounded neural network weight is a stable optimal solution, and at the same time of high fidelity, the fluctuation of the result is very small, as shown in the figure, there is a bounded neural network weight interval 52.
  • Figure 6 shows the correlation function estimates given by different schemes under the same correlation function.
  • the left figure is the gap between the correlation function and the true value of early stopping (1000 rounds of optimization)
  • the right figure is the gap between the correlation function and the true value after convergence.
  • the correlation between early stopping and final convergence There is not much difference in the estimation of the function, as shown in the figure, there is a neural network weight interval 61 and a bounded neural network weight interval 62 . Because the optimization of the free energy of the Renyi thermalization state in the later stage of training is caused by the overfitting of the Gibbs thermalization state target, it does not significantly improve the estimation of the correlation function.
  • Fig. 7 is a block diagram of a thermalized state preparation device in a quantum system provided by an embodiment of the present application.
  • the device has the function of realizing the thermalization state preparation method under the quantum system described above, and the function can be realized by hardware, and can also be realized by hardware executing corresponding software.
  • the device may be a computer device, or may be set in the computer device.
  • the device 700 may include: a measurement result acquisition module 710 , a weight parameter acquisition module 720 , a correlation function calculation module 730 , an objective function calculation module 740 , a variational parameter adjustment module 750 and a thermalization state acquisition module 760 .
  • the measurement result acquisition module 710 is used to obtain n sets of measurement results obtained by performing n measurements on the output quantum state of the parameterized quantum circuit after the input quantum state of the combined qubit is transformed by the parameterized quantum circuit;
  • the combination qubit includes an auxiliary qubit and a system qubit of the target quantum system, and each set of measurement results includes: a first measurement result corresponding to the system qubit, and a second measurement result corresponding to the auxiliary qubit Measurement results, n is a positive integer.
  • the weight parameter acquisition module 720 is configured to process the second measurement result through a neural network to obtain weight parameters.
  • a correlation function calculation module 730 configured to calculate a value of a correlation function of the mixed state of the target quantum system based on the weight parameter and the first measurement result.
  • the objective function calculation module 740 is configured to calculate the expected value of the objective function based on the correlation function value of the mixed state.
  • the variational parameter adjustment module 750 is configured to adjust the variational parameters with the goal of convergence of the expected value of the objective function; wherein the variational parameters include at least one of the following: parameters of the parameterized quantum circuit, the parameters of the neural network.
  • the thermalization state obtaining module 760 is configured to obtain the mixed state of the target quantum system to approximately characterize the thermalization state of the target quantum system when the expected value of the target function satisfies the convergence condition.
  • the correlation function calculation module 730 is configured to perform a weighted average on the calculation results corresponding to the n first measurement results respectively based on the weight parameters corresponding to the n second measurement results respectively, to obtain The value of the correlation function of the mixed state of the target quantum system.
  • the correlation function calculation module 730 is further configured to use a target correlation function to perform calculation processing on the n first measurement results respectively, to obtain calculation results corresponding to the n first measurement results respectively; wherein , the objective correlation function is used to obtain the correlation function value of the mixed state of the target quantum system under the objective Pauli string.
  • the objective function calculation module 740 is configured to obtain the correlation function value of the mixed state under a plurality of different Pauli character strings; wherein, the mixed state is in a plurality of different Pauli characters
  • the correlation function value under the string is obtained by using different correlation functions; based on the correlation function value of the mixed state under a plurality of different Pauli strings, the expected value of the Hamiltonian corresponding to the mixed state is calculated; based on the The expected value of the Hamiltonian corresponding to the mixed state and the entropy corresponding to the mixed state are calculated to obtain the expected value of the objective function.
  • the objective function is the free energy corresponding to the thermalization state in the second form; wherein, the first The thermalized state of the form and the thermalized state of the second form are two different forms of the thermalized state, and there is a local area between the thermalized state of the first form and the thermalized state of the second form Approximate properties.
  • said first form of thermalized state is a Gibbs thermalized state and said second form of thermalized state is a Renyi thermalized state.
  • the weight parameter acquisition module 720 is configured to process the second measurement result through the neural network, and limit the value range of the output result of the neural network to obtain the Weight parameters within the range of values mentioned above.
  • the value range is [1/r, r], where r is a value greater than 1.
  • system qubits and the auxiliary qubits are arranged in an overlapping manner.
  • the input quantum state of the system qubit and the auxiliary qubit is first processed through the parameterized quantum circuit, and then through The neural network processes the measurement results corresponding to the auxiliary qubits to obtain the corresponding weight parameters, and uses the weight parameters to approximate the probability in the mixed state, and then calculates the expected value of the objective function based on the correlation function of the built mixed state.
  • the expected value convergence of the objective function is the goal, and the parameters of the parameterized quantum circuit and the parameters of the neural network are optimized, so that when the expected value of the objective function meets the convergence condition, the mixed state of the target quantum system is obtained to approximately represent the thermalization of the target quantum system state.
  • This solution introduces the neural network output weight parameter, and uses the weight parameter to adjust the weight corresponding to different auxiliary qubit measurement results, thereby enhancing the overall expression ability of the circuit through the trainable parameters of the neural network, achieving more efficient and accurate To prepare the effect of thermalization state.
  • the division of the above-mentioned functional modules is used as an example for illustration. In practical applications, the above-mentioned function allocation can be completed by different functional modules according to the needs.
  • the internal structure of the device is divided into different functional modules to complete all or part of the functions described above.
  • the device provided by the above embodiment belongs to the same idea as the method embodiment, and its specific implementation process is detailed in the method embodiment, and will not be repeated here.
  • FIG. 8 shows a schematic structural diagram of a computer device provided by an embodiment of the present application.
  • the computer device may be a classic computer.
  • the computer equipment can be used to implement the thermalization state preparation method under the quantum system provided in the above embodiments. Specifically:
  • the computer device 800 includes a processing unit (such as CPU (Central Processing Unit, central processing unit), GPU (Graphics Processing Unit, graphics processing unit) and FPGA (Field Programmable Gate Array, field programmable logic gate array) etc.) 801, including RAM (Random-Access Memory, random access memory) 802 and ROM (Read-Only Memory, read-only memory) 803 system memory 804, and a system bus 805 connecting the system memory 804 and the central processing unit 801.
  • the computer device 800 also includes a basic input/output system (Input Output System, I/O system) 806 that helps to transmit information between various devices in the server, and is used to store an operating system 813, an application program 814 and other program modules 815 mass storage device 807.
  • I/O system Input Output System
  • the basic input/output system 806 includes a display 808 for displaying information and input devices 809 such as a mouse and a keyboard for users to input information.
  • input devices 809 such as a mouse and a keyboard for users to input information.
  • both the display 808 and the input device 809 are connected to the central processing unit 801 through the input and output controller 810 connected to the system bus 805 .
  • the basic input/output system 806 may also include an input output controller 810 for receiving and processing input from a number of other devices such as a keyboard, a mouse, or an electronic stylus.
  • input output controller 810 also provides output to a display screen, printer, or other type of output device.
  • the mass storage device 807 is connected to the central processing unit 801 through a mass storage controller (not shown) connected to the system bus 805 .
  • the mass storage device 807 and its associated computer-readable media provide non-volatile storage for the computer device 800 . That is to say, the mass storage device 807 may include a computer-readable medium (not shown) such as a hard disk or a CD-ROM (Compact Disc Read-Only Memory, CD-ROM) drive.
  • a computer-readable medium such as a hard disk or a CD-ROM (Compact Disc Read-Only Memory, CD-ROM) drive.
  • Computer readable media may comprise computer storage media and communication media.
  • Computer storage media includes volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storage of information such as computer readable programs, data structures, program modules or other data.
  • Computer storage media include RAM, ROM, EPROM (Erasable Programmable Read-Only Memory, Erasable Programmable Read-Only Memory), EEPROM (Electrically Erasable Programmable Read-Only Memory, Electrically Erasable Programmable Read-Only Memory), flash memory or Other solid-state storage technologies, CD-ROM, DVD (Digital Video Disc, high-density digital video disc) or other optical storage, tape cartridges, tapes, magnetic disk storage or other magnetic storage devices.
  • the aforementioned system memory 804 and mass storage device 807 may be collectively referred to as memory.
  • the computer device 800 can also run on a remote computer connected to the network through a network such as the Internet. That is, the computer device 800 can be connected to the network 812 through the network interface unit 811 connected to the system bus 805, or in other words, the network interface unit 816 can also be used to connect to other types of networks or remote computer systems (not shown) .
  • the memory also includes a computer program, which is stored in the memory and is configured to be executed by one or more processors, so as to realize the method for preparing a thermalized state in the quantum system described above.
  • a computer device is also provided, and the computer device is used for realizing the above method for preparing a thermalized state in a quantum system.
  • the computer device is a quantum computer, or a classical computer, or a mixed device execution environment of a quantum computer and a classical computer.
  • a computer-readable storage medium is also provided, and a computer program is stored in the storage medium, and when the computer program is executed by a processor of a computer device, the above method for preparing a thermalized state in a quantum system is realized. .
  • the computer-readable storage medium may include: ROM (Read-Only Memory, read-only memory), RAM (Random-Access Memory, random access memory), SSD (Solid State Drives, solid state drive) or an optical disc, etc.
  • the random access memory may include ReRAM (Resistance Random Access Memory, resistive random access memory) and DRAM (Dynamic Random Access Memory, dynamic random access memory).
  • a computer program product includes a computer program, and the computer program is stored in a computer-readable storage medium.
  • the processor of the computer device reads the computer program from the computer-readable storage medium, and the processor executes the computer program, so that the computer device executes the method for preparing a thermalized state under the quantum system.
  • a system for preparing a thermalized state in a quantum system includes: a parameterized quantum circuit and a computer device.
  • the parameterized quantum circuit is used to transform the input quantum state of the combined qubit to obtain the output quantum state of the parameterized quantum circuit; wherein the combined qubit includes a system of auxiliary qubits and a target quantum system qubit.
  • the computer device is configured to obtain n sets of measurement results obtained by performing n measurements on the output quantum state of the parameterized quantum circuit; wherein, each set of measurement results includes: a first measurement corresponding to the system qubit As a result, and a second measurement result corresponding to the auxiliary qubit, n is a positive integer.
  • the computer device is further configured to process the second measurement result through a neural network to obtain a weight parameter; based on the weight parameter and the first measurement result, calculate and obtain the correlation of the mixed state of the target quantum system function value; based on the correlation function value of the mixed state, the expected value of the objective function is calculated.
  • the computer device is further configured to adjust the variational parameters with the goal of convergence of the expected value of the objective function; when the expected value of the objective function satisfies the convergence condition, obtain the mixed state of the target quantum system to Approximately characterizing the thermalization state of the target quantum system; wherein the variational parameters include at least one of the following: parameters of the parameterized quantum circuit, parameters of the neural network.
  • the system further includes: a measurement line.
  • the measurement circuit is used to perform n measurements on the output quantum state of the parameterized quantum circuit to obtain n sets of measurement results.
  • the computer device is configured to perform a weighted average on the calculation results corresponding to the n first measurement results respectively based on the weight parameters respectively corresponding to the n second measurement results to obtain the target Correlation function values for mixed states of quantum systems.
  • the computer device is further configured to use an objective correlation function to perform calculation processing on the n first measurement results respectively, to obtain calculation results corresponding to the n first measurement results respectively; wherein, the The target correlation function is used to obtain the correlation function value of the mixed state of the target quantum system under the target Pauli string.
  • the computer device is configured to obtain the correlation function value of the mixed state under a plurality of different Pauli strings; wherein, the value of the mixed state under a plurality of different Pauli strings
  • the correlation function value is obtained by using different correlation functions; based on the correlation function values of the mixed state under a plurality of different Pauli strings, the expected value of the Hamiltonian corresponding to the mixed state is calculated; based on the mixed state The expected value of the corresponding Hamiltonian and the entropy corresponding to the mixed state are calculated to obtain the expected value of the objective function.
  • the objective function is the free energy corresponding to the thermalization state in the second form; wherein, the first The thermalized state of the form and the thermalized state of the second form are two different forms of the thermalized state, and there is a local area between the thermalized state of the first form and the thermalized state of the second form Approximate properties.
  • said first form of thermalized state is a Gibbs thermalized state and said second form of thermalized state is a Renyi thermalized state.
  • the computer device is configured to process the second measurement result through the neural network, and limit the value range of the output result of the neural network to obtain the weight parameters in range.
  • the value range is [1/r, r], where r is a value greater than 1.
  • system qubits and the auxiliary qubits are arranged in an overlapping manner.
  • This application does not limit the specific architecture of the thermal state preparation system under the quantum system, which may include computer equipment, computer equipment and parameterized quantum circuits, or computer equipment, parameterized quantum circuits and measurement circuits.
  • the "plurality” mentioned herein refers to two or more than two.
  • “And/or” describes the association relationship of associated objects, indicating that there may be three types of relationships, for example, A and/or B may indicate: A exists alone, A and B exist simultaneously, and B exists independently.
  • the character "/” generally indicates that the contextual objects are an "or” relationship.
  • the numbering of the steps described herein only exemplarily shows a possible sequence of execution among the steps. In some other embodiments, the above-mentioned steps may not be executed according to the order of the numbers, such as two different numbers The steps are executed at the same time, or two steps with different numbers are executed in the reverse order as shown in the illustration, which is not limited in this embodiment of the present application.

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Abstract

一种量子体系下的热化态制备方法、设备及存储介质，涉及量子技术领域。上述方法包括：获取经参数化量子线路对组合量子比特的输入量子态进行变换处理后，得到的n组测量结果(210)；通过神经网络对第二测量结果进行处理，得到权重参数(220)；基于权重参数和第一测量结果，计算得到目标量子系统的混态的关联函数值(230)；基于混态的关联函数值，计算得到目标函数的期望值(240)；以目标函数的期望值收敛为目标，对变分参数进行调整(250)；在目标函数的期望值满足收敛条件的情况下，获取目标量子系统的混态以近似表征目标量子系统的热化态(260)。本方案能够更加高效且精确地制备热化态。

Description

量子体系下的热化态制备方法、设备及存储介质
本申请要求于2021年12月06日提交的申请号为202111479010.4、发明名称为“量子体系下的热化态制备方法、设备及存储介质”的中国专利申请的优先权，其全部内容通过引用结合在本申请中。
技术领域
本申请实施例涉及量子技术领域，特别涉及一种量子体系下的热化态制备方法、设备及存储介质。
背景技术
在一些已有的研究中，提出了通过参数化线路制备热化态的方案。以制备Gibbs(吉布斯)热化态为例，参数化线路中参数优化的损失函数是Gibbs自由能，需要对该Gibbs自由能中的Gibbs熵进行测量。
对于常规的通过参数化线路制备热化态的方案，通过对辅助量子比特取偏迹的方式，制备系统量子比特上的混态。此时，该混态的Gibbs熵由于是密度矩阵非线性的对数函数，无法直接高效测量，需要进行消耗指数资源的态层析。这里所说的“指数资源”是指测量次数与系统量子比特的数量呈指数级关系，从而导致测量耗时过大。
因此，目前的通过参数化线路制备热化态的方案，效率较低。
发明内容
本申请实施例提供了一种量子体系下的热化态制备方法、设备及存储介质。所述技术方案如下：
根据本申请实施例的一个方面，提供了一种量子体系下的热化态制备方法，所述方法包括：
获取经参数化量子线路对组合量子比特的输入量子态进行变换处理后，对所述参数化量子线路的输出量子态进行n次测量，得到的n组测量结果；其中，所述组合量子比特包括辅助量子比特和目标量子系统的系统量子比特，每组测量结果包括：与所述系统量子比特对应的第一测量结果，以及与所述辅助量子比特对应的第二测量结果，n为正整数；
通过神经网络对所述第二测量结果进行处理，得到权重参数；
基于所述权重参数和所述第一测量结果，计算得到所述目标量子系统的混态的关联函数值；
基于所述混态的关联函数值，计算得到目标函数的期望值；
以所述目标函数的期望值收敛为目标，对变分参数进行调整；其中，所述变分参数包括以下至少一项：所述参数化量子线路的参数、所述神经网络的参数；
在所述目标函数的期望值满足收敛条件的情况下，获取所述目标量子系统的混态以近似表征所述目标量子系统的热化态。
根据本申请实施例的一个方面，提供了一种量子体系下的热化态制备装置，所述装置包括：
测量结果获取模块，用于获取经参数化量子线路对组合量子比特的输入量子态进行变换处理后，对所述参数化量子线路的输出量子态进行n次测量，得到的n组测量结果；其中，所述组合量子比特包括辅助量子比特和目标量子系统的系统量子比特，每组测量结果包括：与所述系统量子比特对应的第一测量结果，以及与所述辅助量子比特对应的第二测量结果，n为正整数；
权重参数获取模块，用于通过神经网络对所述第二测量结果进行处理，得到权重参数；
关联函数计算模块，用于基于所述权重参数和所述第一测量结果，计算得到所述目标量子系统的混态的关联函数值；
目标函数计算模块，用于基于所述混态的关联函数值，计算得到目标函数的期望值；
变分参数调整模块，用于以所述目标函数的期望值收敛为目标，对变分参数进行调整；其中，所述变分参数包括以下至少一项：所述参数化量子线路的参数、所述神经网络的参数；
热化态获取模块，用于在所述目标函数的期望值满足收敛条件的情况下，获取所述目标量子系统的混态以近似表征所述目标量子系统的热化态。
根据本申请实施例的一个方面，提供了一种计算机设备，所述计算机设备用于实现上述量子体系下的热化态制备方法。可选地，所述计算机设备是量子计算机，或经典计算机，或量子计算机和经典计算机的混合设备执行环境。
根据本申请实施例的一个方面，提供了一种计算机可读存储介质，所述存储介质中存储有计算机程序，所述计算机程序由处理器加载并执行以实现上述量子体系下的热化态制备方法。
根据本申请实施例的一个方面，提供了一种计算机程序产品，所述计算机程序产品或计算机程序包括计算机程序，所述计算机程序存储在计算机可读存储介质中，处理器从所述计算机可读存储介质读取并执行所述计算机程序，以实现上述量子体系下的热化态制备方法。
根据本申请实施例的一个方面，提供了一种量子体系下的热化态制备系统，所述系统包括：参数化量子线路和计算机设备；
所述参数化量子线路，用于对组合量子比特的输入量子态进行变换处理，得到所述参数化量子线路的输出量子态；其中，所述组合量子比特包括辅助量子比特和目标量子系统的系统量子比特；
所述计算机设备，用于获取对所述参数化量子线路的输出量子态进行n次测量，得到的n组测量结果；其中，每组测量结果包括：与所述系统量子比特对应的第一测量结果，以及与所述辅助量子比特对应的第二测量结果，n为正整数；
所述计算机设备，还用于通过神经网络对所述第二测量结果进行处理，得到权重参数；基于所述权重参数和所述第一测量结果，计算得到所述目标量子系统的混态的关联函数值；基于所述混态的关联函数值，计算得到目标函数的期望值；
所述计算机设备，还用于以所述目标函数的期望值收敛为目标，对变分参数进行调整；在所述目标函数的期望值满足收敛条件的情况下，获取所述目标量子系统的混态以近似表征所述目标量子系统的热化态；其中，所述变分参数包括以下至少一项：所述参数化量子线路的参数、所述神经网络的参数。
本申请实施例提供的技术方案可以带来如下有益效果：
在制备目标量子系统的热化态时，通过引入神经网络后处理的方案，首先通过参数化量子线路对系统量子比特和辅助量子比特的输入量子态进行处理，然后通过神经网络对辅助量子比特对应的测量结果进行处理，得到相应的权重参数，利用该权重参数来近似表征混态中的概率，然后基于构建的混态的关联函数，计算得到目标函数的期望值，以目标函数的期望值收敛为目标，优化参数化量子线路的参数和神经网络的参数，从而在目标函数的期望值满足收敛条件的情况下，获取目标量子系统的混态以近似表征目标量子系统的热化态。本方案通过引入神经网络输出权重参数，利用该权重参数来调节不同的辅助量子比特测量结果所对应的权重，从而通过神经网络的可训练参数，增强了线路整体的表达能力，达到更加高效且精确地制备热化态的效果。
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图3是本申请另一个实施例提供的量子体系下的热化态制备方法的流程图；
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图6是本申请另一个实施例提供的实验结果的示意图；
图7是本申请一个实施例提供的量子体系下的热化态制备装置的框图；
图8是本申请一个实施例提供的计算机设备的示意图。
具体实施方式
为使本申请的目的、技术方案和优点更加清楚，下面将结合附图对本申请实施方式作进一步地详细描述。
在对本申请技术方案进行介绍之前，先对本申请中涉及的一些关键术语进行解释说明。
1.量子计算：基于量子逻辑的计算方式，存储数据的基本单元是量子比特(qubit)。
2.量子比特：量子计算的基本单元。传统计算机使用0和1作为二进制的基本单元。不同的是量子计算可以同时处理0和1，系统可以处于0和1的线性叠加态：|ψ>＝α|0>+β|1>，这边α,β代表系统在0和1上的复数概率幅。它们的模平方|α| 2,|β| 2分别代表处于0和1的概率。
3.量子线路：量子通用计算机的一种表示，代表了相应量子算法/程序在量子门模型下的硬件实现。若量子线路中包含可调的控制量子门的参数，则被称为参数化量子线路(Parameterized Quantum Circuit，简称PQC)或变分量子线路(Variational Quantum Circuit，简称VQC)，两者为同一概念。
4.哈密顿量：描述量子系统总能量的一个厄密共轭的矩阵。哈密顿量是一个物理词汇，是一个描述系统总能量的算符，通常以H表示。
5.本征态：对于一个哈密顿量矩阵H，满足方程：H|ψ>＝E|ψ>的解称之为H的本征态|ψ>，具有本征能量E。基态则对应了量子系统能量最低的本征态。
6.量子经典混合计算：一种内层利用量子线路(如PQC)进行计算得出相应物理量或损失函数，外层用传统的经典优化器调节量子线路变分参数的计算范式，可以最大限度地发挥量子计算的优势，被相信是有潜力证明量子优势的重要方向之一。
7.NISQ(Noisy Intermediate-Scale Quantum)：近期中等规模有噪声的量子硬件，是量子计算发展现在所处的阶段和研究的重点方向。这一阶段量子计算暂时由于规模和噪声的限制，无法作为通用计算的引擎应用，但在部分问题上，已经可以实现超越最强经典计算机的结果，这通常被称作量子霸权或量子优势。
8.变分量子本征求解器(Variational Quantum Eigensolver，简称VQE)：通过变分线路(即PQC/VQC)实现特定量子系统基态能量的估计，是一种典型的量子经典混合计算范式，在量子化学领域有广泛的应用。
9.后选择(post-selection)：对于量子计算机输出的测量结果，基于某些比特位对应的比特字符串(bitstring)的具体值选择保留或者舍弃该次测量结果，这被称为后选择。后选择出现在很多现在的研究热点领域，包括但不限于线性酉矩阵组合实现LCU(linear combinations of unitary operations，酉运算的线性组合(线性组合算子))，测量导致的纠缠熵相变等。
10.Pauli string(泡利字符串)：在不同格点多个泡利矩阵的直积组成的项，一般的哈密顿量通常可以拆解为一组泡利字符串之和。VQE的测量也一般都按照泡利字符串分解来逐项测量。
11.非幺正：所谓幺正矩阵，即是满足
Figure PCTCN2022132997-appb-000001
的全部矩阵，所有量子力学直接允许的演化过程，都可以通过幺正矩阵描述。其中，U为幺正矩阵(Unitary Matrix)，也称为酉矩阵、么正矩阵等，
Figure PCTCN2022132997-appb-000002
是U的共轭转置。另外，不满足该条件的矩阵则是非幺正的，其需要通过 辅助手段甚至指数多的资源才可在实验上实现，但非幺正矩阵往往具有更强的表达能力和更快的基态投影效果。上述“指数多的资源”是指资源的需求量随着量子比特数量的增加，呈指数级增加，该指数多的资源可以是指需要测量的量子线路的总数是指数多个，也即相应需要指数多的计算时间。
12.比特字符串(bitstring)：一串由0，1组成的数字。对量子线路每次测量得到的经典结果，可以根据在测量基上的自旋构型的上下分别由0，1表示，从而总的一次测量结果对应一个比特字符串。
13.泡利算符：也称为泡利矩阵，是一组三个2×2的幺正厄米复矩阵(又称酉矩阵)，一般都以希腊字母σ(西格玛)来表示。其中，泡利X算符为
Figure PCTCN2022132997-appb-000003
泡利Y算符为
Figure PCTCN2022132997-appb-000004
泡利Z算符为
Figure PCTCN2022132997-appb-000005
14.混态：和波函数表示的纯态相对应，由一组{p i,|ψ i>}描述，其表示的意义是该系统有p i的经典概率处在波函数|ψ i>态上。该状态可以用密度矩阵的数学结构描述，密度矩阵ρ定义为ρ＝∑ ip i|ψ i><ψ i|。
15.Gibbs热化态：是指满足热平衡分布的量子混态，也即其经典概率满足玻尔兹曼分布
Figure PCTCN2022132997-appb-000006
Z是配分函数(归一化因子)，
Figure PCTCN2022132997-appb-000007
是系统温度倒数，E i是物理系统的本征能谱。该Gibbs热化态，利用哈密顿量H的矩阵指数可以更简洁地表达为
Figure PCTCN2022132997-appb-000008
如果可以高效地制备Gibbs热化态，即可实现有限温热平衡系统的物理性质和关联函数测量。Gibbs热化态也是以下带Gibbs熵的自由能损失函数最小时对应的混合态ρ：
Figure PCTCN2022132997-appb-000009
其中，该式第一项Tr(Hρ)为能量项，第二项
Figure PCTCN2022132997-appb-000010
可以化简为
Figure PCTCN2022132997-appb-000011
S称作Gibbs熵。Gibbs熵是平衡态热力学平衡下体系熵的通用表达式。如果体系有n个能级，占第i个能级的机率是p i，体系的熵就是
Figure PCTCN2022132997-appb-000012
其中k B是玻尔兹曼常数(Boltzmann constant)，这条公式叫Gibbs熵公式。
16.Renyi(瑞丽)热化态：是一种最小化带Renyi熵(Renyi entropy，瑞丽熵)的自由能损失函数，对应的混合态ρ：
Figure PCTCN2022132997-appb-000013
其中，第二项
Figure PCTCN2022132997-appb-000014
为Renyi熵乘以温度因子。α是Renyi熵的阶数(大于或等于2的正整数)，本申请中只关心α＝2的情形，其他情况也是类似的，但由于高阶Renyi熵的线路测量需要消耗更多的资源，一般实际应用中利用α＝2即可。值得注意的是，这里的1/β α应该理解为一个无物理意义的拉格朗日因子，不一定对应温度的倒数，调整β α使得最优的ρ对应的能量和温度β时的Gibbs热化态相同时，我们说这时Renyi热化态的温度倒数是β。虽然数值实验表明，在较大温度区间内β α＝β。对于α＝2的Renyi热化态，其在能量本征基上对应的概率分布为：
Figure PCTCN2022132997-appb-000015
其中
Figure PCTCN2022132997-appb-000016
是使得相应热化态最小化Renyi自由能的常数值。
17.保真度(fidelity)：两个混态ρ 0、ρ之间保真度的定义为：
Figure PCTCN2022132997-appb-000017
完全相同的两个混态间的保真度为1。
18.迹距离(trace distance)：两个混态ρ,σ之间的迹距离T的定义为：
Figure PCTCN2022132997-appb-000018
完全相同的两个混态间的迹距离为0。
19.有限温系统：是指温度大于0的体系，和研究基态对应的零温系统相对。在有限温系统的平衡态并不是基态，而是Gibbs热化态代表的混态。
20.自由能：是指在某一个热力学过程中，系统减少的内能中可以转化为对外做功的部分，它衡量的是：在一个特定的热力学过程中，系统可对外输出的“有用能量”。可分为Helmholtz(亥姆霍兹)自由能和Gibbs自由能。
本申请提供的技术方案，有助于加快和增强NISQ时期量子硬件的发展和实用性。本申请提出的神经网络变分后选择的加强方案充分考虑了NISQ时代量子硬件的特点，可以通过经典神经网络部分增加较浅的量子线路的表达能力。此外该方案和其他NISQ变分后处理方案，如变分量子-神经网络混合本征求解器(Variational Quantum Neural network Hybrid Eigensolver，简称VQNHE)等完美兼容(本申请方案神经网络作用在辅助量子比特上，VQNHE方案神经网络作用在系统量子比特上)，可以联合使用进一步提升混态制备，也即有限温度VQE的效果。该方案为在NISQ硬件上展现有效的量子优势奠定了基础，加速量子计算机商业化应用的可能。
本申请方案可在中短期内，较容易地应用到量子硬件评估测试科研和实际生产中。其应用包括但不限于对来自量子多体物理和量子化学问题中体系的哈密顿量的有限温状态进行模拟。
本申请实施例提供的量子体系下的热化态制备方法，其可以由经典计算机(如PC(Personal Computer，个人计算机))执行实现，例如通过经典计算机执行相应的计算机程序以实现该方法；也可以由量子计算机实现该方法；或者也可以在经典计算机和量子计算机的混合设备环境下执行，例如由经典计算机和量子计算机配合来实现该方法。示例性地，量子计算机用于实现本申请实施例中对量子态的处理和测量，经典计算机用于实现本申请实施例中诸如神经网络计算、目标函数计算、变分参数优化等其他步骤。
在下述方法实施例中，为了便于说明，仅以各步骤的执行主体为计算机设备进行介绍说明。应当理解的是，该计算机设备可以是经典计算机，也可以是量子计算机，还可以包括经典计算机和量子计算机的混合执行环境，本申请实施例对此不作限定。
本申请一示例性实施例提供的量子体系下的热化态制备框架如图1所示，包括：参数化量子线路(PQC)10、神经网络20和优化器30。参数化量子线路10用于对组合量子比特的输入量子态进行变换处理，得到对应的输出量子态。其中，组合量子比特包括辅助量子比特和目标量子系统的系统量子比特。对参数化量子线路10的输出量子态进行n次测量，得到n组测量结果，每组测量结果包括与系统量子比特对应的第一测量结果，以及与辅助量子比特对应的第二测量结果，n为正整数。神经网络20用于对第二测量结果进行处理，得到权重参数。基于权重参数和第一测量结果，计算得到目标量子系统的混态的关联函数值，进而基于该混态的关联函数值计算得到目标函数的期望值。优化器30用于以目标函数的期望值收敛为目标，对目标对象(如包括参数化量子线路10和/或神经网络20)的参数进行调整。在目标函数的期望值满足收敛条件的情况下，获取目标量子系统的混态，此时获得的混态能够近似表征目标量子系统的热化态。
图2是本申请一个实施例提供的量子体系下的热化态制备方法的流程图，该方法可应用于图1所示的框架中，例如各步骤的执行主体可以是计算机设备。该方法可以包括如下几个步骤(210～260)：
步骤210，获取经参数化量子线路对组合量子比特的输入量子态进行变换处理后，对参数化量子线路的输出量子态进行n次测量，得到的n组测量结果；其中，组合量子比特包括 辅助量子比特和目标量子系统的系统量子比特，每组测量结果包括：与系统量子比特对应的第一测量结果，以及与辅助量子比特对应的第二测量结果，n为正整数。
目标量子系统可以是任一需要研究的量子系统，通过本实施例提供的技术方案，能够近似地制备出该目标量子系统在有限温系统下的热化态。例如，目标量子系统可以是任一量子物理系统或者量子化学系统，所获得的该目标量子系统的热化态可以用来评估该系统的实际材料在有限温状态下的真实性质，也可以用来研究该系统在非热平衡系统的行为。系统量子比特即是指该目标量子系统中包含的量子比特，如目标量子系统中包含5个量子比特，则系统量子比特的数量也为5。辅助量子比特是为了获得目标量子系统的混态而制备的，本申请对辅助量子比特的数量不作限定，例如辅助量子比特的数量可以和系统量子比特的数量相同，也可以小于或者大于系统量子比特的数量。原则上，辅助量子比特的数量越多，例如辅助量子比特的数量越接近系统量子比特的数量，最终制备的热化态的近似效果越好，但是辅助量子比特的数量增加也会导致整个处理过程的复杂度增加，因此可以在综合考虑精度和复杂度的情况下，选择合适数量的辅助量子比特。
参数化量子线路的输入包括组合量子比特的输入量子态，即包括系统量子比特和辅助量子比特的输入量子态。输入量子态一般可以使用是全0态、均匀叠加态或者Hartree-Fock(哈特里-福克)态，该输入量子态也被称作试探态。
在本申请实施例中，对系统量子比特和辅助量子比特的排布方式不作限定。例如，系统量子比特和辅助量子比特可以采用交叠出现的排布方式，如系统量子比特和辅助量子比特逐一间隔排列，或者每间隔若干个系统量子比特插入一个辅助量子比特等等。采用交叠出现的排布方式，能够提升系统量子比特和辅助量子比特之间的纠缠尽可能最大化，从而参数化量子线路可以使用更浅的线路深度，降低复杂度。
参数化量子线路会对组合量子比特的输入量子态进行变换处理，输出对应的输出量子态。通过对系统量子比特对应的输出量子态进行测量，可以得到第一测量结果。通过对辅助量子比特对应的输出量子态进行测量，可以得到第二测量结果。上述第一测量结果可以是一个比特字符串，本申请称之为第一比特字符串，图1中该第一比特字符串以s′表示。上述第二测量结果也可以是一个比特字符串，本申请称之为第二比特字符串，图1中该第二比特字符串以s表示。通过对参数化量子线路的输出量子态进行多次测量，每一次测量可以得到一组测量结果，最终得到多组测量结果。任意两次得到的测量结果，可能相同，也可能不同。
在本申请实施例中，通过参数化量子线路对组合量子比特的输入量子态进行变换处理，并对参数化量子线路的输出量子态进行n次测量，得到n组测量结果。计算机设备获取上述n组测量结果，并执行下文介绍的后续步骤。其中，可以通过测量线路对参数化量子线路的输出量子态进行n次测量，得到n组测量结果。在本申请实施例中，对测量线路的具体结构不作限定，任一能够实现对参数化量子线路的输出量子态进行测量的线路都可。
步骤220，通过神经网络对第二测量结果进行处理，得到权重参数。
在本申请实施例中，使用神经网络对辅助量子比特对应的第二测量结果(如第二比特字符串s)进行处理，我们将神经网络的输出结果称为权重参数。将第二测量结果输入神经网络，通过神经网络计算得到权重参数。在本申请实施例中，对神经网络的结构不作限定，其可以是简单的全连接结构，也可以是其他较为复杂的结构，本申请对此不作限定。
步骤230，基于权重参数和第一测量结果，计算得到目标量子系统的混态的关联函数值。
可选地，基于n个第二测量结果分别对应的权重参数，对n个第一测量结果分别对应的运算结果进行加权平均，得到目标量子系统的混态的关联函数值。由于第一测量结果和第二测量结果是一一对应的，对于属于同一组测量结果的第一测量结果和第二测量结果，基于该第二测量结果得到的权重参数，用于与其同组的第一测量结果所对应的运算结果进行相乘，得到一个乘积结果。这样，n组测量结果就可以得到n个乘积结果，将该n个乘积结果相加，得到加权求和结果，然后基于该加权求和结果计算得到目标量子系统的混态的关联函数值。 例如，将该加权求和结果除以n个第二测量结果分别对应的权重参数之和，得到目标量子系统的混态的关联函数值。
可选地，采用目标关联函数对n个第一测量结果分别进行运算处理，得到n个第一测量结果分别对应的运算结果。其中，目标关联函数用于获取目标量子系统的混态的关联函数值。
步骤240，基于混态的关联函数值，计算得到目标函数的期望值。
目标函数用于优化变分参数。可选地，目标函数的期望值是基于混态的关联函数值计算得到的混态的自由能。
步骤250，以目标函数的期望值收敛为目标，对变分参数进行调整；其中，变分参数包括以下至少一项：参数化量子线路的参数、神经网络的参数。
以目标函数的期望值收敛为优化目标，可选地，以目标函数的期望值收敛为最小值为目标，对变分参数进行优化调整。当然，在一些其他可能的实施例中，也可能以目标函数的期望值收敛为最大值为目标，对变分参数进行优化调整。本申请对目标函数的期望值的收敛方向不作限定。
可选地，变分参数包括参数化量子线路的参数和神经网络的参数。也即，对参数化量子线路和神经网络的参数均进行优化。以目标函数的期望值收敛为目标，对参数化量子线路的参数和神经网络的参数进行调整，经过这样的多轮迭代优化，使得目标函数的期望值满足收敛条件。另外，参数化量子线路的参数和神经网络的参数可以同步进行调整，也可以依次先后进行调整，即固定其中一组参数调整另一组参数，本申请对此不作限定。
另外，在一些其他可能的实施例中，也可以仅对参数化量子线路的参数进行调整，而不对神经网络的参数进行调整，或者仅对神经网络的参数进行调整，而不对参数化量子线路的参数进行调整，本申请对此不作限定。
步骤260，在目标函数的期望值满足收敛条件的情况下，获取目标量子系统的混态以近似表征目标量子系统的热化态。
在目标函数的期望值满足收敛条件的情况下，此时通过上述方法制备得到的目标量子系统的混态，可以近似等于目标量子系统的热化态。
具体来讲，在目标函数的期望值满足收敛条件的情况下，获取经参数化量子线路输出的系统量子比特所对应的多组输出量子态，以及神经网络输出的辅助量子比特所对应的多组权重参数，将权重参数看作是概率值，将该多组权重参数和该多组输出量子态一一对应，得到目标量子系统的混态，此时得到的混态用来近似表征目标量子系统的热化态。
本申请提供的技术方案，在制备目标量子系统的热化态时，通过引入神经网络后处理的方案，首先通过参数化量子线路对系统量子比特和辅助量子比特的输入量子态进行处理，然后通过神经网络对辅助量子比特对应的测量结果进行处理，得到相应的权重参数，利用该权重参数来近似表征混态中的概率，然后基于构建的混态的关联函数，计算得到目标函数的期望值，以目标函数的期望值收敛为目标，优化参数化量子线路的参数和神经网络的参数，从而在目标函数的期望值满足收敛条件的情况下，获取目标量子系统的混态以近似表征目标量子系统的热化态。本方案通过引入神经网络输出权重参数，利用该权重参数来调节不同的辅助量子比特测量结果所对应的权重，从而通过神经网络的可训练参数，增强了线路整体的表达能力，达到更加高效且精确地制备热化态的效果。
图3是本申请另一个实施例提供的量子体系下的热化态制备方法的流程图，该方法可应用于图1所示的框架中，例如各步骤的执行主体可以是计算机设备。该方法可以包括如下几个步骤(310～390)：
步骤310，获取经参数化量子线路对组合量子比特的输入量子态进行变换处理后，对参数化量子线路的输出量子态进行n次测量，得到的n组测量结果；其中，组合量子比特包括辅助量子比特和目标量子系统的系统量子比特，每组测量结果包括：与系统量子比特对应的 第一测量结果，以及与辅助量子比特对应的第二测量结果，n为正整数。
可选地，系统量子比特和辅助量子比特采用交叠出现的排布方式。由于参数化量子线路需要一定的纠缠，且单层创造的纠缠越大，需要的路线层数就越少。采用系统量子比特和辅助量子比特采用交叠出现的排布方式，通过上述排布方式，使得系统量子比特和辅助量子比特的纠缠最大，参数化量子线路所需要的路线深度也就越浅。
步骤320，通过神经网络对第二测量结果进行处理，并对神经网络的输出结果进行取值范围的限制，得到在取值范围之内的权重参数。
考虑到将不同的第二测量结果输入至神经网络后，由神经网络输出的权重参数的涨落可能过大，可能会造成估计的相对误差难以控制。其原因在于，权重参数近似表征混态中的概率，这和对辅助量子比特对应的输出量子态进行测量得到第二测量结果的概率可能错配比较严重，相当于重要性采样分布和实际分布不符，导致误差比较大。因此，我们可以对神经网络的输出结果进行取值范围的限制，从而防止估计关联函数值时需要的测量次数随体系大小指数发散。我们将这种对神经网络的输出结果进行取值范围限制的热化态制备方案，称为有界神经网络后处理的热化态制备方案。
可选地，上述取值范围设置为[1/r，r]，r是大于1的数值。将取值范围设置为[1/r，r]，可以在数学上严格地控制在达到指定精度的情况下，采用本申请方案进行热化态制备所需的测量次数，相较于采用普通VQE框架进行本征态估计所需的测量次数，仅多出r的多项式倍。其中，随着r的取值越大，热化态制备框架的表达能力越好，但误差也会越大，因此为了保证拥有一定表达能力的同时不产生过大的误差，经过实验发现，可以设置r的取值为e e≈15。
另外，本申请对取值范围的限制方式不作限定。在一种可能的实施方式中，可以直接限制神经网络的输出，让神经网络的输出不会出现取值范围之外的数值，只能够输出取值范围之内的数值，这种方式下可以直接将神经网络输出的数值作为权重参数。在另一种可能的实施方式中，可以不直接对神经网络的输出进行限制，神经网络的输出可以是位于取值范围之外的数值，然后对神经网络的输出再做一个数值映射，得到一个位于取值范围之内的数值，作为最终的权重参数。
步骤330，采用目标关联函数对n个第一测量结果分别进行运算处理，得到n个第一测量结果分别对应的运算结果。
其中，目标关联函数用于获取目标量子系统的混态在目标泡利字符串下的关联函数值。
可选地，从多个不同的泡利字符串对系统量子比特对应的第一测量结果进行运算，得到不同的泡利字符串所对应的运算结果。例如，采用不同的目标关联函数，对第一测量结果分别进行运算处理，可以得到目标量子系统的混态在多个不同的泡利字符串下的关联函数值。然后，基于混态在多个不同的泡利字符串下的关联函数值，计算得到混态对应的哈密顿量的期望值，基于混态对应的哈密顿量的期望值和混态对应的熵，计算得到目标函数的期望值。可选地，基于混态在多个不同的泡利字符串下的关联函数值的求和结果，计算得到混态对应的哈密顿量的期望值。目标函数是基于哈密顿量以及一些其他参数构建的，因此基于混态对应的哈密顿量的期望值，以及混态对应的熵，便可计算得到目标函数的期望值。有关目标函数的具体实现形式，请参见下文介绍说明。
步骤340，基于n个第二测量结果分别对应的权重参数，对n个第一测量结果分别对应的运算结果进行加权平均，得到目标量子系统的混态在目标泡利字符串下的关联函数值。
示例性地，目标量子系统的混态在目标泡利字符串下的关联函数值C n为：
Figure PCTCN2022132997-appb-000019
其中，w(s)表示第二测量结果(如第二比特字符串s)对应的权重参数，C(s′)表示第一测量结果(如第一比特字符串s′)对应的运算结果，C()代表目标关联函数。
示例性地，C(s′)的计算公式如下：
Figure PCTCN2022132997-appb-000020
其中，s′ m表示第一比特字符串s′中第m个比特位的取值，s′ m＝0或1，m表示第一比特字符串s′的长度，表示第一比特字符串s′中的比特位数量，m为正整数。
例如，当第一比特字符串s′的长度为2时，假设第一比特字符串s′＝s′ 1s′ 2＝01，则C(s′)＝(1-2*0)*(1-2*1)＝-1。
步骤350，获取混态在多个不同的泡利字符串下的关联函数值。
其中，混态在多个不同的泡利字符串下的关联函数值，采用不同的关联函数得到。
在本申请实施例中，可以从多个不同的泡利字符串，对系统量子比特对应的输出量子态进行测量，并基于不同的泡利字符串的测量结果，得到混态在多个不同的泡利字符串下的关联函数值。
步骤360，基于混态在多个不同的泡利字符串下的关联函数值，计算得到混态对应的哈密顿量的期望值。
可选地，基于混态在多个不同的泡利字符串下的关联函数值的求和结果，计算得到混态对应的哈密顿量的期望值。
步骤370，基于混态对应的哈密顿量的期望值，以及混态对应的熵，计算得到目标函数的期望值。
基于混态对应的哈密顿量的期望值以及该混态对应的熵，计算得到目标函数的期望值。可选地，上述混态对应的熵可以是混态对应的Gibbs熵或Renyi熵。可选地，目标函数可以采用混态对应的自由能的计算公式来表示。当目标量子系统的混态对应的自由能收敛(如取最小值时)，这个时候的混态即可看作是该目标量子系统在有限温系统下的热化态。
可选地，在需要获取目标量子系统的第一形式的热化态的情况下，目标函数是第二形式的热化态所对应的自由能；其中，第一形式的热化态和第二形式的热化态是两种不同形式的热化态，且第一形式的热化态和第二形式的热化态之间具有局域近似特性。所谓局域近似特征，是指在某些特定的情况下，上述两种形式的热化态给出的局域观察量的期望相似。
在一些实施例中，第一形式的热化态是Gibbs热化态，第二形式的热化态是Renyi热化态。Gibbs热化态和Renyi热化态具有局域近似特性，Renyi自由能最小化的混态与Gibbs热化态在局域关联上在热力学极限一致。因此，如果我们想要得到目标量子系统的Gibbs热化态，最直接的方式是将Gibbs自由能作为目标函数，但是由于在量子计算机上测量时，Gibbs自由能中的Gibbs熵的测量和求解过于复杂，因此我们利用上述局域近似特性，可以将Renyi自由能作为目标函数。在量子计算机上测量时，Renyi自由能中的Renyi熵的测量和求解，相比于Gibbs熵的测量和求解更加简单高效。而需要说明的是，在经典计算机上进行数值模拟时，Gibbs熵和Renyi熵的计算复杂度并无太大区别。
示例性地，如果我们想要得到目标量子系统的Gibbs热化态，我们使用Renyi自由能作为目标函数，此时目标函数即为：
Figure PCTCN2022132997-appb-000021
其中，H表示混态对应的哈密顿量，ρ混态对应的密度矩阵，β和α为温度参数，Tr表示求矩阵的迹。
可选地，在取α＝2和β 2＝β时的Renyi热化态来近似表征Gibbs热化态。
另外，从数值实验的角度，如果我们想要得到目标量子系统的Gibbs热化态，我们也可以直接使用Gibbs自由能作为目标函数，此时目标函数即为：
Figure PCTCN2022132997-appb-000022
其中，H表示混态对应的哈密顿量，ρ混态对应的密度矩阵，β为温度参数，Tr表示求矩阵 的迹。
步骤380，以目标函数的期望值收敛为目标，对变分参数进行调整；其中，变分参数包括以下至少一项：参数化量子线路的参数、神经网络的参数。
参数化量子线路和神经网络的参数优化可以采用梯度优化或无梯度优化的方案，这与其他的变分量子算法一致。唯一需要注意的是，这里的神经网络加权的期望并不满足参数平移求解析梯度的条件，因此只能通过有限差分的形式，来估算量子线路参数部分的梯度。
步骤390，在目标函数的期望值满足收敛条件的情况下，获取目标量子系统的混态以近似表征目标量子系统的热化态。
在目标函数的期望值满足收敛条件的情况下，此时通过上述方法制备得到的目标量子系统的混态，可以近似等于目标量子系统的热化态。
在本实施例中，采用有界神经网络后处理的热化态制备方案，通过对神经网络的输出结果进行取值范围的限制，使得最终得到的权重参数被限制在上述取值范围之内，这可以避免因神经网络输出的权重参数的涨落可能过大，可能会造成估计的相对误差难以控制的问题，有助于进一步提升最终得到的热化态的精度。
另外，还通过基于混态在多个不同的泡利字符串下的关联函数值，计算得到混态对应的哈密顿量的期望值，然后基于混态对应的哈密顿量的期望值以及混态对应的熵，计算得到目标函数的期望值，使得目标函数的求解综合考虑了混态在多个不同的泡利字符串下的信息，提升了目标函数的精度，这也有助于进一步提升最终得到的热化态的精度。
另外，还通过利用Gibbs热化态和Renyi热化态具有局域近似特性，在我们想要得到目标量子系统的Gibbs热化态时，使用Renyi自由能作为目标函数，相比于直接使用Gibbs自由能作为目标函数，能够简化计算复杂度，提升效率。利用Renyi熵，特别是低阶Renyi熵在线路上较易测量的特点，我们成功实现了在多项式资源下对热化态的高效近似。例如，取α＝2的Renyi2阶的Renyi熵，需要资源和测量次数显著减少。
在相关技术中，还提供了另外一种制备Gibbs热化态的方案(我们称之为方案二)：采用特定架构，使得Gibbs熵可以约化到经典概率模型的计算。这一方案将首先通过经典神经网络概率模型生成和系统量子比特一样自由度的比特字符串，对应经典概率是p(i)，p(i)代表测量得到比特字符串是i的概率，然后将比特字符串i对应的量子直积态|i>输入到只作用在系统量子比特上的参数化量子线路V上，从而构造对应的混态，数学上该混态对应的密度矩阵ρ即为：
Figure PCTCN2022132997-appb-000023
其中，|i s>代表系统量子比特s上的比特字符串。
此时，由于不同输出态V|i s>之间正交，该混态对应的Gibbs熵恰好约化为经典Gibbs熵：
Figure PCTCN2022132997-appb-000024
其中，p i和上式中p(i)的含义相同。
由此，Gibbs熵可以高效地计算，而不需要额外的测量。
但这种方案在近似热化态的精度上相比本申请的方法有很大的差距。
下面，介绍本申请提供的量子线路+神经网络后处理的方法，相比于上述相关技术提供的神经网络前置+量子线路的方法，在表达能力上优势。
我们通过基于优化带熵自由能的数值模拟结果，来说明在可类比情形下，本申请技术方案可以更接近严格的热化态，具有更好的表达能力。
采用N＝8格点的周期性边界条件的横场伊辛模型(TFTM)作为测试体系，该横场伊辛模型的哈密顿量可表示为：
Figure PCTCN2022132997-appb-000025
其中，Z代表泡利Z算符，X代表泡利X算符，n为正整数，i为小于或等于n的正整数。
该系统在温度β＝1时，对应的热平衡态的自由能为-11.35678。
我们选取的参数化量子路线的结构为：
Figure PCTCN2022132997-appb-000026
其中，P为重复结构
Figure PCTCN2022132997-appb-000027
的数目，H i是作用在第i个量子比特上的哈达玛(Hadamard)门，其矩阵表示为
Figure PCTCN2022132997-appb-000028
量子比特和系统量子比特交叠出现的排布，这是由于这种排布可以使得物理系统和辅助系统的纠缠最大，可以用更浅的线路深度热化物理系统的部分。因为线路总需要一定的纠缠，单层创造的纠缠大，需要的线路层数就少。由此，我们的方案需要2N＝16个比特的系统。相应的方案二对应的线路采用同样结构，只占据8个物理系统的比特。也就是说，我们的方案使用的量子比特数是方案二的二倍。由此为了量子门数目可比，我们应至少比较现有方案和两倍深度的方案二的表达能力。实际上，我们采取了更复杂的[ZZ,Rx,Ry]*P的变分线路结构应用到之前方案的架构上。而我们的方案仅取更保守的[ZZ,Rx]*P的线路结构。由于这里我们比较的是线路的表达能力，因此数值上两者都用带Gibbs熵的自由能作为优化目标函数。结果证明，即使不考虑噪声对于更深的线路退相干更严重的影响，我们的方案的热化态制备仍然具有更强的表达能力。
我们的方案在P＝8时，优化得到混态，给出-11.347的自由能，与严格Gibbs热化态的保真度达到了0.997。反之对于方案二，量子门数目类似的P＝16的同样线路拟设，优化后给出的自由能为-11.301，劣于我们的方案，相应的保真度仅为0.976，也差于我们的方案。更具体的，两种方案在带Gibbs熵的自由能优化下的性能对比如表1。可以看出即使只有P＝2的变分线路，在神经网络后处理架构中，仍然保持着很好的近似效果(甚至好于线路拟设更复杂，层数为2P＝16的方案二)。
表1
Figure PCTCN2022132997-appb-000029
由此可以说明量子线路+神经网络后处理的方案(也即本申请方案)在量子资源相仿的情况下，制备混态的表达能力远优于神经网络前置+量子线路的方案(也即方案二)。因此虽然方案二可以高效计算Gibbs熵，但还是利用前者的架构来进行优化和近似，可以更加有效利用有限的量子硬件资源。
接下来，通过数值模拟的方式，对不同方案制备热化态的效果进行刻画和比较，以说明本申请方案的优势。仍以上个实施例中的N＝8的横场伊辛模型TFIM进行实验。
如图4所示，图4示出了每次训练迭代(也即参数更新迭代)时的各种方案Gibbs热化态的保真度，其中左图是β＝5时每次测量时的保真度，显而易见的，没有神经网络权重曲线41的保真度最差，而有有界神经网络权重曲线42的保真度最高，右图是β＝1高温区时每次测量时的保真度，在高温区时，方案一曲线43表现最差，甚至最低低于0.6，而有有界神经网络权重曲线44的表现最好，以下依次为有神经网络权重曲线45和无神经网络权重曲线46。
但不管是任意一种方案，在高温区时，随着训练迭代次数的增加，热化态的保真度随之下降，这是由于存在过拟合问题，可以通过增加体系的尺寸而缓解。
如图5所示，图5示出了不同温度，不同方案，不同次独立优化得到的收敛的Gibbs自由能保真度，可以看出不加神经网络后处理的结果涨落很大，训练很不稳定，如图中没有神经网络权重区间51。相比之下，有有界神经网络权重是稳定的最优方案，在高保真度的同时，结果的涨落很小，如图中有有界神经网络权重区间52。
如图6所示，图6示出了在同样的关联函数的情况下，不同方案给出的关联函数估计。其中，左图是早停(1000轮优化)的关联函数和真值的差距，右图是收敛后关联函数和真值的差距，对于有神经网络权重的方案，早停和最后收敛对应的关联函数的估计差距不大，如图中的有神经网络权重区间61和有有界神经网络权重区间62。因为训练后期Renyi热化态的自由能的优化是对Gibbs热化态目标的过拟合所致，不在显著改善关联函数估计。对于方案一区间63，早停和最后收敛对应的关联函数的估计差距很大，其中偏差超过0.2的部分未在图上显示。而没有神经网络权重的方案，训练方差涨落较大，期望估计也多数情形偏离更大，如图中没有神经网络权重区间64。由于Renyi热化态和Gibbs热化态给出局域关联一致这一事实在热力学极限成立，因此随着模拟系统体系(也就是指量子比特数目)的增加，对关联函数的估计将有望变得比这里的数值结果更加准确。
如图4至6所示，不同灰度的线对应不同的方案。
下述为本申请装置实施例，可以用于执行本申请方法实施例。对于本申请装置实施例中未披露的细节，请参照本申请方法实施例。
图7是本申请一个实施例提供的量子体系下的热化态制备装置的框图。该装置具有实现上述量子体系下的热化态制备方法的功能，所述功能可以由硬件实现，也可以由硬件执行相应的软件实现。该装置可以是计算机设备，也可以设置在计算机设备中。该装置700可以包括：测量结果获取模块710、权重参数获取模块720、关联函数计算模块730、目标函数计算模块740、变分参数调整模块750和热化态获取模块760。
测量结果获取模块710，用于获取经参数化量子线路对组合量子比特的输入量子态进行变换处理后，对所述参数化量子线路的输出量子态进行n次测量，得到的n组测量结果；其中，所述组合量子比特包括辅助量子比特和目标量子系统的系统量子比特，每组测量结果包括：与所述系统量子比特对应的第一测量结果，以及与所述辅助量子比特对应的第二测量结果，n为正整数。
权重参数获取模块720，用于通过神经网络对所述第二测量结果进行处理，得到权重参数。
关联函数计算模块730，用于基于所述权重参数和所述第一测量结果，计算得到所述目标量子系统的混态的关联函数值。
目标函数计算模块740，用于基于所述混态的关联函数值，计算得到目标函数的期望值。
变分参数调整模块750，用于以所述目标函数的期望值收敛为目标，对变分参数进行调整；其中，所述变分参数包括以下至少一项：所述参数化量子线路的参数、所述神经网络的参数。
热化态获取模块760，用于在所述目标函数的期望值满足收敛条件的情况下，获取所述目标量子系统的混态以近似表征所述目标量子系统的热化态。
在一些实施例中，所述关联函数计算模块730，用于基于n个所述第二测量结果分别对应的权重参数，对n个所述第一测量结果分别对应的运算结果进行加权平均，得到所述目标量子系统的混态的关联函数值。
在一些实施例中，所述关联函数计算模块730还用于采用目标关联函数对n个所述第一测量结果分别进行运算处理，得到n个所述第一测量结果分别对应的运算结果；其中，所述目标关联函数用于获取所述目标量子系统的混态在目标泡利字符串下的关联函数值。
在一些实施例中，所述目标函数计算模块740，用于获取所述混态在多个不同的泡利字符串下的关联函数值；其中，所述混态在多个不同的泡利字符串下的关联函数值，采用不同的关联函数得到；基于所述混态在多个不同的泡利字符串下的关联函数值，计算得到所述混态对应的哈密顿量的期望值；基于所述混态对应的哈密顿量的期望值，以及所述混态对应的熵，计算得到所述目标函数的期望值。
在一些实施例中，在需要获取所述目标量子系统的第一形式的热化态的情况下，所述目标函数是第二形式的热化态所对应的自由能；其中，所述第一形式的热化态和所述第二形式的热化态是两种不同形式的热化态，且所述第一形式的热化态和所述第二形式的热化态之间具有局域近似特性。
在一些实施例中，所述第一形式的热化态是Gibbs热化态，所述第二形式的热化态是Renyi热化态。
在一些实施例中，所述权重参数获取模块720，用于通过所述神经网络对所述第二测量结果进行处理，并对所述神经网络的输出结果进行取值范围的限制，得到在所述取值范围之内的权重参数。
在一些实施例中，所述取值范围为[1/r，r]，r是大于1的数值。
在一些实施例中，所述系统量子比特和所述辅助量子比特采用交叠出现的排布方式。
本申请提供的技术方案，在制备目标量子系统的热化态时，通过引入神经网络后处理的方案，首先通过参数化量子线路对系统量子比特和辅助量子比特的输入量子态进行处理，然后通过神经网络对辅助量子比特对应的测量结果进行处理，得到相应的权重参数，利用该权重参数来近似表征混态中的概率，然后基于构建的混态的关联函数，计算得到目标函数的期望值，以目标函数的期望值收敛为目标，优化参数化量子线路的参数和神经网络的参数，从而在目标函数的期望值满足收敛条件的情况下，获取目标量子系统的混态以近似表征目标量子系统的热化态。本方案通过引入神经网络输出权重参数，利用该权重参数来调节不同的辅助量子比特测量结果所对应的权重，从而通过神经网络的可训练参数，增强了线路整体的表达能力，达到更加高效且精确地制备热化态的效果。
需要说明的是，上述实施例提供的装置，在实现其功能时，仅以上述各功能模块的划分进行举例说明，实际应用中，可以根据需要而将上述功能分配由不同的功能模块完成，即将设备的内部结构划分成不同的功能模块，以完成以上描述的全部或者部分功能。另外，上述实施例提供的装置，与方法实施例属于同一构思，其具体实现过程详见方法实施例，这里不再赘述。
请参考图8，其示出了本申请一个实施例提供的计算机设备的结构示意图。该计算机设备可以是经典计算机。该计算机设备可用于实施上述实施例中提供的量子体系下的热化态制备方法。具体来讲：
该计算机设备800包括处理单元(如CPU(Central Processing Unit，中央处理器)、GPU(Graphics Processing Unit，图形处理器)和FPGA(Field Programmable Gate Array，现场可编程逻辑门阵列)等)801、包括RAM(Random-Access Memory，随机存储器)802和ROM(Read-Only Memory，只读存储器)803的系统存储器804，以及连接系统存储器804和中央处理单元801的系统总线805。该计算机设备800还包括帮助服务器内的各个器件之间传输 信息的基本输入/输出系统(Input Output System，I/O系统)806，和用于存储操作系统813、应用程序814和其他程序模块815的大容量存储设备807。
可选地，该基本输入/输出系统806包括有用于显示信息的显示器808和用于用户输入信息的诸如鼠标、键盘之类的输入设备809。其中，该显示器808和输入设备809都通过连接到系统总线805的输入输出控制器810连接到中央处理单元801。该基本输入/输出系统806还可以包括输入输出控制器810以用于接收和处理来自键盘、鼠标、或电子触控笔等多个其他设备的输入。类似地，输入输出控制器810还提供输出到显示屏、打印机或其他类型的输出设备。
可选地，该大容量存储设备807通过连接到系统总线805的大容量存储控制器(未示出)连接到中央处理单元801。该大容量存储设备807及其相关联的计算机可读介质为计算机设备800提供非易失性存储。也就是说，该大容量存储设备807可以包括诸如硬盘或者CD-ROM(Compact Disc Read-Only Memory，只读光盘)驱动器之类的计算机可读介质(未示出)。
不失一般性，该计算机可读介质可以包括计算机存储介质和通信介质。计算机存储介质包括以用于存储诸如计算机可读程序、数据结构、程序模块或其他数据等信息的任何方法或技术实现的易失性和非易失性、可移动和不可移动介质。计算机存储介质包括RAM、ROM、EPROM(Erasable Programmable Read-Only Memory，可擦写可编程只读存储器)、EEPROM(Electrically Erasable Programmable Read-Only Memory，电可擦写可编程只读存储器)、闪存或其他固态存储其技术，CD-ROM、DVD(Digital Video Disc，高密度数字视频光盘)或其他光学存储、磁带盒、磁带、磁盘存储或其他磁性存储设备。当然，本领域技术人员可知该计算机存储介质不局限于上述几种。上述的系统存储器804和大容量存储设备807可以统称为存储器。
根据本申请实施例，该计算机设备800还可以通过诸如因特网等网络连接到网络上的远程计算机运行。也即计算机设备800可以通过连接在该系统总线805上的网络接口单元811连接到网络812，或者说，也可以使用网络接口单元816来连接到其他类型的网络或远程计算机系统(未示出)。
所述存储器还包括计算机程序，该计算机程序存储于存储器中，且经配置以由一个或者一个以上处理器执行，以实现上述量子体系下的热化态制备方法。
在示例性实施例中，还提供了一种计算机设备，所述计算机设备用于实现上述量子体系下的热化态制备方法。可选地，该计算机设备是量子计算机，或经典计算机，或量子计算机和经典计算机的混合设备执行环境。
在示例性实施例中，还提供了一种计算机可读存储介质，该存储介质中存储有计算机程序，该计算机程序在被计算机设备的处理器执行时实现上述量子体系下的热化态制备方法。
可选地，该计算机可读存储介质可以包括：ROM(Read-Only Memory，只读存储器)、RAM(Random-Access Memory，随机存储器)、SSD(Solid State Drives，固态硬盘)或光盘等。其中，随机存取记忆体可以包括ReRAM(Resistance Random Access Memory，电阻式随机存取记忆体)和DRAM(Dynamic Random Access Memory，动态随机存取存储器)。
在示例性实施例中，还提供了一种计算机程序产品，计算机程序产品包括计算机程序，计算机程序存储在计算机可读存储介质中。计算机设备的处理器从计算机可读存储介质中读取计算机程序，处理器执行计算机程序，使得计算机设备执行上述量子体系下的热化态制备方法。
在示例性实施例中，还提供了一种量子体系下的热化态制备系统，所述系统包括：参数化量子线路和计算机设备。
所述参数化量子线路，用于对组合量子比特的输入量子态进行变换处理，得到所述参数化量子线路的输出量子态；其中，所述组合量子比特包括辅助量子比特和目标量子系统的系 统量子比特。
所述计算机设备，用于获取对所述参数化量子线路的输出量子态进行n次测量，得到的n组测量结果；其中，每组测量结果包括：与所述系统量子比特对应的第一测量结果，以及与所述辅助量子比特对应的第二测量结果，n为正整数。
所述计算机设备，还用于通过神经网络对所述第二测量结果进行处理，得到权重参数；基于所述权重参数和所述第一测量结果，计算得到所述目标量子系统的混态的关联函数值；基于所述混态的关联函数值，计算得到目标函数的期望值。
所述计算机设备，还用于以所述目标函数的期望值收敛为目标，对变分参数进行调整；在所述目标函数的期望值满足收敛条件的情况下，获取所述目标量子系统的混态以近似表征所述目标量子系统的热化态；其中，所述变分参数包括以下至少一项：所述参数化量子线路的参数、所述神经网络的参数。
在一些实施例中，所述系统还包括：测量线路。
所述测量线路，用于对参数化量子线路的输出量子态进行n次测量，得到n组测量结果。
在一些实施例中，所述计算机设备，用于基于n个所述第二测量结果分别对应的权重参数，对n个所述第一测量结果分别对应的运算结果进行加权平均，得到所述目标量子系统的混态的关联函数值。
在一些实施例中，所述计算机设备，还用于采用目标关联函数对n个所述第一测量结果分别进行运算处理，得到n个所述第一测量结果分别对应的运算结果；其中，所述目标关联函数用于获取所述目标量子系统的混态在目标泡利字符串下的关联函数值。
在一些实施例中，所述计算机设备，用于获取所述混态在多个不同的泡利字符串下的关联函数值；其中，所述混态在多个不同的泡利字符串下的关联函数值，采用不同的关联函数得到；基于所述混态在多个不同的泡利字符串下的关联函数值，计算得到所述混态对应的哈密顿量的期望值；基于所述混态对应的哈密顿量的期望值，以及所述混态对应的熵，计算得到所述目标函数的期望值。
在一些实施例中，在需要获取所述目标量子系统的第一形式的热化态的情况下，所述目标函数是第二形式的热化态所对应的自由能；其中，所述第一形式的热化态和所述第二形式的热化态是两种不同形式的热化态，且所述第一形式的热化态和所述第二形式的热化态之间具有局域近似特性。
在一些实施例中，所述第一形式的热化态是Gibbs热化态，所述第二形式的热化态是Renyi热化态。
在一些实施例中，所述计算机设备，用于通过所述神经网络对所述第二测量结果进行处理，并对所述神经网络的输出结果进行取值范围的限制，得到在所述取值范围之内的权重参数。
在一些实施例中，所述取值范围为[1/r，r]，r是大于1的数值。
在一些实施例中，所述系统量子比特和所述辅助量子比特采用交叠出现的排布方式。
本申请对于量子体系下的热化态制备系统的具体架构不作限定，可以包括计算机设备，也可以包括计算机设备和参数化量子线路，还可以包括计算机设备、参数化量子线路和测量线路。
另外，对于该系统实施例中未详细说明的细节，可参见上文方法实施例。
应当理解的是，在本文中提及的“多个”是指两个或两个以上。“和/或”，描述关联对象的关联关系，表示可以存在三种关系，例如，A和/或B，可以表示：单独存在A，同时存在A和B，单独存在B这三种情况。字符“/”一般表示前后关联对象是一种“或”的关系。另外，本文中描述的步骤编号，仅示例性示出了步骤间的一种可能的执行先后顺序，在一些其它实施例中，上述步骤也可以不按照编号顺序来执行，如两个不同编号的步骤同时执行，或 者两个不同编号的步骤按照与图示相反的顺序执行，本申请实施例对此不作限定。
以上仅为本申请的示例性实施例，并不用以限制本申请，凡在本申请的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本申请的保护范围之内。

Claims (14)

  1. 一种量子体系下的热化态制备方法，所述方法由计算机设备执行，所述方法包括：
    获取经参数化量子线路对组合量子比特的输入量子态进行变换处理后，对所述参数化量子线路的输出量子态进行n次测量，得到的n组测量结果；其中，所述组合量子比特包括辅助量子比特和目标量子系统的系统量子比特，每组测量结果包括：与所述系统量子比特对应的第一测量结果，以及与所述辅助量子比特对应的第二测量结果，n为正整数；
    通过神经网络对所述第二测量结果进行处理，得到权重参数；
    基于所述权重参数和所述第一测量结果，计算得到所述目标量子系统的混态的关联函数值；
    基于所述混态的关联函数值，计算得到目标函数的期望值；
    以所述目标函数的期望值收敛为目标，对变分参数进行调整；其中，所述变分参数包括以下至少一项：所述参数化量子线路的参数、所述神经网络的参数；
    在所述目标函数的期望值满足收敛条件的情况下，获取所述目标量子系统的混态以近似表征所述目标量子系统的热化态。
  2. 根据权利要求1所述的方法，其中，所述基于所述权重参数和所述第一测量结果，计算得到所述目标量子系统的混态的关联函数值，包括：
    基于n个所述第二测量结果分别对应的权重参数，对n个所述第一测量结果分别对应的运算结果进行加权平均，得到所述目标量子系统的混态的关联函数值。
  3. 根据权利要求2所述的方法，其中，所述方法还包括：
    采用目标关联函数对n个所述第一测量结果分别进行运算处理，得到n个所述第一测量结果分别对应的运算结果；
    其中，所述目标关联函数用于获取所述目标量子系统的混态在目标泡利字符串下的关联函数值。
  4. 根据权利要求3所述的方法，其中，所述基于所述混态的关联函数值，计算得到目标函数的期望值，包括：
    获取所述混态在多个不同的泡利字符串下的关联函数值；其中，所述混态在多个不同的泡利字符串下的关联函数值，采用不同的关联函数得到；
    基于所述混态在多个不同的泡利字符串下的关联函数值，计算得到所述混态对应的哈密顿量的期望值；
    基于所述混态对应的哈密顿量的期望值，以及所述混态对应的熵，计算得到所述目标函数的期望值。
  5. 根据权利要求1所述的方法，其中，在需要获取所述目标量子系统的第一形式的热化态的情况下，所述目标函数是第二形式的热化态所对应的自由能；
    其中，所述第一形式的热化态和所述第二形式的热化态是两种不同形式的热化态，且所述第一形式的热化态和所述第二形式的热化态之间具有局域近似特性。
  6. 根据权利要求5所述的方法，其中，所述第一形式的热化态是吉布斯Gibbs热化态，所述第二形式的热化态是瑞丽Renyi热化态。
  7. 根据权利要求1所述的方法，其中，所述通过神经网络对所述第二测量结果进行处理，得到权重参数，包括：
    通过所述神经网络对所述第二测量结果进行处理，并对所述神经网络的输出结果进行取值范围的限制，得到在所述取值范围之内的权重参数。
  8. 根据权利要求7所述的方法，其中，所述取值范围为[1/r，r]，r是大于1的数值。
  9. 根据权利要求1所述的方法，其中，所述系统量子比特和所述辅助量子比特采用交叠出现的排布方式。
  10. 一种量子体系下的热化态制备装置，所述装置包括：
    测量结果获取模块，用于获取经参数化量子线路对组合量子比特的输入量子态进行变换处理后，对所述参数化量子线路的输出量子态进行n次测量，得到的n组测量结果；其中，所述组合量子比特包括辅助量子比特和目标量子系统的系统量子比特，每组测量结果包括：与所述系统量子比特对应的第一测量结果，以及与所述辅助量子比特对应的第二测量结果，n为正整数；
    权重参数获取模块，用于通过神经网络对所述第二测量结果进行处理，得到权重参数；
    关联函数计算模块，用于基于所述权重参数和所述第一测量结果，计算得到所述目标量子系统的混态的关联函数值；
    目标函数计算模块，用于基于所述混态的关联函数值，计算得到目标函数的期望值；
    变分参数调整模块，用于以所述目标函数的期望值收敛为目标，对变分参数进行调整；其中，所述变分参数包括以下至少一项：所述参数化量子线路的参数、所述神经网络的参数；
    热化态获取模块，用于在所述目标函数的期望值满足收敛条件的情况下，获取所述目标量子系统的混态以近似表征所述目标量子系统的热化态。
  11. 一种计算机设备，所述计算机设备用于实现如权利要求1至9任一项所述的方法。
  12. 一种计算机可读存储介质，所述存储介质中存储有计算机程序，所述计算机程序由处理器加载并执行以实现如权利要求1至9任一项所述的方法。
  13. 一种计算机程序产品，所述计算机程序产品包括计算机程序，所述计算机程序存储在计算机可读存储介质中，处理器从所述计算机可读存储介质读取并执行所述计算机程序，以实现如权利要求1至9任一项所述的方法。
  14. 一种量子体系下的热化态制备系统，所述系统包括：参数化量子线路和计算机设备；
    所述参数化量子线路，用于对组合量子比特的输入量子态进行变换处理，得到所述参数化量子线路的输出量子态；其中，所述组合量子比特包括辅助量子比特和目标量子系统的系统量子比特；
    所述计算机设备，用于获取对所述参数化量子线路的输出量子态进行n次测量，得到的n组测量结果；其中，每组测量结果包括：与所述系统量子比特对应的第一测量结果，以及与所述辅助量子比特对应的第二测量结果，n为正整数；
    所述计算机设备，还用于通过神经网络对所述第二测量结果进行处理，得到权重参数；基于所述权重参数和所述第一测量结果，计算得到所述目标量子系统的混态的关联函数值；基于所述混态的关联函数值，计算得到目标函数的期望值；
    所述计算机设备，还用于以所述目标函数的期望值收敛为目标，对变分参数进行调整；在所述目标函数的期望值满足收敛条件的情况下，获取所述目标量子系统的混态以近似表征所述目标量子系统的热化态；其中，所述变分参数包括以下至少一项：所述参数化量子线路的参数、所述神经网络的参数。
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