Quantum variation method, device and storage medium for simulating quantum system

Abstract

The present disclosure discloses a method for obtaining optimal variational parameters of a ground state wave function of a Hamiltonian system. The method includes initializing a plurality of variational parameters and sending the variational parameters to a quantum computing part to output a plurality of measurement results. The method includes transmitting the measurement results to a classical computing part to update the plurality of variational parameters based on the plurality of measurement results and an update rule, and determining whether the measured energy satisfies a convergence rule. When the measured energy does not satisfy the convergence rule, the method includes sending the plurality of updated variational parameters to the quantum computing part for the next iteration; and when the measured energy satisfies the convergence rule, the method includes obtaining a plurality of optimal variational parameters of the Hamiltonian system.

Description

[0001] Related Applications

[0002] This application claims priority to U.S. Application No. 16 / 505,179, filed in the U.S. Patent and Trademark Office on July 8, 2019, the entire contents of which are incorporated by reference. Technical Field

[0003] The present invention relates to the field of quantum system simulation technology, and in particular to a method, an apparatus, a computer device and a storage medium for obtaining multiple optimal variational parameters of a wave function of a Hamiltonian system. Background Art

[0004] The simulation of quantum systems is used in a variety of different fields. However, simulating complex quantum systems with classical computers can be difficult due to the exponential scaling of the resources required on classical computers as the size of the quantum system increases.

[0005] The present disclosure describes a variational parameter optimization method, apparatus, and storage medium for simulating quantum systems that addresses at least one of the above disadvantages. Summary of the invention

[0006] In view of this, it is contemplated that embodiments of the present disclosure provide a variational parameter optimization method, apparatus, and storage medium.

[0007] According to one aspect, an embodiment of the present disclosure provides a method for obtaining multiple optimal variational parameters of a wave function of a Hamiltonian system. The method includes initializing multiple variational parameters of a wave function of a Hamiltonian system by a device including a quantum computing part and a classical computing part communicating with the quantum computing part. The method includes sending multiple variational parameters to the quantum computing part by the device to start iteration, so that the quantum computing part performs multiple measurements based on multiple variational parameters, wave functions and Hamiltonian system to output multiple measurement results. The method includes transmitting multiple measurement results from the quantum computing part to the classical computing part by the device, so that the classical computing part updates multiple variational parameters based on multiple measurement results and update rules. The method includes determining by the device whether the measured energy satisfies the convergence rule. The method includes, in response to determining that the measured energy does not satisfy the convergence rule, sending multiple updated variational parameters as multiple variational parameters to the quantum computing part for the next iteration. The method includes setting multiple updated variational parameters by the device in response to determining that the measured energy satisfies the convergence rule to obtain multiple optimal variational parameters of the Hamiltonian system.

[0008] According to another aspect, an embodiment of the present disclosure provides a computer device. The computer device includes a memory storing instructions and a processor communicating with the memory. When the processor executes the instructions, the processor is configured to cause the computer device to initialize multiple variational parameters of the wave function of the Hamiltonian system. When the processor executes the instructions, the processor is configured to cause the computer device to send multiple variational parameters to the quantum computing part to start iteration, so that the quantum computing part performs multiple measurements based on multiple variational parameters, wave functions and Hamiltonian systems to output multiple measurement results. When the processor executes the instructions, the processor is configured to cause the computer device to transfer multiple measurement results from the quantum computing part to the classical computing part, so that the classical computing part updates multiple variational parameters based on multiple measurement results and update rules. When the processor executes the instructions, the processor is configured to cause the computer device to determine whether the measured energy satisfies the convergence rule. When the processor executes the instructions, the processor is configured to cause the computer device to respond to determining that the measured energy does not satisfy the convergence rule, and send multiple updated variational parameters as multiple variational parameters to the quantum computing part for the next iteration. When the processor executes the instructions, the processor is configured to cause the computer device to set a plurality of updated variational parameters in response to determining that the measured energy satisfies the convergence rule to obtain a plurality of optimal variational parameters of the Hamiltonian system.

[0009] According to another aspect, an embodiment of the present disclosure provides a device for obtaining multiple optimal variational parameters of a wave function of a Hamiltonian system. The device includes an initialization module for initializing multiple variational parameters of a wave function of a Hamiltonian system; a first sending module for sending multiple variational parameters to a quantum computing part to start iteration, so that the quantum computing part performs multiple measurements based on multiple variational parameters, wave functions and Hamiltonian systems to output multiple measurement results; a transmission module for transmitting multiple measurement results from the quantum computing part to the classical computing part, so that the classical computing part updates multiple variational parameters based on multiple measurement results and update rules; a determination module for determining whether the measured energy satisfies the convergence rule; a second sending module for sending multiple updated variational parameters as multiple variational parameters to the quantum computing part for the next iteration in response to determining that the measured energy does not satisfy the convergence rule; and an acquisition module for setting multiple updated variational parameters in response to determining that the measured energy satisfies the convergence rule to obtain multiple optimal variational parameters of the Hamiltonian system.

[0010] On the other hand, an embodiment of the present disclosure provides a non-transitory computer-readable storage medium storing instructions. When the instruction is executed by a processor, the instruction causes the processor to initialize multiple variational parameters of the wave function of the Hamiltonian system. When the instruction is executed by the processor, the instruction causes the processor to send multiple variational parameters to the quantum computing part to start iteration, so that the quantum computing part performs multiple measurements based on multiple variational parameters, wave functions and Hamiltonian system to output multiple measurement results. When the instruction is executed by the processor, the instruction causes the processor to transfer multiple measurement results from the quantum computing part to the classical computing part, so that the classical computing part updates multiple variational parameters based on multiple measurement results and update rules. When the instruction is executed by the processor, the instruction causes the processor to determine whether the measured energy satisfies the convergence rule. When the instruction is executed by the processor, the instruction causes the processor to send multiple updated variational parameters as multiple variational parameters to the quantum computing part for the next iteration in response to determining that the measured energy does not satisfy the convergence rule. When the instructions are executed by the processor, the instructions cause the processor to set a plurality of updated variational parameters in response to determining that the measured energy satisfies a convergence rule to obtain a plurality of optimal variational parameters of the Hamiltonian system.

[0011] Embodiments of the present disclosure provide methods, apparatus, and non-transitory computer-readable storage media for obtaining multiple optimal variational parameters of a wave function of a Hamiltonian system. The method includes: initializing multiple variational parameters of a wave function of a Hamiltonian system by a device including a quantum computing part and a classical computing part, the classical computing part communicating with the quantum computing part; sending the multiple variational parameters to the quantum computing part by the device to start iteration, so that the quantum computing part performs multiple measurements based on the multiple variational parameters, the wave function and the Hamiltonian system to output multiple measurement results; transmitting the multiple measurement results from the quantum computing part to the classical computing part by the device, so that the classical computing part updates the multiple variational parameters based on the multiple measurement results and an update rule; determining by the device whether the measured energy satisfies a convergence rule; in response to determining that the measured energy does not satisfy the convergence rule, sending multiple updated variational parameters as the multiple variational parameters to the quantum computing part for the next iteration; and in response to determining that the measured energy satisfies the convergence rule, setting the multiple updated variational parameters by the device to obtain multiple optimal variational parameters of the Hamiltonian system. It can be seen that in the technical solution of the present invention, the disclosed combination of quantum imaginary time evolution and restricted Boltzmann machine (RBM) ansatz can overcome the problems associated with other quantum phase estimation, for example, the need for quantum error correction that may not be easily available in near-term or mid-term quantum computers. The disclosed method may not require the difficult high-dimensional noise classical optimization associated with other hybrid variational algorithms. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] FIG. 1 is a flow chart of an embodiment disclosed in the present disclosure.

[0013] Figure 2 is a schematic diagram of an embodiment of a restricted Boltzmann machine structure disclosed in the present disclosure.

[0014] Figure 3 is a schematic diagram of an embodiment of an apparatus disclosed in the present disclosure.

[0015] Figure 4 A schematic diagram of a classical computer system is shown.

[0016] Figure 5 A schematic diagram of a quantum computer system is shown.

[0017] Figure 6 is a graph of examples of ground state energies of hydrogen molecules simulated using the disclosed method. DETAILED DESCRIPTION

[0018] The present invention will now be described in detail below with reference to the accompanying drawings, which form a part of the present invention and illustrate specific examples of implementation by way of illustration. However, it is noted that the present invention may be implemented in a variety of different forms, and therefore, the subject matter covered or claimed is intended to be construed as not being limited to any of the implementations to be set forth below. It is also noted that the present invention may be implemented as a method, device, component, or system. Thus, embodiments of the present invention may, for example, take the form of hardware, software, firmware, or any combination thereof.

[0019] Throughout the specification and claims, terms may have slightly different meanings that are suggested or implied in the context beyond the explicitly stated meaning. The phrases "in one embodiment" or "in some embodiments" as used herein do not necessarily refer to the same embodiment, and the phrases "in another embodiment" or "in other embodiments" as used herein do not necessarily refer to different embodiments. Similarly, the phrases "in one implementation" or "in some implementations" as used herein do not necessarily refer to the same implementation, and the phrases "in another implementation" or "in other implementations" as used herein do not necessarily refer to different implementations. For example, it is intended that the claimed subject matter includes combinations of the whole or part of the exemplary embodiments / implementations.

[0020] Typically, terms can be understood at least in part from usage in context. For example, as used herein, terms such as "and", "or" or "and / or" can include various meanings, which can depend at least in part on the context in which such terms are used. Typically, if "or" is used for an association list, such as A, B or C, then "or" is intended to represent A, B and C, which are used here in an inclusive sense, and A, B or C, which are used here in an exclusive sense. In addition, at least in part depending on the context, as used herein, the terms "one or more" or "at least one" can be used to describe any feature, structure or characteristic in a singular sense, or can be used to describe a combination of features, structures or characteristics in a plural sense. Similarly, terms such as "one", "an" or "the" can also be understood to convey singular usage or to convey plural usage, which depends at least in part on the context. In addition, the term "based on" or "determined by..." can be understood to not necessarily be intended to convey an exclusive set of factors, and can alternatively allow the presence of additional factors that are not necessarily explicitly described, which also depends at least in part on the context.

[0021] The simulation of quantum systems can be used in a variety of different fields, such as drug synthesis, the design of new catalysts and battery materials, and the discovery of new superconducting materials. Quantum simulation can be one of the first killer applications of quantum computers. In quantum simulation, one of the main tasks can be to find the ground state of a quantum system (e.g., a molecule or a solid-state material). The quantum system can be a simple molecule, such as a hydrogen molecule, or a complex molecule, such as a protein.

[0022] Finding the ground state of a quantum system can involve solving a giant matrix, such as a matrix based on the Hamiltonian of the quantum system, for the eigenstate with the lowest eigenvalue. Quantum phase estimation and quantum classical hybrid variational algorithms, such as variational quantum eigensolvers, can be used to find the ground state of a quantum system.

[0023] One of the existing problems is that it is difficult to simulate complex quantum systems using classical computers due to the exponential scaling of the required resources as a function of the system size. Another existing problem is that in the context of recent quantum computing architectures, quantum computers may have a limited number of qubits and / or may be prone to errors. For example, phase estimation can produce almost exact eigenstates, but may appear impractical without error correction. For another example, although somewhat robust to error and noise, variational algorithms may be limited in accuracy for fixed assumptions (Ansatz) and may involve difficult high-dimensional noisy classical optimization.

[0024] The present disclosure describes a method that provides a computationally feasible solution to at least one existing problem. The method may include a quantum simulation technique to simulate a wave function of a quantum system using a device including at least one of a classical computing part and a quantum computing part. The wave function of the quantum system may include multiple variational parameters. When the multiple variational parameters are optimized, the wave function of the quantum system may be obtained.

[0025] The quantum computing portion may include a quantum processor, which may include a quantum computing system, such as, but not limited to, superconducting circuits, trapped ions, optical lattices, quantum dots, and linear optical devices. The quantum processor may include a plurality of qubits and associated local bias devices, such as, for example, two or more qubits. The quantum processor may also employ a coupling device (i.e., a "coupler") that provides communicative coupling between qubits.

[0026] The present disclosure may be applied to any suitable quantum computing architecture with a quantum processor and may not depend on the underlying architecture of the quantum processor. The quantum processor may be any suitable quantum computing architecture that can perform general quantum computations. Examples of quantum computing architectures may include superconducting qubits, ion traps, and optical quantum computers. The classical analog of a quantum processor is a central processing unit (CPU).

[0027] If the obtained wave function of the quantum system is the ground state wave function, the ground state energy can be calculated using E=<Ψ|H|Ψ>, where E is the ground state energy, H is the Hamiltonian of the quantum system, and Ψ is the ground state wave function.

[0028] This disclosure describes a method for obtaining the wave function of a quantum system by combining quantum imaginary time evolution and restricted Boltzmann machines (RBMs). The quantum imaginary time evolution method may be a powerful method for material simulation in quantum computers, and the choice of the wave function ansatz of the quantum imaginary time evolution method may limit its application potential. The restricted Boltzmann machine is a neural network and can be a powerful wave function ansatz in classical quantum Monte Carlo simulations.

[0029] In this disclosure, a new quantum algorithm is described for simulating the ground state of a molecule or other quantum system of interest by combining quantum imaginary time evolution and restricted Boltzmann machines. The algorithm can be a hybrid algorithm that uses a device that includes a classical computing part and a quantum computing part to perform the calculations. This hybrid quantum classical approach can be used to simulate complex physical systems using noisy intermediate-scale quantum computers with shallow circuits.

[0030] Figure 1 A flow chart of a method 100 for obtaining a plurality of optimal variational parameters of a wave function ansatz of a quantum system having a Hamiltonian is shown. Method 100 may include step 110: initializing multiple variational parameters of a wave function of a Hamiltonian system by a device including a quantum computing part and a classical computing part communicating with the quantum computing part; step 120: sending the multiple variational parameters to the quantum computing part by the device, so that the quantum computing part performs multiple measurements based on the multiple variational parameters, the wave function and the Hamiltonian system to output multiple measurement results; step 130: transmitting the multiple measurement results from the quantum computing part to the classical computing part by the device, so that the classical computing part updates the multiple variational parameters based on the multiple measurement results and the update rule; step 140: determining by the device whether the measured energy satisfies the convergence rule; step 150: in response to determining that the measured energy does not satisfy the convergence rule, sending the multiple updated variational parameters as multiple variational parameters to the quantum computing part for the next round; and step 160: in response to determining that the measured energy satisfies the convergence rule, setting the multiple updated variational parameters by the device to obtain the multiple optimal variational parameters of the Hamiltonian system.

[0031] Reference Figure 1 , step 110 may include initializing a plurality of variational parameters of a wave function of the Hamiltonian system by a device including a quantum computing portion and a classical computing portion in communication with the quantum computing portion.

[0032] A quantum system may have a system Hamiltonian H and a ground state wave function Ψ, and imaginary time may be applied, i.e., τ = i*t, where i is an imaginary unit and t is time. Under imaginary time evolution, the ground state wave function can be expressed by the imaginary time Schrödinger equation The ground state energy can be obtained by E τ = <Ψ(τ)|H|Ψ(τ)>. Due to the non-unitary decomposition, it may be difficult to directly implement the above imaginary-time Schrödinger equation in a quantum computer.

[0033] In one embodiment, a hybrid variational algorithm may be used. The wave function of a quantum system may be obtained by parameterizing a trial wave function: To approximate, is a set of quantum operations that can be implemented in quantum circuits, which are determined by the parameters control. Multiple variational parameters can be included. Thus, the power of imaginary time evolution can be exploited through parameterization of the wave function.

[0034] In one implementation, the equation of motion for the variational parameter is Can satisfy where A is a matrix with elements and C is a matrix with vector elements where “Re” represents the real part of a complex number.

[0035] gradient The form of can be obtained by analysis. Then the matrix elements of A and the vector elements of C can be measured in a quantum computer. For example, A can be measured in a quantum computer mn and C n In one implementation, the gradient can be analytically obtained by traditional paper and pencil methods. In another implementation, the gradient can be analytically obtained by calculation on a classical computer.

[0036] Therefore, the variational parameters at the next imaginary time τ+δτ can be updated based on the variational parameters at the imaginary time τ as Where δτ can be the step size of imaginary time, that is, the time step.

[0037] In one implementation, a restricted Boltzmann machine (RBM) wave function ansatz may be used for quantum imaginary time evolution.

[0038] Reference Figure 2, an example of the RBM structure 200 can be used to simulate a quantum system. The RBM structure 200 can include one or more hidden spins 220 and one or more visible spins 230. The number of the one or more hidden spins 220 can be any non-zero integer, such as 2, 3, 10, 100, or 10,000. The number of the one or more visible spins 230 can be any non-zero integer, such as 2, 3, 10, 100, or 10,000.

[0039] Reference Figure 2 , there may be a connection 240 between one of the hidden spins 220 and one of the visible spins 230. In one implementation, there may not be a connection between one of the hidden spins and another; and there may not be a connection between one of the visible spins and another.

[0040] In one implementation using the RBM structure, the RBM wave function may include the following form: in can be a projection operator that projects all hidden spins onto the |+> state, and N can be a normalization factor. For example, the |+> state can include Wherein, |0> may represent hidden spin, and |1> may represent visible spin. The number of |+> states in the RBM wave function may be the total number of hidden spins and visible spins in the RBM structure.

[0041] The RBM Hamiltonian is given by is given by , where v and h are the Pauli-Z matrices representing the visible spin and hidden spin, respectively.

[0042] In the context of the RBM wave function ansazt, the variational parameter θ n can be the coefficients in the RBM Hamiltonian (i.e. b i 、m j and W ij ). During the quantum imaginary time evolution, the variational parameter b can be updated i 、m j and W ij .

[0043] In one implementation, initial values ​​of multiple variational parameters of the wave function of a quantum system with a Hamiltonian may be randomly assigned. In another implementation, initial values ​​of multiple variational parameters of the wave function of a quantum system with a Hamiltonian may be assigned based on previous experience and / or results from similar quantum systems.

[0044] Figure 3An embodiment of a device 320 including a quantum computing portion 330 and a classical computing portion 350 is shown. The device 320 may include a memory storing instructions and a processor in communication with the memory. The processor may be configured to execute the instructions stored in the memory. When the processor executes the instructions, the processor may be configured to cause the device to perform method 100.

[0045] The quantum computing portion 330 may include a quantum processor 332, and the classical computing portion 350 may include a classical processor 352. Optionally, the quantum computing portion 330 may include a quantum memory 334. In another implementation, the quantum computing portion 330 may include a classical memory. The quantum processor 332 and / or the quantum memory 334 may be implemented by the same type or different types of quantum computing systems, such as but not limited to superconducting circuits, trapped ions, optical lattices, quantum dots, and linear optical devices. In one implementation, the classical computing portion 350 may include a classical memory 354. Input data 310 representing a physical system may be input into the device 320, and after simulation / optimization, output data 370 including optimal variational parameters of a wave function representing the physical system may be output from the device 320.

[0046] Reference Figure 4 In one implementation, the classical computer portion may be part of a classical computer system 400. The classical computer system 400 may include a communication interface 402, a system circuit 404, an input / output (I / O) interface 406, a quantum classical interface 407, a storage device 409, and a display circuit 408, which generates a machine interface 410 locally or generates a machine interface for remote display, such as in a web browser running on a local or remote machine. The machine interface 410 and the I / O interface 406 may include a GUI, a touch-sensitive display, voice or facial recognition input, buttons, switches, speakers, and other user interface elements.

[0047] The machine interface 410 and the I / O interface 406 may also include a communication interface with the PSG, PSA, the first detector, and / or the second detector. The communication between the computer system 400 and the PSG, PSA, the first detector, and / or the second detector may include wired communication or wireless communication. The communication may include, but is not limited to, serial communication, parallel communication; Ethernet communication, USB communication, and general purpose interface bus (GPIB) communication.

[0048] Additional examples of I / O interfaces 406 include microphones, video and still image cameras, headphone and microphone input / output jacks, universal serial bus (USB) connectors, memory card slots, and other types of inputs. I / O interfaces 406 may also include magnetic or optical media interfaces (e.g., CDROM or DVD drives), serial and parallel bus interfaces, and keyboard and mouse interfaces. Quantum classical interfaces may include interfaces for communicating with quantum computers.

[0049] The communication interface 402 may include a wireless transmitter and receiver ("transceiver") 412 and any antenna 414 used by the transmit and receive circuits of the transceiver 412. The transceiver 412 and the antenna 414 may support, for example, Wi-Fi network communications under any version of IEEE 802.11, such as 802.11n or 802.11ac. The communication interface 402 may also include a wired transceiver 416. The wired transceiver 416 may provide a physical layer interface for any of a variety of communication protocols, such as Ethernet, cable data service interface specification (DOCSIS), digital subscriber line (DSL), synchronous optical network (SONET), or any type of other protocols. In another implementation, the communication interface 402 may also include a communication interface with a PSG, a PSA, a first detector, and / or a second detector.

[0050] The storage device 409 may be used to store various initial, intermediate or final data. In one implementation, the storage device 409 of the computer system 400 may be integrated with a database server. The storage device 409 may be centralized or distributed, and may be local or remote to the computer system 400. For example, the storage device 409 may be remotely hosted by a cloud computing service provider.

[0051] System circuitry 404 may include hardware, software, firmware, or other circuitry in any combination. System circuitry 404 may be implemented, for example, with one or more systems on a chip (SoCs), application specific integrated circuits (ASICs), microprocessors, discrete analog and digital circuits, and other circuitry.

[0052] For example, the system circuit 404 may include one or more instruction processors 421 and a memory 422. The memory 422 stores, for example, control instructions 426 and an operating system 424. The control instructions 426 may include, for example, instructions for generating a patterned mask or for controlling a PSA. In one implementation, the instruction processor 421 executes the control instructions 426 and the operating system 424 to perform any desired functions related to the controller.

[0053] Reference Figure 5In one implementation, the quantum computer portion may be part of a quantum computer system 500. The quantum computer system 500 may include a quantum classical interface 510, a readout device 520, an initialization device 530, a qubit controller 540, and a coupling controller 550. The quantum classical interface 510 may provide an interface for communicating with a classical computer. The initialization device 530 may initialize the quantum computer system 500.

[0054] The quantum computer system 500 may include a form of a quantum processor including a plurality of qubits including qubit 1 580a, qubit 2 580b, ..., and qubit N 580c. The plurality of qubits may form an interconnected topology. The quantum computer system 500 may include a plurality of coupling devices including coupling 1 590a, coupling 2 590b, ..., and coupling M 590c.

[0055] The readout device 520 can be connected to a plurality of qubits within the interconnect topology 580. The readout device 520 can output a voltage or current signal, which can be a digital or analog signal. The qubit controller 540 can include one or more controllers for the interconnect topology of the plurality of qubits. The coupling controller 550 can include one or more coupling controllers for a plurality of coupling devices. Each respective coupling controller can be configured to tune the coupling strength of the corresponding coupling device from zero to a maximum value. For example, the coupling device can be tuned to provide coupling between two or more corresponding qubits.

[0056] Reference Figure 1 , step 120 may include sending the plurality of variational parameters to the quantum computing part through the device, so that the quantum computing part performs a plurality of measurements based on the plurality of variational parameters, the wave function and the Hamiltonian system to output a plurality of measurement results.

[0057] Send the initialized variational parameters to Figure 3 The quantum computing part 330 of the invention can be implemented as follows. In one implementation, the information of the initialized variational parameters can be sent to the quantum computing part via a series of quantum gates. For example, in the case of superconducting qubits, the information of the initialized variational parameters can be sent via a sequence of microwave pulses, wherein the details of these quantum gates, such as pulse amplitude and / or phase, can depend on the variational parameters.

[0058] The quantum computing portion can perform multiple measurements via measurements of the states of the qubits in the quantum computing portion. The quantum computing portion 330 can measure a series of measurements, which can include energies corresponding to a wave function including a variational parameter. The energy can be based on E τ = <Ψ(τ)|H|Ψ(τ)> measured.

[0059] In one implementation, a series of measurements performed by the quantum computing portion may include a and The measurement of the matrix elements of .

[0060] Reference Figure 1 , step 130 may include transmitting the plurality of measurement results from the quantum computing part to the classical computing part through the device, so that the classical computing part updates the plurality of variational parameters based on the plurality of measurement results and the update rule.

[0061] The quantum computing part can transmit multiple measurement results to the classical computing part, such as Figure 3 As shown by arrow 362. The classical computation portion may take a time step, and update a plurality of variational parameters based on the time step, a plurality of measurement results, and an update rule. In one implementation, the update rule may include Where A is the matrix with elements measured by the quantum computation part The matrix A -1 is the inverse matrix of A, and C is the vector with elements measured by the quantum computation part Vector.

[0062] In one implementation, the time step may be a predetermined fixed value, such as but not limited to 0.1, 0.001, and 0.000001.

[0063] In another implementation, the time step may be a variable value, for example, the time step may depend on the convergence of the measured energy. For example, when the difference between the measured energy in the current iteration and the measured energy in the previous iteration becomes smaller, the time step may also become smaller.

[0064] Reference Figure 1 , step 140 may include determining, by the device, whether the measured energy satisfies a convergence rule.

[0065] In one implementation, the classical calculation portion may calculate the difference between the measured energy in the current iteration and the measured energy in the previous iteration, and determine whether the difference satisfies a convergence rule. For example, the convergence rule may include determining whether the difference is less than a predetermined threshold. For example, the predetermined threshold may be l×l0 -4 , 1×10 -6 or 1×10 -9 .

[0066] In another implementation, the convergence rule may include determining whether the ratio of the difference to the corresponding measured energy is less than a predetermined threshold. For example, for a measured energy (E+dE) in the current iteration and a measured energy (E) in the previous iteration, the difference is dE, and thus the ratio of the difference to the corresponding measured energy is equal to dE / E. For example, the predetermined threshold may be 1×10 -4 , 5×10 -6 or 2×10 -9 .

[0067] In one implementation, the difference may be the absolute value of the difference between the measured energy in the current iteration and the measured energy in the previous iteration.

[0068] Reference Figure 1 , step 150 may include, in response to determining that the measured energy does not satisfy the convergence rule, sending the plurality of updated variational parameters as the plurality of variational parameters to the quantum computing portion for a next iteration.

[0069] When the measured energy does not satisfy the convergence rule, the classical calculation part may set the multiple updated variational parameters as the multiple variational parameters; and may repeat step 120 as the next iteration. Figure 3 As shown by arrow 364, the multiple variational parameters are sent to the quantum computing part, and the quantum computing part performs multiple measurements to output multiple measurement results.

[0070] Reference Figure 1 , step 160 may include: in response to determining that the measured energy satisfies the convergence rule, setting a plurality of updated variational parameters by the device to obtain a plurality of optimal variational parameters of the Hamiltonian system.

[0071] When the measured energy satisfies the convergence rule, the classical calculation part can set the multiple updated variational parameters as the multiple optimal variational parameters of the Hamiltonian system.

[0072] Optionally, Figure 3 The device 320 can also output the measured energy of the final iteration as the ground state energy of the Hamiltonian system.

[0073] In another embodiment, step 140 may include determining whether the number of iterations reaches a predetermined iteration threshold. The predetermined iteration threshold may be 1000, 20000, etc. Step 150 may include: in response to determining that the number of iterations does not reach the predetermined iteration threshold, sending the multiple updated variational parameters as multiple variational parameters to the quantum computing part for the next iteration. Step 160 may include: in response to determining that the number of iterations reaches the predetermined iteration threshold, setting the multiple updated variational parameters by the device to obtain multiple optimal variational parameters of the Hamiltonian system.

[0074] Example - Hydrogen molecule

[0075] A hydrogen molecule can consist of two hydrogen atoms. The Hamiltonian of a hydrogen molecule can be expressed by the two-qubit Hamiltonian H(R) = g0(R) + g1(R)σ z1 +g2(R)σ z2 +g3(R)σ z1 σ z2 +g4(R)σ y1 σ y2 +g5(R)σ x1 σ x2 where R is the distance between the two hydrogen atoms (i.e., the bond length), and g i is a coefficient that depends on R.

[0076] The RBM structure consisting of 2 visible spins and 2 hidden spins can be used to simulate the hydrogen molecule.

[0077] The corresponding RBM Hamiltonian can be

[0078] The RBM wave function can be in can be a projection operator that projects the two hidden spins onto the |+> state. The normalization constant N can be

[0079] The gradient can be calculated analytically. i 、m j and W ij When is a real number, the gradient can be:

[0080]

[0081]

[0082] in, and In this example of a quantum system with hydrogen molecules, the coefficients may be real numbers.

[0083] Once these gradients are known, the matrix elements and vector elements This can be done in the quantum computing part by measuring various operators (e.g. <v i >, <h i >, <v ij >, …) expectations.

[0084] Once all matrix elements in A and C are found, for example, by the quantum computing part from the measurement, the classical computing part can Update various variational parameters.

[0085] For any given distance between two hydrogen atoms (ie, bond length), the ground state energy can be calculated from the RBM ansatz using a step size of δτ = 0.01 and a total number of iterations of 1000.

[0086] Figure 6 A graph 600 showing the ground state energy of a hydrogen molecule as a function of bond length. The ground state energy may be plotted along the y-axis 630 and the bond length may be plotted along the x-axis 640.

[0087] The ground state energy calculated from the RBM ansatz is point 620, while the ground state energy calculated from the exact diagonalization is solid line 610. For bond lengths between 0 and 3 angstroms, the two results (solid line 610 and point 620) agree well with each other.

[0088] The present disclosure provides methods, apparatus, and non-transitory computer-readable storage media for obtaining multiple optimal variational parameters of a wave function of a Hamiltonian system. The present disclosure describes a combination of quantum imaginary time evolution and restricted Boltzmann machine (RBM) ansatz that can overcome problems associated with other quantum phase estimations, such as the need for quantum error correction that may not be readily available in near- or mid-term quantum computers. The disclosed method may not require difficult high-dimensional noisy classical optimization associated with other hybrid variational algorithms.

[0089] Although specific inventions have been described with reference to illustrative embodiments, this description is not meant to be limiting. Based on this specification, various modifications of the illustrative embodiments of the present invention and additional embodiments will be apparent to those of ordinary skill in the art. Those skilled in the art will readily recognize that these and various other modifications may be made to the exemplary embodiments shown and described herein without departing from the spirit and scope of the present invention. Therefore, it is contemplated that the appended claims will cover any such modifications and alternative embodiments. Certain proportions in the illustrations may be exaggerated, while other proportions may be minimized. Therefore, the present disclosure and the accompanying drawings should be considered illustrative rather than restrictive.

Claims

1. A method for obtaining multiple optimal variational parameters of a wave function of a Hamiltonian system, characterized in that: The method comprises: Initializing a plurality of variational parameters of a wave function of a Hamiltonian system by a device including a quantum computing portion and a classical computing portion, the classical computing portion being in communication with the quantum computing portion; sending the plurality of variational parameters to the quantum computing part through the device to start iteration, so that the quantum computing part performs a plurality of measurements based on the plurality of variational parameters, the wave function and the Hamiltonian system to output a plurality of measurement results; transmitting the plurality of measurement results from the quantum computing part to the classical computing part through the device, so that the classical computing part updates the plurality of variational parameters based on the plurality of measurement results and an update rule; determining, by the device, whether the measured energy satisfies a convergence rule; In response to determining that the measured energy does not satisfy the convergence rule, sending a plurality of updated variational parameters as the plurality of variational parameters to the quantum computing portion for a next iteration; and In response to determining that the measured energy satisfies the convergence rule, setting, by the device, the plurality of updated variational parameters so as to obtain a plurality of optimal variational parameters of the Hamiltonian system; The Hamiltonian system includes a Hamiltonian H and a ground state wave function Ψ(τ), and the Hamiltonian H and the ground state wave function Ψ(τ) satisfy the imaginary time Schrödinger equation Where τ = i*t, i is the imaginary unit, t is the time, and E τ is the energy of the Hamiltonian system; the ground state wave function contains an approximately parameterized wave function.

2. The method according to claim 1, characterized in that Initializing the plurality of variational parameters comprises: The plurality of variational parameters are randomly initialized by the device.

3. The method according to claim 1, characterized in that: The ground state wave function Ψ(τ) comprises the approximate parameterized wave function in is a set of quantum operations that can be implemented in quantum circuits, includes multiple variational parameters; and The plurality of measurements includes a plurality of gradients Among them, θ n is one of the multiple variational parameters.

4. The method according to claim 3, characterized in that: The update rules include where δτ is the time step and A is a matrix with elements The matrix A -1 is the inverse matrix of A, and C is a matrix with vector elements The vector of 5. The method according to any one of claims 1 to 4, characterized in that: The wave function includes a restricted Boltzmann machine (RBM) wave function having an RBM structure, and the RBM wave function satisfies in, is a projection operator that projects the hidden spin in the RBM structure onto the |+> state, N is a normalization factor, and the |+> state includes |0> represents the hidden spin in the RBM structure, |1> represents the visible spin in the RBM structure, and the number of |+> states in the RBM wave function is the number of hidden spins and visible spins in the RBM structure.

6. The method according to any one of claims 1 to 4, characterized in that The method further comprises: Obtaining a ground state wave function based on a plurality of optimal variational parameters of the Hamiltonian system; and The quantum properties of the Hamiltonian system are obtained based on the obtained ground state wave function.

7. A computer device, characterized in that: The computer device comprises: a memory storing instructions; and A processor in communication with the memory, wherein when the processor executes the instructions, the processor is configured to cause the computer device to perform the method of any one of claims 1 to 6.

8. A device for obtaining a plurality of optimal variational parameters of a wave function of a Hamiltonian system, characterized in that: The device comprises: An initialization module, used to initialize multiple variational parameters of the wave function of the Hamiltonian system; A first sending module, used for sending a plurality of variational parameters to the quantum computing part to start iteration, so that the quantum computing part performs a plurality of measurements based on the plurality of variational parameters, the wave function and the Hamiltonian system to output a plurality of measurement results; A transmission module, used to transmit the multiple measurement results from the quantum computing part to the classical computing part, so that the classical computing part updates the multiple variational parameters based on the multiple measurement results and the update rule; A determination module, used to determine whether the measured energy satisfies the convergence rule; A second sending module, for sending the plurality of updated variational parameters as a plurality of variational parameters to the quantum computing part for a next iteration in response to determining that the measured energy does not satisfy the convergence rule; and an obtaining module for setting a plurality of updated variational parameters in response to determining that the measured energy satisfies a convergence rule to obtain a plurality of optimal variational parameters of the Hamiltonian system; The Hamiltonian system includes a Hamiltonian H and a ground state wave function Ψ(τ), and the Hamiltonian H and the ground state wave function Ψ(τ) satisfy the imaginary time Schrödinger equation Where τ = i*t, i is the imaginary unit, t is the time, and E τ is the energy of the Hamiltonian system; the ground state wave function contains an approximately parameterized wave function.

9. A non-transitory computer-readable storage medium storing instructions, characterized in that: When the instructions are executed by a processor, the processor is caused to perform the method of any one of claims 1 to 6.

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