阅读说明：本技术 用于模拟量子系统的量子变分方法、装置及存储介质 (Quantum variational method and device for simulating quantum system and storage medium ) 是由 李曲空 孙启明 于 2020-06-12 设计创作，主要内容包括：本公开内容公开了用于获得哈密顿量系统的基态波函数的最优变分参数的方法。该方法包括初始化多个变分参数并且将变分参数发送到量子计算部分以输出多个测量结果。该方法包括将测量结果传输到经典计算部分以基于多个测量结果和更新规则更新多个变分参数,并且确定测量的能量是否满足收敛规则。当测量的能量不满足收敛规则时,该方法包括将多个更新的变分参数发送到量子计算部分以用于下一迭代；并且当测量的能量满足收敛规则时,该方法包括获得哈密顿量系统的多个最优变分参数。(The present disclosure discloses a method for obtaining an optimal variation parameter of a ground-state wave function of a Hamiltonian system. The method includes initializing a plurality of variation parameters and transmitting the variation parameters to a quantum computation portion to output a plurality of measurement results. The method includes transmitting the measurement results to a classical calculation section to update a plurality of variation 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 a plurality of updated variation parameters to the quantum computation portion for a next iteration; and when the measured energy satisfies a convergence rule, the method includes obtaining a plurality of optimal variation parameters of the Hamiltonian system.)

1. A method for obtaining a plurality of optimal variational parameters of a wave function of a hamiltonian system, the method comprising:

initializing, by an apparatus comprising a quantum computation portion and a classical computation portion, a plurality of variational parameters of a wave function of a Hamiltonian system, the classical computation portion in communication with the quantum computation portion;

sending, by the device, the plurality of variation parameters to the quantum computing portion to start an iteration such that the quantum computing portion performs a plurality of measurements based on the plurality of variation parameters, the wave function, and the Hamiltonian system to output a plurality of measurement results;

transmitting, by the device, the plurality of measurements from the quantum computing portion to the classical computing portion such that the classical computing portion updates the plurality of variation parameters based on the plurality of measurements 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 computation portion for a next iteration; and is

Setting, by the device, the plurality of updated variation parameters to obtain a plurality of optimal variation parameters for the Hamiltonian system in response to determining that the measured energy satisfies the convergence rule.

2. The method of claim 1, wherein initializing the plurality of variational parameters comprises:

initializing, by the device, the plurality of variation parameters randomly.

3. The method of claim 1, wherein:

the Hamiltonian system includes a Hamiltonian H and a ground state wave function ψ (τ) that satisfy an imaginary Schrodinger equationWhere τ ═ i × t, i is an imaginary unit, t is time, and E_τIs the energy of the hamiltonian system.

4. The method of claim 3, wherein:

the ground state wave function ψ (τ) comprises an approximately parameterized wave functionWhereinIs a set of quantum operations that can be implemented in quantum circuits,comprises a plurality of variation parameters; and is

The plurality of measurements includes a plurality of gradientsWherein, theta_nIs one of the plurality of variation parameters.

5. The method of claim 4, wherein:

the update rule comprisesWhere δ τ is the time step and A is the time step having the matrix elementsA matrix of^-1Is the inverse of A, C isHaving vector elementsA vector of (a) and

6. the method of claim 1, wherein:

the wave function includes a Boltzmann machine (RBM) wave function having a RBM structure, the RBM wave function satisfyingWherein the content of the first and second substances,is to project the hidden spin in the RBM structure to | +>Projection operator on state, N is a normalization factor, the | +>States include|0>Can represent a hidden spin in the RBM structure, |1>Can represent the visible spin in the RBM structure and | +in the RBM wave function>The number of states is the number of hidden and visible spins in the RBM structure.

7. The method of claim 1, further comprising:

obtaining a ground state wave function based on a plurality of optimal variation parameters of the Hamiltonian system; and is

Obtaining quantum characteristics of the Hamiltonian system based on the obtained ground state wave function.

8. An apparatus for obtaining a plurality of optimal variation parameters for a wave function of a Hamiltonian system, the apparatus comprising:

a memory storing instructions; and

a processor in communication with the memory, wherein the processor, when executing the instructions, is configured to cause the apparatus to:

initializing a plurality of variation parameters of a wave function of the Hamiltonian system,

sending the plurality of variation parameters to a quantum computing portion to start an iteration such that the quantum computing portion performs a plurality of measurements based on the plurality of variation parameters, the wave function, and the Hamiltonian system to output a plurality of measurement results,

transmitting the plurality of measurement results from the quantum computation portion to a classical computation portion such that the classical computation portion updates the plurality of variation parameters based on the plurality of measurement results and an update rule,

it is determined 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 variation parameters as the plurality of variation parameters to the quantum computation portion for a next iteration, and

in response to determining that the measured energy satisfies the convergence rule, setting the plurality of updated variation parameters to obtain a plurality of optimal variation parameters for the Hamiltonian system.

9. The apparatus of claim 8, wherein when the processor is configured to cause the apparatus to initialize the plurality of variation parameters, the processor is configured to further cause the apparatus to:

the plurality of variation parameters are initialized randomly.

10. The apparatus of claim 8, wherein:

the Hamiltonian system includes a Hamiltonian H and a ground state wave function ψ (τ) that satisfy an imaginary Schrodinger equationWhere τ ═ i × t, i is an imaginary unit, t is time, and E_τIs the ground state energy.

11. The apparatus of claim 10, wherein:

the ground state wave function ψ (τ) comprises an approximately parameterized wave functionWhereinIs a set of quantum operations that can be implemented in quantum circuits,comprises a plurality of variation parameters; and is

The plurality of measurements includes a plurality of gradientsWherein, theta_nIs one of the plurality of variation parameters.

12. The apparatus of claim 11, wherein:

the update rule comprisesWhere δ τ is the time step and A is the time step having matrix elementsA matrix of^-1Is the inverse of A, C is a vector of elementsA vector of (a) and

13. the apparatus of claim 8, wherein:

the wave function includes a Boltzmann machine (RBM) wave function having a RBM structure, the RBM wave function satisfyingWhereinIs to project the hidden spin in the RBM structure to | +>Projection operator on state, N is a normalization factor, the | +>States include|0>Can represent a hidden spin in the RBM structure, |1>Can represent the visible spin in the RBM structure and | +in the RBM wave function>The number of states is the number of hidden and visible spins in the RBM structure.

14. The apparatus of claim 8, wherein the instructions, when executed by the processor, are configured to further cause the apparatus to:

obtaining a ground state wave function based on a plurality of optimal variation parameters of the Hamiltonian system; and is

Obtaining quantum characteristics of the Hamiltonian system based on the obtained ground state wave function.

15. A non-transitory computer-readable storage medium storing instructions that, when executed by a processor, cause the processor to:

initializing a plurality of variation parameters of a wave function of a Hamiltonian system;

sending the plurality of variation parameters to a quantum computing portion to start an iteration such that the quantum computing portion performs a plurality of measurements based on the plurality of variation 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 portion to a classical computing portion such that the classical computing portion updates the plurality of variation parameters based on the plurality of measurement results and an update rule;

determining 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 computation portion for a next iteration; and is

In response to determining that the measured energy satisfies the convergence rule, setting the plurality of updated variation parameters to obtain a plurality of optimal variation parameters for the Hamiltonian system.

16. The non-transitory computer readable storage medium of claim 15, wherein when the instructions cause the processor to initialize the plurality of variation parameters, the instructions cause the processor to:

the plurality of variation parameters are initialized randomly.

17. The non-transitory computer-readable storage medium of claim 15, wherein:

the Hamiltonian system includes a Hamiltonian H and a ground state wave function ψ (τ) that satisfy an imaginary Schrodinger equationWhere τ ═ i × t, i is an imaginary unit, t is time, and E_τIs the ground state energy.

18. The non-transitory computer-readable storage medium of claim 17, wherein:

the ground state wave function Ψ (τ) includes an approximation parameterWave function of chemicalWhereinIs a set of quantum operations that can be implemented in quantum circuits,comprises a plurality of variation parameters; and is

The plurality of measurements includes a plurality of gradientsWherein, theta_nIs one of the plurality of variation parameters.

19. The non-transitory computer-readable storage medium of claim 18, wherein:

the update rule comprisesWhere δ τ is the time step and A is the time step having the matrix elementsA matrix of^-1Is the inverse of A, C is a vector of elementsA vector of (a) and

20. the non-transitory computer-readable storage medium of claim 15, wherein:

the wave function includes a Boltzmann machine (RBM) wave function having a RBM structure, the RBM waveFunction satisfactionWherein the content of the first and second substances,is to project the hidden spin in the RBM structure to | +>Projection operator on state, N is a normalization factor, said | +>States include|0>Can represent hidden spins, |1, in the RBM structure>Can represent the visible spin in the RBM structure and | +in the RBM wave function>The number of states is the number of hidden and visible spins in the RBM structure.

Technical Field

The present disclosure relates to simulation of quantum systems, and more particularly, to a variation parameter optimization method, apparatus, and storage medium for simulating a quantum system.

Background of the disclosure

The simulation of quantum systems is used in a variety of different fields. However, as the size of the quantum system increases, it can be difficult to simulate a complex quantum system with a classical computer due to the exponential scaling of the resources required by the classical computer.

The present disclosure describes a variational parameter optimization method, apparatus, and storage medium for modeling quantum systems that addresses at least one of the above disadvantages.

Disclosure of Invention

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

According to one aspect, embodiments of the present disclosure provide a method for obtaining a plurality of optimal variation parameters of a wave function of a hamiltonian system. The method includes initializing, by an apparatus including a quantum computing portion and a classical computing portion in communication with the quantum computing portion, a plurality of variation parameters of a wave function of a Hamiltonian system. The method includes sending, by the device, a plurality of variation parameters to a quantum computing portion to start an iteration such that the quantum computing portion performs a plurality of measurements based on the plurality of variation parameters, a wave function, and a Hamiltonian system to output a plurality of measurement results. The method includes transmitting, by the device, the plurality of measurements from the quantum computing portion to the classical computing portion, such that the classical computing portion updates the plurality of variation parameters based on the plurality of measurements and an update rule. The method includes determining, by the device, whether the measured energy satisfies a convergence rule. The method includes, in response to determining that the measured energy does not satisfy the convergence rule, sending a plurality of updated variation parameters as a plurality of variation parameters to the quantum computation portion for a next iteration. The method includes setting, by the device, a plurality of updated variation parameters to obtain a plurality of optimal variation parameters for the hamiltonian system in response to determining that the measured energy satisfies a convergence rule.

According to another aspect, embodiments of the present disclosure provide an apparatus for obtaining a plurality of optimal variation parameters of a wave function of a hamiltonian system. The apparatus includes a memory storing instructions and a processor in communication with the memory. When the processor executes the instructions, the processor is configured to cause the apparatus to initialize a plurality of variational parameters of a wave function of the Hamiltonian system. When the processor executes the instructions, the processor is configured to cause the apparatus to send the plurality of variation parameters to the quantum computing portion to start an iteration such that the quantum computing portion performs a plurality of measurements based on the plurality of variation parameters, the wave function, and the hamiltonian system to output a plurality of measurement results. When the processor executes the instructions, the processor is configured to cause the apparatus to transmit the plurality of measurement results from the quantum computation portion to the classical computation portion such that the classical computation portion updates the plurality of variation parameters based on the plurality of measurement results and the update rule. When the processor executes the instructions, the processor is configured to cause the apparatus to determine whether the measured energy satisfies a convergence rule. When the processor executes the instructions, the processor is configured to cause the apparatus to send the plurality of updated variation parameters as a plurality of variation parameters to the quantum computing portion for a next iteration in response to determining that the measured energy does not satisfy the convergence rule. When the processor executes the instructions, the processor is configured to cause the apparatus to set a plurality of updated variation parameters to obtain a plurality of optimal variation parameters for the hamiltonian system in response to determining that the measured energy satisfies the convergence rule.

In another aspect, embodiments of the present disclosure provide a non-transitory computer-readable storage medium storing instructions. The instructions, when executed by the processor, cause the processor to initialize a plurality of variational parameters of a wave function of a Hamiltonian system. When executed by the processor, the instructions cause the processor to send the plurality of variation parameters to the quantum computing portion to start an iteration such that the quantum computing portion performs a plurality of measurements based on the plurality of variation parameters, the wave function, and the Hamiltonian system to output a plurality of measurement results. When executed by the processor, the instructions cause the processor to transmit the plurality of measurements from the quantum computing portion to the classical computing portion such that the classical computing portion updates the plurality of variation parameters based on the plurality of measurements and the update rule. The instructions, when executed by the processor, cause the processor to determine whether the measured energy satisfies a convergence rule. When executed by the processor, the instructions cause the processor to send the plurality of updated variation parameters as a plurality of variation parameters to the quantum computing portion for a next iteration in response to determining that the measured energy does not satisfy the convergence rule. The instructions, when executed by the processor, cause the processor to set a plurality of updated variation parameters to obtain a plurality of optimal variation parameters for the hamiltonian system in response to determining that the measured energy satisfies a convergence rule.

Embodiments of the present disclosure provide methods, apparatuses, and non-transitory computer-readable storage media for obtaining a plurality of optimal variation parameters for a wave function of a hamiltonian system. It can be seen that in embodiments of the present disclosure, the disclosed combination of quantum virtual time evolution with a constrained boltzmann machine (RBM) hypothesis (ansatz) may overcome problems associated with other quantum phase estimates, for example, requiring quantum error correction that may not be readily available in near or medium term quantum computers. The disclosed method may not require the difficult high-dimensional noise classical optimization associated with other hybrid variational algorithms.

Drawings

Figure i is a flow chart of an embodiment disclosed in the present disclosure.

Fig. 2 is a schematic diagram of an embodiment of a restricted boltzmann machine structure disclosed in the present disclosure.

Fig. 3 is a schematic diagram of an embodiment of the apparatus disclosed in the present disclosure.

FIG. 4 shows a schematic diagram of a classical computer system.

Fig. 5 shows a schematic diagram of a quantum computer system.

FIG. 6 is a graph of an example of ground state energy of a hydrogen molecule simulated with the disclosed method.

Detailed Description

The present invention will now be described in detail hereinafter with reference to the accompanying drawings, which form a part hereof, and which show, by way of illustration, specific examples of embodiments. It is to be noted, however, that the present invention may be embodied in various different forms, and therefore, it is intended that the encompassed or claimed subject matter is to be construed as being limited to any one of the embodiments to be set forth below. It is also noted that the present invention may be embodied as a method, apparatus, component, or system. Accordingly, embodiments of the invention may take the form of, for example, hardware, software, firmware or any combination thereof.

Throughout the specification and claims, terms may have meanings suggested or implied above or below, with slight differences beyond the meanings explicitly set forth. The phrase "in one embodiment" or "in some embodiments" as used herein does not necessarily refer to the same embodiment, and the phrase "in another embodiment" or "in other embodiments" as used herein does not necessarily refer to a different embodiment. Likewise, the phrase "in one implementation" or "in some implementations" as used herein does not necessarily refer to the same implementation, and the phrase "in another implementation" or "in other implementations" as used herein does not necessarily refer to a different implementation. For example, it is intended that the claimed subject matter include all or a partial combination of the example embodiments/implementations.

In general, terms may be understood at least in part from the context of usage. For example, as used herein, terms such as "and," "or," or "and/or" may include various meanings that may depend at least in part on the context in which such terms are used. Generally, if "or" is used in association lists, such as A, B or C, then "or" is intended to mean A, B and C, used herein in an inclusive sense, and A, B or C, used herein in an exclusive sense. In addition, the terms "one or more" or "at least one," as used herein, may be used to describe any feature, structure, or characteristic in a singular sense or may be used to describe a combination of features, structures, or characteristics in a plural sense, depending at least in part on the context. Similarly, terms such as "a," "an," or "the" may likewise be understood to convey a singular use or to convey a plural use, depending, at least in part, on the context. Moreover, the term "based on" or "determined by … …" may be understood as not necessarily intended to convey an exclusive set of factors, and may instead allow for the presence of additional factors not necessarily explicitly described, again depending at least in part on the context.

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

Finding the ground state of the quantum system may involve solving for the eigenstates of a giant matrix having the lowest eigenvalues, such as a matrix based on the Hamiltonian of the quantum system. Quantum phase estimation and quantum classical hybrid variational algorithms, such as a variational quantum eigensolver, can be used to find the ground state of a quantum system.

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 may produce nearly accurate eigenstates, but may appear impractical without error correction. For another example, while somewhat robust to errors and noise, for the fixed-fit (Ansatz), the variational algorithm may be limited in accuracy and may involve difficult classical optimization of high-dimensional noise.

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 with a device including at least one of a classical computation part and a quantum computation part. The wave function of a quantum system may include a plurality of variation parameters. When a plurality of variation parameters are optimized, a wave function of a quantum system can be obtained.

The quantum computing portion may include a quantum processor that may include a quantum computing system such as, but not limited to, superconducting circuits, trapped ions, optical lattices, quantum dots, and linear optics. A quantum processor may include a plurality of qubits and associated local bias devices, e.g., two or more qubits. Quantum processors may also employ coupling devices (i.e., "couplers") that provide communicative coupling between qubits.

The present disclosure may be applied to any suitable quantum computing architecture having quantum processors, and may not be dependent on the underlying architecture of the quantum processors. The quantum processor may be any suitable quantum computing architecture that can perform general-purpose quantum computing. Examples of quantum computing architectures may include superconducting qubits, ion traps, and optical quantum computers. A classical simulation of a quantum processor is the Central Processing Unit (CPU).

If the wave function of the obtained quantum system is a ground state wave function, the ground state energy can be calculated with 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.

The present disclosure describes a method of obtaining a wave function of a quantum system by combining quantum virtual time evolution and a constrained boltzmann machine (RBM). The quantum virtual time evolution method may be a powerful method for material simulation in quantum computers, and the selection of the wave function ansatz of the quantum virtual time evolution method may limit its application potential. The constrained boltzmann machine is a neural network and can be a powerful wave function ansatz in classical quantum monte carlo simulations.

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 virtual time evolution with a constrained boltzmann machine. The algorithm may be a hybrid algorithm that performs computations using a device that includes a classical computation portion and a quantum computation portion. The mixed quantum classical approach can be used to simulate complex physical systems using noisy, mesoscale quantum computers with shallow circuits.

Fig. 1 shows a flow diagram of a method 100 for obtaining a plurality of optimal variation parameters of a wave function ansatz of a quantum system with a hamilton quantity. The method 100 may include the step 110: initializing, by an apparatus comprising a quantum computing portion and a classical computing portion in communication with the quantum computing portion, a plurality of variation parameters of a wave function of a Hamiltonian system; step 120: transmitting, by the device, the plurality of variation parameters to the quantum computing portion such that the quantum computing portion performs a plurality of measurements based on the plurality of variation parameters, the wave function, and the Hamiltonian system to output a plurality of measurement results; step 130: transmitting, by the device, the plurality of measurement results from the quantum computing portion to the classical computing portion, such that the classical computing portion updates the plurality of variation parameters based on the plurality of measurement results and the update rule; step 140: determining, by the appliance, whether the measured energy satisfies a convergence rule; step 150: in response to determining that the measured energy does not satisfy the convergence rule, sending the plurality of updated variation parameters as a plurality of variation parameters to the quantum computing portion for a next round; and step 160: in response to determining that the measured energy satisfies the convergence rule, a plurality of updated variation parameters are set by the device to obtain a plurality of optimal variation parameters for the Hamiltonian system.

Referring to fig. 1, step 110 can include initializing a plurality of variation parameters of a wave function of a hamiltonian system via an apparatus including a quantum computing portion and a classical computing portion in communication with the quantum computing portion.

A quantum system may have a system Hamiltonian (Hamiltonian) H and a ground-state wave function Ψ, and an imaginary time may be applied, i.e., τ i t, where i is an imaginary unit and t is time. Under the evolution of the virtual time, the time-domain,the ground state wave function can be passed through the virtual time Schrodinger equationLong time constraints of. The ground state energy can be passed through E_τ＝<Ψ(τ)|H|Ψ(τ)>To obtain the final product. Due to non-unitary decomposition, it may be difficult to directly implement the above virtual time schrodinger equation in a quantum computer.

In one embodiment, a hybrid variational algorithm may be used. The wave function of a quantum system can be determined by parameterizing the test wave function:to approximate, whereinIs a set of quantum operations that can be implemented in quantum circuits, these operations being defined by parametersAnd (5) controlling.A plurality of variation parameters may be included. Thus, the capability of virtual time evolution (power) can be exploited by parameterization of the wave function.

In one implementation, equations of motion for the variational parametersCan satisfyWherein A is a matrix having matrix elementsAnd C is a matrix with vector elementsWherein "Re" represents the real of a complex numberAnd (4) a section.

Gradient of gradientCan be obtained by analysis. 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_mnAnd C_n. In one implementation, the gradient may be analytically obtained by a conventional paper and pen method. In another implementation, the gradient may be obtained analytically by computation of a classical computer.

Thus, the variation parameter at the next imaginary time τ + δ τ may be updated to be the variation parameter at the next imaginary time τ + δ τ based on the variation parameter at the imaginary time τWhere δ τ may be a step of the imaginary time, i.e. a time step.

In one implementation, a limited boltzmann machine (RBM) wave function ansatz may be used for quantum virtual time evolution.

Referring to fig. 2, an example of an 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 one or more hidden spins 220 can be any non-zero integer, such as 2, 3, 10, 100, or 10000. The number of one or more visible spins 230 can be any non-zero integer, such as 2, 3, 10, 100, or 10000.

Referring to fig. 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 be no connection between one of the hidden spins and the other; and there may not be a connection between one of the visible spins and the other.

In one implementation using an RBM structure, the RBM wave function may be of a form includingWhereinMay be to project all hidden spins to | +>Projection operator on a state, and N may be a normalization factor (normalization factor). For example, | +>The state may includeWherein, |0>Hidden spins can be represented, and |1) can represent visible spins. | +in RBM wave function>The number of states can be the total number of hidden and visible spins in the RBM structure.

RBM Hamilton quantity ofGiven, where v and h are Pauli-Z matrices representing visible and hidden spins, respectively.

In the context of the RBM wave function ansazt, the variation parameter θ_nMay be a coefficient in the RBM hamiltonian (i.e., b)_i、m_jAnd W_ij). During quantum virtual time evolution, the variation parameter b can be updated_i、m_jAnd W_ij。

In one implementation, initial values of a plurality of variation parameters of a wave function for a quantum system having a Hamiltonian amount may be randomly assigned. In another implementation, initial values of a plurality of variation parameters of a wave function for a quantum system having a Hamiltonian amount may be assigned based on previous experience and/or results from similar quantum systems.

Fig. 3 shows an embodiment of a device 320 comprising a quantum computing part 330 and a classical computing part 350. The device 320 may include a memory to store instructions and a processor in communication with the memory. The processor may be configured to execute instructions stored in the memory. When the processor executes the instructions, the processor may be configured to cause the device to perform the method 100.

Quantum computation portion 330 may include quantum processor 332 and classical computation portion 350 may include 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. Quantum processor 332 and/or 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 optics. In one implementation, classical calculation portion 350 may include classical memory 354. Input data 310 representing the physical system may be input into the device 320 and, after the simulation/optimization, output data 370 including optimal variational parameters representing a wave function of the physical system may be output from the device 320.

Referring to FIG. 4, in one implementation, the classic computer portion can be part of classic computer system 400. Classic computer system 400 may include a communication interface 402, system circuitry 404, input/output (I/O) interface 406, quantum classic interface 407, storage 409, and display circuitry 408 that 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 GUIs, touch-sensitive displays, voice or facial recognition inputs, buttons, switches, speakers, and other user interface elements.

The machine interface 410 and the I/O interface 406 may also include a communication interface with the PSG, the PSA, the first detector, and/or the second detector. The communication between computer system 400 and the PSG, PSA, first detector, and/or second detector may include wired communication or wireless communication. Communications may include, but are not limited to, serial communications, parallel communications; ethernet communications, USB communications, and General Purpose Interface Bus (GPIB) communications.

Additional examples of I/O interfaces 406 include a microphone, video and still image cameras, headphones, and a microphone input/output jack, a Universal Serial Bus (USB) connector, a memory card slot, and other types of inputs. The I/O interface 406 may also include a magnetic or optical media interface (e.g., CDROM or DVD drive), serial and parallel bus interfaces, and a keyboard and mouse interface. A quantum classic interface may include an interface to communicate with a quantum computer.

The communication interface 402 may include a wireless transmitter and receiver ("transceiver") 412 and any antenna 414 used by the transmit and receive circuitry of the transceiver 412. The transceiver 412 and antenna 414 may support Wi-Fi network communications, for example, under any version of IEEE 802.11, such as 802.11n or 802.1 lac. 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 any type of ethernet, Data Over Cable Service Interface Specification (DOCSIS), Digital Subscriber Line (DSL), Synchronous Optical Network (SONET), or other protocol. In another implementation, the communication interface 402 may also include a communication interface with the PSG, the PSA, the first detector, and/or the second detector.

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

The system circuitry 404 may include hardware, software, firmware, or other circuitry in any combination. The system circuitry 404 may be implemented, for example, with one or more systems on a chip (SoC), Application Specific Integrated Circuits (ASICs), microprocessors, discrete analog and digital circuits, and other circuitry.

For example, system circuitry 404 may include one or more instruction processors 421 and memory 422. Memory 422 stores, for example, control instructions 426 and an operating system 424. Control instructions 426 may include, for example, instructions for generating a patterned mask (mask) or for controlling a PSA. In one implementation, instruction processor 421 executes control instructions 426 and operating system 424 to perform any desired functions with respect to the controller.

Referring to fig. 5, in one implementation, the quantum computer portion may be part of a quantum computer system 500. Quantum computer system 500 may include a quantum classical interface 510, a readout device 520, an initialization device 530, a quantum bit controller 540, and a coupling controller 550. Quantum classical interface 510 may provide an interface for communicating with a classical computer. The initialization apparatus 530 may initialize the quantum computer system 500.

Quantum computer system 500 may include a form of quantum processor that includes qubits including qubit 1580 a, qubits 2580 b, … …, and qubit N580 c. A plurality of qubits may form an interconnected topology. Quantum computer system 500 may include a plurality of coupling devices including coupling 1590 a, couplings 2590 b, … …, and coupling M590 c.

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

Referring to fig. 1, step 120 may include transmitting, by the device, the plurality of variation parameters to the quantum computing portion, such that the quantum computing portion performs a plurality of measurements based on the plurality of variation parameters, the wave function, and the hamiltonian system to output a plurality of measurement results.

The initialized variation parameters are transmitted to the quantum computation portion 330 of fig. 3. In one implementation, the information of the initialized variation parameters may be transmitted to the quantum computing section via a series of quantum gates. For example, in the case of superconducting qubits, information of the initialized variation parameters can be transmitted via a microwave pulse sequence, wherein the details of these quantum gates, such as pulse amplitude and/or phase, can depend on the variation parameters.

The quantum computing portion may be configured to compute the state of the qubit via a measurement of the state of the qubit in the quantum computing portionThe quantity to perform a plurality of measurements. The quantum computing portion 330 may measure a series of measurements, which may include energies corresponding to wave functions including variation parameters. The energy may be based on E_τ＝<Ψ(τ)|H|Ψ(τ)>And (4) measuring.

In one implementation, the series of measurements made by the quantum computing portion may include a series of measurements based on a quantum computationAndof the matrix elements of (a).

Referring to fig. 1, step 130 may include transmitting, by the device, the plurality of measurements from the quantum computing portion to the classical computing portion, such that the classical computing portion updates the plurality of variation parameters based on the plurality of measurements and the update rule.

The quantum computing portion may transmit the plurality of measurements to the classical computing portion, as indicated by arrow 362 of fig. 3. The classical calculation part may spend a time step and update the plurality of variation parameters based on the time step, the plurality of measurement results, and the update rule. In one implementation, the update rules may includeWherein A is a matrix element having a value measured by a quantum computing sectionA matrix of^-1Is an inverse matrix of A, and C is a vector element having a vector measured by a quantum computing sectionThe vector of (2).

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.

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.

Referring to fig. 1, step 140 may include determining, by the appliance, whether the measured energy satisfies a convergence rule.

In one implementation, the classical calculation portion may calculate a 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 lxl0^-4、1x10^-6Or 1x10^-9。

In another implementation, the convergence rule may include determining whether a ratio of the difference to the corresponding measured energy is less than a predetermined threshold. For example, for one measured energy (E + dE) in the current iteration and the measured energy (E) in the previous iteration, the difference is dE, and thus the ratio of the difference and the corresponding measured energy is equal to dE/E. For example, the predetermined threshold may be 1x10^-4、5x10^-6Or 2x10^-9。

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

Referring to fig. 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 a plurality of variational parameters to the quantum computation portion for a next iteration.

When the measured energy does not satisfy the convergence rule, the classical calculation section may set a plurality of updated variation parameters as a plurality of variation parameters; and step 120 may be repeated as the next iteration. Accordingly, as indicated by an arrow 364 of fig. 3, a plurality of variation parameters are transmitted to the quantum computing section, and the quantum computing section performs a plurality of measurements to output a plurality of measurement results.

Referring to fig. 1, step 160 may include: in response to determining that the measured energy satisfies the convergence rule, a plurality of updated variation parameters are set by the device to obtain a plurality of optimal variation parameters for the Hamiltonian system.

When the measured energy satisfies the convergence rule, the classical calculation section may set a plurality of updated variation parameters as a plurality of optimal variation parameters of the hamiltonian system.

Optionally, the device 320 of fig. 3 may also output the measured energy of the final iteration as the ground state energy of the hamiltonian system.

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 has not reached the predetermined iteration threshold, sending the plurality of updated variation parameters as a plurality of variation parameters to the quantum computation portion for a next iteration. Step 160 may include: in response to determining that the number of iterations reaches a predetermined iteration threshold, a plurality of updated variation parameters are set by the device to obtain a plurality of optimal variation parameters for the Hamiltonian system.

example-Hydrogen molecule

The hydrogen molecule may include two hydrogen atoms. The Hamiltonian of a hydrogen molecule can be represented by a two-qubit Hamiltonian H (R) ═ g₀(R)+g₁(R)σ_z1+g₂(R)σ_z2+g₃(R)σ_z1σ_z2+g₄(R)σ_y1σ_y2+g₅(R)σ_x1σ_x2Wherein R is the distance between two hydrogen atoms (i.e., the bond length), and g_iIs a coefficient dependent on R.

An RBM structure comprising 2 visible spins and 2 hidden spins can be used to mimic a hydrogen molecule. The corresponding RBM Hamilton amount may be

The RBM wave function may beWhereinMay be to project two hidden spins to | +>And (5) projection operators on the states. The normalization constant N may be

The gradient can be calculated analytically. At b_i、m_jAnd W_ijIn the case of real numbers, the gradient may be:

wherein the content of the first and second substances,and isIn this example of a quantum system with hydrogen molecules, the coefficients may be real numbers.

Once these gradients are known, the matrix elementsSum vector elementIt may be possible to perform the computation by measuring various operators in the quantum computation portion (e.g.,<v_i>，<h_i>，<v_ih_j>，…) is obtained.

Once all matrix elements in A and C are found from the measurements, for example by the quantum computing part, the classical computing part can be based onVarious variational parameters are updated.

For any given distance between two hydrogen atoms (i.e., bond length), the ground state energy can be calculated from RBM ansatz using a total number of iterations with step size δ τ of 0.01 and 1000.

Fig. 6 shows a graph 600 of the ground state energy of hydrogen molecules as a function of bond length. The ground state energy may be plotted along a y-axis 630 and the bond length may be plotted along an x-axis 640.

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

The present disclosure provides methods, apparatuses, and non-transitory computer-readable storage media for obtaining a plurality of optimal variation parameters for a wave function of a hamiltonian system. The present disclosure describes a combination of quantum virtual time evolution and a constrained boltzmann machine (RBM) ansatz that may overcome problems associated with other quantum phase estimates, e.g., requiring quantum error correction that may not be readily available in near or medium term quantum computers. The disclosed method may not require the difficult high-dimensional noise classical optimization associated with other hybrid variational algorithms.

While certain inventions have been described with reference to illustrative embodiments, this description is not meant to be limiting. Various modifications of the illustrative embodiments, as well as additional embodiments of the invention, will be apparent to persons skilled in the art upon reference to this description. Those skilled in the art will readily recognize these and various other modifications that may be made to the exemplary embodiments shown and described herein without departing from the spirit and scope of the present invention. It is therefore contemplated that the appended claims will cover any such modifications and alternative embodiments. Some proportions may be exaggerated in the drawings, while other proportions may be minimized. The present disclosure and the figures are accordingly to be regarded as illustrative rather than restrictive.