CN114512193A

CN114512193A - Method for preparing system test state based on spin symmetry and equivalent particle characteristics

Info

Publication number: CN114512193A
Application number: CN202210099643.0A
Authority: CN
Inventors: 李叶; 窦猛汉
Original assignee: Origin Quantum Computing Technology Co Ltd
Current assignee: Origin Quantum Computing Technology Co Ltd
Priority date: 2022-01-27
Filing date: 2022-01-27
Publication date: 2022-05-17
Anticipated expiration: 2042-01-27
Also published as: CN114512193B

Abstract

The application provides a method, a device, electronic equipment and a medium for preparing a system test state based on spin symmetry and equivalent particle characteristics, wherein the method for preparing the system test state based on spin symmetry and equivalent particle characteristics comprises the following steps: determining a system and the number of orbits and electrons of the system; determining the number of excitation terms included by a Fermi-form cluster operator of the system and coefficients corresponding to the excitation terms according to the number of orbitals and the number of electrons of the system based on spin symmetry and equivalent particle characteristics; calculating a fermi form cluster operator of the system according to the number of the excitation terms and coefficients corresponding to the excitation terms; solving the trial state of the system based on the fermi form of the system's cluster operator. The method belongs to the field of quantum computing, solves the technical problem that complex molecules are difficult to simulate in the prior art, saves computing resources, and improves the simulation efficiency of the complex molecules.

Description

Method for preparing system test state based on spin symmetry and equivalent particle characteristics

Technical Field

The application belongs to the field of quantum computing, and particularly relates to a method and a device for preparing a system test state based on spin symmetry and equivalent particle characteristics, electronic equipment and a medium.

Background

Quantum computers are physical devices that perform high-speed mathematical and logical operations, store and process quantum information in compliance with the laws of quantum mechanics. When a device processes and calculates quantum information and runs quantum algorithms, the device is a quantum computer. Quantum computers have the ability to handle mathematical problems more efficiently than ordinary computers. It will be appreciated that the key properties of a chemical or material depend on the electronic properties of the chemical or material, so it is critical to accurately mimic the electronic properties of the chemical or material.

For a long time, theoretical explanations of the energy and properties of molecules and materials at the atomic level have been considered as one of the most direct applications of quantum computing, which has received much attention as a new computational paradigm. In recent years, an algorithm for acquiring molecular energy by using a quantum computer has been the focus of attention, but due to the limits of quantum bit number and coherence time, the simulation of a complex molecular system still has difficulty.

Disclosure of Invention

The application aims to provide a method, a device, electronic equipment and a medium for preparing a system test state based on spin symmetry and equivalent particle characteristics, so as to solve the technical problem that complex molecules are difficult to simulate in the prior art, save computing resources and improve the simulation efficiency of the complex molecules.

In a first aspect, the present application provides a method for preparing a system test state based on spin symmetry and equivalent particle characteristics, comprising:

determining a system and the number of orbits and electrons of the system;

determining the number of excitation terms included by a Fermi-form cluster operator of the system and coefficients corresponding to the excitation terms according to the number of orbitals and the number of electrons of the system based on spin symmetry and equivalent particle characteristics;

calculating a fermi form cluster operator of the system according to the number of the excitation terms and coefficients corresponding to the excitation terms;

solving the trial state of the system based on the fermi form of the system's cluster operator.

Optionally, the determining, based on spin symmetry and equivalent particle characteristics, the number of excitation terms included in the fermi form of the system and coefficients corresponding to the excitation terms according to the number of orbitals and the number of electrons of the system includes:

acquiring a Hartree-Fock state of the system according to the number of the tracks and the number of the electrons of the system;

and determining the number of excitation terms included by the fermi-form cluster operator of the system and coefficients corresponding to the excitation terms according to a preselected set mode and based on spin symmetry, equivalent particle characteristics and the Hartree-Fock state of the system.

Optionally, the determining, according to a preselected proposed mode, the number of excitation terms included in the fermi form of the system based on spin symmetry, equivalent particle characteristics, and a Hartree-Fock state of the system includes:

when the proposed mode is a single excitation coupling cluster, confirming that the Fermi-form cluster operator of the system only comprises a single excitation item number;

determining the number of the single excitation terms as excitation terms corresponding to other orbits with the same spin direction from the orbit of the original spin direction to the excitation terms corresponding to the orbits with the same spin direction of each electron in the system based on spin symmetry and Hartree-Fock state;

and combining the cluster operators corresponding to the two single excitation terms with the same excitation probability in the determined number of the single excitation terms based on the equivalent particle characteristics, wherein the coefficient of the combined single excitation term is twice that of the single excitation term before combination.

when the preselected simulation mode is a single-double excitation coupling cluster, confirming that the Fermi-form cluster operator of the system only comprises a single excitation number and a double excitation number;

determining the number of the single excitation terms as excitation terms corresponding to other orbits with the same spin direction from the orbit of the original spin direction to the excitation terms corresponding to the orbits with the same spin direction of each electron in the system based on spin symmetry and Hartree-Fock state; determining the number of the double excitation terms as an excitation term of each two electrons in the system which are excited from the original spin direction orbit to the other two orbits with the corresponding spin directions consistent together;

based on the characteristics of equivalent particles, combining cluster operators corresponding to two single excitation terms with the same excitation probability in the determined number of the single excitation terms, wherein the coefficient of the combined single excitation term is twice that of the single excitation term before combination; and combining the cluster operators corresponding to the two double excitation terms with the same excitation probability in the determined number of the double excitation terms, wherein the coefficient of the combined double excitation terms is twice of the coefficient of the double excitation terms before combination.

Optionally, the solving the experimental state of the system based on the fermi form cluster operator of the system includes:

transforming the Fermi operator form cluster operator of the system into a Paglie operator form cluster operator according to a preselected mapping mode;

decomposing the cluster operator in the form of the Pagli operator into a corresponding unitary operator form and carrying out evolution to obtain an evolved quantum state; wherein the evolved quantum state is a test state of the system.

Optionally, decomposing the cluster operator in the form of the bubble operator into a corresponding unitary operator and performing evolution to obtain an evolved quantum state includes:

constructing a quantum simulation line based on the unitary operator corresponding to the decomposed cluster operator in the form of the Pally operator;

and carrying out analog evolution according to the quantum analog circuit to obtain an evolved quantum state.

Optionally, the mapping manner is one of Jordan-Wigner transformation, Parity transformation, Bravyi-Kitaev transformation, and SegmentParity transformation.

In a second aspect, the present application also provides an apparatus for preparing a system test state based on spin symmetry and equivalent particle characteristics, comprising:

the system comprises a first determining module, a second determining module and a control module, wherein the first determining module is used for determining a system and the track number and the electron number of the system;

the second determination module is used for determining the number of excitation terms and coefficients corresponding to the excitation terms included by the Fermi-form cluster operators of the system according to the orbit number and the electron number of the system based on the spin symmetry and the equivalent particle characteristics;

the calculation module is used for calculating the Fermi form cluster operator of the system according to the number of the excitation terms and the coefficients corresponding to the excitation terms;

and the solving module is used for determining the cluster operator based on the Fermi form of the system and solving the experimental state of the system.

Optionally, the second determining module includes:

the acquisition unit is used for acquiring the Hartree-Fock state of the system according to the number of the tracks and the number of the electrons of the system;

and the determining unit is used for determining the number of excitation terms included by the fermi form cluster operator of the system and coefficients corresponding to the excitation terms according to a pre-selected proposed mode and based on spin symmetry, equivalent particle characteristics and the Hartree-Fock state of the system.

Optionally, the determining unit is further configured to: when the proposed mode is a single excitation coupling cluster, determining that the Fermi form cluster operator of the system only comprises a single excitation item number; determining the number of the single excitation terms as excitation terms corresponding to other orbits with the same spin direction from the orbit of the original spin direction to the excitation terms corresponding to the orbits with the same spin direction of each electron in the system based on spin symmetry and Hartree-Fock state; and combining the cluster operators corresponding to the two single excitation terms with the same excitation probability in the determined number of the single excitation terms based on the equivalent particle characteristics, wherein the coefficient of the combined single excitation term is twice that of the single excitation term before combination.

Optionally, the determining unit is further configured to: when the preselected simulation mode is a single-double excitation coupling cluster, determining that the Fermi-form cluster operator of the system only comprises a single excitation number and a double excitation number; determining the number of the single excitation terms as excitation terms corresponding to other orbits with the same spin direction from the orbit of the original spin direction to the excitation terms corresponding to the orbits with the same spin direction of each electron in the system based on spin symmetry and Hartree-Fock state; determining the number of the double excitation terms as an excitation term of each two electrons in the system which are excited from the original spin direction orbit to the other two orbits with the corresponding spin directions consistent together; based on the characteristics of equivalent particles, combining cluster operators corresponding to two single excitation terms with the same excitation probability in the determined number of the single excitation terms, wherein the coefficient of the combined single excitation term is twice that of the single excitation term before combination; and combining the cluster operators corresponding to the two double excitation terms with the same excitation probability in the determined number of the double excitation terms, wherein the coefficient of the combined double excitation terms is twice of the coefficient of the double excitation terms before combination.

Optionally, the second determining module further includes:

a transformation unit for transforming the Fermi operator form of the system into a Paglie operator form of cluster operators according to a preselected mapping manner;

the evolution unit is used for decomposing the cluster operator in the form of the Pagli operator into a corresponding unitary operator form and carrying out evolution so as to obtain an evolved quantum state; wherein the evolved quantum state is a test state of the system.

Optionally, the evolution unit is further configured to: constructing a quantum simulation line based on the unitary operator corresponding to the decomposed cluster operator in the form of the Pally operator; and carrying out analog evolution according to the quantum analog circuit to obtain an evolved quantum state.

In a third aspect, the present application further provides an electronic device, including:

a processor;

a memory for storing processor-executable instructions;

wherein the processor implements the method of any of the first aspect above by executing the executable instructions.

In a fourth aspect, the present application also provides a computer storage medium having stored thereon computer instructions which, when executed by a processor, implement the steps of the method of any of the first aspects described above.

In the process of preparing the system test state, when the Fermi form cluster operator of the system is calculated, due to the fact that the spin symmetry and the equivalent particle characteristics are considered, the number of excitation terms needing to be calculated in the Fermi form cluster operator is smaller than that when the spin symmetry is not considered in the prior art, complexity of the system is reduced, further when the test state of the system is solved, the calculation amount is reduced, the technical problem that complex molecules are difficult to simulate in the prior art is solved, calculation resources are saved, calculation of subsequent system energy is facilitated, and simulation efficiency of the complex molecules is improved.

Drawings

FIG. 1 is a block diagram of a hardware configuration of a computer terminal for a method for preparing a trial state of a system based on spin symmetry and equivalent particle characterization according to an exemplary embodiment of the present application;

FIG. 2 is a schematic flow chart diagram of a method for preparing a system test state based on spin symmetry and equivalent particle characteristics as provided in an exemplary embodiment of the present application;

fig. 3 is a schematic diagram of a quantum wire structure corresponding to an exemplary embodiment of the present application;

FIG. 4 is a schematic illustration of a hydrogen molecular orbital provided by an exemplary embodiment of the present application;

FIG. 5 is a drawing illustrating an exemplary embodiment of the present application, H₁Corresponding quantum wire schematic;

FIG. 6 is a drawing illustrating an exemplary embodiment of the present application providing H₁And H₂Corresponding quantum wire schematic;

FIG. 7 is a drawing illustrating an exemplary embodiment of the present application providing H₁、H₂And H₃Corresponding quantum wire schematic;

FIG. 8 is a drawing illustrating an exemplary embodiment of the present application providing H₁、H₂、H₃And H₄Corresponding quantum wire schematic;

FIG. 9 is a drawing illustrating an exemplary embodiment of the present application providing H₁、H₂、H₃、H₄And H₅A corresponding quantum wire schematic;

FIG. 10 is a schematic diagram of an apparatus for preparing a system test state based on spin symmetry and equivalent particle characteristics according to an exemplary embodiment of the present application.

Detailed Description

This will be described in detail below by way of example as it would run on a computer terminal. Fig. 1 is a block diagram of a hardware structure of a computer terminal of a method for preparing a system test state based on spin symmetry and equivalent particle characteristics according to an exemplary embodiment of the present application. As shown in fig. 1, the computer terminal may include one or more (only one shown in fig. 1) processors 102 (the processor 102 may include, but is not limited to, a processing device such as a microprocessor MCU or a programmable logic device FPGA) and a memory 104 for storing data, and optionally, a transmission device 106 for communication functions and an input-output device 108. It will be understood by those skilled in the art that the structure shown in fig. 1 is only an illustration and is not intended to limit the structure of the computer terminal. For example, the computer terminal may also include more or fewer components than shown in FIG. 1, or have a different configuration than shown in FIG. 1.

The memory 104 may be used to store software programs and modules of application software, such as program instructions/modules corresponding to experimental states of the preparation system based on spin symmetry and equivalent particle characteristics in the embodiments of the present application, and the processor 102 executes various functional applications and data processing by executing the software programs and modules stored in the memory 104, so as to implement the method described above. The memory 104 may include high speed random access memory, and may also include non-volatile memory, such as one or more magnetic storage devices, flash memory, or other non-volatile solid-state memory. In some examples, the memory 104 may further include memory located remotely from the processor 102, which may be connected to a computer terminal over a network. Examples of such networks include, but are not limited to, the internet, intranets, local area networks, mobile communication networks, and combinations thereof.

The transmission device 106 is used for receiving or transmitting data via a network. Specific examples of the network described above may include a wireless network provided by a communication provider of the computer terminal. In one example, the transmission device 106 includes a Network adapter (NIC) that can be connected to other Network devices through a base station to communicate with the internet. In one example, the transmission device 106 can be a Radio Frequency (RF) module, which is used to communicate with the internet in a wireless manner.

It should be noted that a true quantum computer is a hybrid structure, which includes two major components: one part is a classic computer which is responsible for executing classic calculation and control; the other part is quantum equipment which is responsible for running a quantum program to further realize quantum computation. The quantum program is a string of instruction sequences which can run on a quantum computer and are written by a quantum language such as a Qrun language, so that the support of the operation of the quantum logic gate is realized, and the quantum computation is finally realized. In particular, a quantum program is a sequence of instructions that operate quantum logic gates in a time sequence.

In practical applications, due to the limited development of quantum device hardware, quantum computation simulation is usually required to verify quantum algorithms, quantum applications, and the like. The quantum computing simulation is a process of realizing the simulation operation of a quantum program corresponding to a specific problem by means of a virtual architecture (namely a quantum virtual machine) built by resources of a common computer. In general, it is necessary to build quantum programs for a particular problem. The quantum program referred to in the embodiments of the present application is a program written in a classical language for characterizing a qubit and its evolution, where the qubit, a quantum logic gate, and the like related to quantum computation are all represented by corresponding classical codes.

A quantum circuit, which is an embodiment of a quantum program and also a weighing sub-logic circuit, is the most common general quantum computation model, and represents a circuit that operates on a quantum bit under an abstract concept, and the circuit includes the quantum bit, a circuit (timeline), and various quantum logic gates, and finally, a result is often read through a quantum measurement operation.

Unlike conventional circuits that are connected by metal lines to pass either voltage or current signals, in quantum circuits, the lines can be viewed as being connected by time, i.e., the state of a qubit evolves naturally over time, in the process being operated on as indicated by the hamiltonian until a logic gate is encountered.

A quantum program corresponds to an overall quantum circuit as a whole, and the quantum program refers to the overall quantum circuit, wherein the total number of quantum bits in the overall quantum circuit is the same as the total number of quantum bits of the quantum program. It can be understood that: a quantum program may consist of quantum wires, measurement operations for quantum bits in the quantum wires, registers to hold measurement results, and control flow nodes (jump instructions), and a quantum wire may contain tens to hundreds or even thousands of quantum logic gate operations. The execution process of the quantum program is a process executed for all the quantum logic gates according to a certain time sequence. It should be noted that timing is the time sequence in which the single quantum logic gate is executed.

It should be noted that in the classical calculation, the most basic unit is a bit, and the most basic control mode is a logic gate, and the purpose of the control circuit can be achieved through the combination of the logic gates. Similarly, the way qubits are handled is quantum logic gates. The quantum state can be evolved by using quantum logic gates, which are the basis for forming quantum circuits, including single-bit quantum logic gates, such as Hadamard gates (H gates, Hadamard gates), pauli-X gates (X gates), pauli-Y gates (Y gates), pauli-Z gates (Z gates), RX gates, RY gates, RZ gates, and the like; two-bit or multi-bit quantum logic gates such as CNOT gates, CR gates, CZ gates, iSWAP gates, Toffoli gates, and the like. Quantum logic gates are typically represented using unitary matrices, which are not only matrix-form but also an operation and transformation. The function of a general quantum logic gate on a quantum state is calculated by multiplying a unitary matrix by a matrix corresponding to a quantum state right vector.

Referring to fig. 2, fig. 2 is a schematic flow chart of a method for preparing a system test state based on spin symmetry and equivalent particle characteristics according to an embodiment of the present application, which may include the following steps:

and S21, determining the system and the number of orbitals and electrons of the system.

Wherein, the system is a chemical molecular model needing simulation. The chemical molecular model may be considered as a model of the molecular structure that the user wants to calculate the ground state energy, including, for example, the types of atoms, the number of atoms, the coordinates of the atoms, the charge and spin multiplicities, etc. that make up the chemical molecule.

The system can be determined by, but is not limited to, the user can input information of the chemical molecular model to be simulated on a computer terminal. For example, a user opens a quantum chemical simulation application software of a computer, and chemical molecular model options to be simulated, such as a hydrogen molecular model, an oxygen molecular model and the like, can be displayed on the quantum chemical simulation application interface. And (4) clicking the chemical molecular model option to be simulated by a user, and determining the chemical molecular model by quantum chemical simulation application. After the chemical molecular model is determined, the number of electrons and the number of electron orbits of the chemical molecular model can be determined.

After the system is determined, the number of orbits and the number of electrons of the system can be determined, and at this time, step S22 is executed.

And S22, determining the number of excitation terms included by the Fermi form cluster operator of the system according to the orbit number and the electron number of the system based on the spin symmetry and the equivalent particle characteristics.

Specifically, based on spin symmetry and equivalent particle characteristics, determining the number of excitation terms included in the fermi form of the system according to the number of orbitals and the number of electrons of the system, and determining coefficients corresponding to the excitation terms, may include the following steps:

s221, acquiring the Hartree-Fock state of the system according to the number of the tracks and the number of the electrons of the system.

For example, the Hartree-Fock state for a hydrogen molecule containing two electrons in four one-electron spin molecular orbitals is represented by quantum state |0011>, i.e., one qubit represents one spin molecular orbit, 0 represents an empty orbit, and 1 represents an occupied orbit. By applying a NOT gate to the corresponding bit, respectively, |0000> can be initialized to |0011> in the quantum wire. For any N-electron system containing M spin molecular orbitals, the corresponding Hartree-Fock states can be expressed in the same way.

S222, determining the number of excitation terms included by the fermi form cluster operator of the system and coefficients corresponding to the excitation terms based on spin symmetry, equivalent particle characteristics and Hartree-Fock state of the system according to a pre-selected proposed mode.

Exemplary, the proposed method includes: UCC (Unitary Coupled Cluster operator) and the like, and the UCC can be specifically divided into a single-excitation Coupled Cluster UCCs and a single-double-excitation Coupled Cluster UCCSD.

Correspondingly, for UCCS and UCCSD, the quantum wires are supposed to be the same, for example, as shown in fig. 3. Fig. 3 is a schematic diagram of a quantum circuit structure corresponding to a proposed method provided in an embodiment of the present application, where the quantum circuit shown in fig. 3 is a quantum circuit with 4 qubits q0, q1, q2, and q3, and X is a quantum circuit with four qubits q0, q1, q2, and q3_-π/2、X_π/2X gate and Y gate with-pi/2 and-pi/2 parameters respectively, indicating CNOT gate by icon ^ and solid line, Z_θRepresenting a Z gate with a parameter theta. The display simulation principle may include: the proposed formula may be, for example, a matrix operator U (θ) corresponding to a quantum line. For UCC, the corresponding approximate formula is as follows:

wherein the content of the first and second substances,

i.e. the pseudo-device, P_iFor generating a primitive, if the electron cluster operator T in UCC is T ═ T₁This is called to be UCCS; if the cluster operator T in UCC is T ═ T₁+T₂This is called the intended UCCSD, where T₁For single-particle excitation operators, T₂Is a two-particle excitation operator. More specifically, in practical applications, T can be understood as a fermi-form of a cluster operator. Its physical definition is as follows:

in the above-mentioned two formulas, the first and second groups,

and

in order to create the operator, the operator is provided with,

and

is an annihilation operator;

and

is a coefficient and generally refers to the amplitude of the corresponding operator.

When the proposed mode is a single excitation coupling cluster, the Fermi form cluster operator of the system only comprises a single excitation item number, and on the basis, the single excitation item number is determined to be an excitation item corresponding to the excitation of each electron in the system from the original spin direction orbit to other orbits with the consistent spin direction based on the spin symmetry and the Hartree-Fock state. The orbitals of the system include both spin-down and spin-up orbitals. That is, based on spin symmetry, if the electron is in the spin-up orbit, it is considered that the electron is excited to other spin-up orbitals. If the electron has the original spin-direction orbit that is the spin-down orbit, then only the electron is considered to be excited to the other spin-down orbit. On the basis, further, based on the equivalent particle characteristics, cluster operators corresponding to two single excitation terms with the same excitation probability in the determined number of single excitation terms are combined, and the coefficient of the combined single excitation term is twice that of the single excitation term before combination.

When the preselected proposed mode is a single-double excitation coupling cluster, the Fermi-form cluster operator of the system only comprises a single excitation item number and a double excitation item number, and on the basis, the single excitation item number is determined to be an excitation item corresponding to the excitation of each electron in the system from the original spin direction orbit to other orbits with the same spin direction based on spin symmetry and Hartree-Fock state; and determining the number of the double excitation terms as the excitation terms of two electrons in the system which are excited from the original spin direction orbit to the other two orbits with the corresponding spin directions consistent. On the basis, further, based on the equivalent particle characteristics, merging cluster operators corresponding to two single excitation terms with the same excitation probability in the determined number of single excitation terms, wherein the coefficient of the merged single excitation term is twice that of the single excitation term before merging; and combining the cluster operators corresponding to the two double excitation terms with the same excitation probability in the determined number of the double excitation terms, wherein the coefficient of the combined double excitation terms is twice of the coefficient of the double excitation terms before combination.

Taking hydrogen molecule as an example, |0011 for describing hydrogen molecule>_Hartree-FockThe above-mentioned T is a cluster operator of Fermi form of hydrogen molecule. Referring to fig. 4, fig. 4 is a schematic diagram of a hydrogen molecular orbital according to an embodiment of the present disclosure. As shown in fig. 4, for hydrogen molecules, 1Sa orbit of hydrogen atom No. a in spin-down and spin-up is conveniently represented by q0 and q1 qubits, and 1Sb orbit of hydrogen atom No. b in spin-down and spin-up is represented by q2 and q3 qubits, respectively.

As shown in FIG. 4, assuming that two electrons of the hydrogen molecule are located above two orbitals q0 and q1, respectively, if one electron is located on the spin orbit represented by quantum state |1> and the spin orbit is empty represented by quantum state |0011>, then the Hartree-Fock state of the hydrogen molecule can be represented as |0011 >.

When an electron at q0 is excited onto q2, i.e., the electron is first "annihilated" from q0 and then "generated" at q2, it can be represented by the fermi operator:

wherein, t₂₀As a function of the number of the coefficients,

to create an operator, a₀Is the annihilation operator.

When an electron at q0 is excited onto q3, i.e., the electron is first "annihilated" from q0 and then "generated" at q3, it can be represented by the fermi operator:

wherein, t₃₀As a function of the number of the coefficients,

to create an operator, a₀Is the annihilation operator.

When an electron at q1 is excited onto q2, i.e., the electron is first "annihilated" from q1 and then "generated" at q2, it can be represented by the fermi operator:

wherein, t₂₁As a function of the number of the coefficients,

to create an operator, a₁Is the annihilation operator.

When an electron at q1 is excited onto q3, i.e., the electron is first "annihilated" from q1 and then "generated" at q3, it can be expressed by the fermi operator:

wherein, t₃₁As a function of the number of the coefficients,

to create an operator, a₁Is the annihilation operator.

When electrons on q0 and q1 are excited simultaneously on q2 and q3, that is, electrons are first "annihilated" from q0 and q1 and then "generated" on q2 and q3, they can be expressed as fermi operators:

wherein, t₃₂₁₀As a function of the number of the coefficients,

to create an operator, a₁、a₀Is the annihilation operator.

[ 0011 ] for describing Hydrogen molecule>_Hartree-FockThe state, T at this time, is the Fermi-form cluster operator H for the hydrogen molecule_u：

Wherein, T₁Is a single particle excitation operator, T₂Is a two-particle excitation operator.

When the proposed mode is single shot coupled cluster, the fermi-form cluster operator of the system includes the number of single shots. Namely for the description of hydrogen molecules|0011>_Hartree-FockState of the art, the prior art does not consider spin symmetry and equivalent particle properties:

the inventors of the present application combined spin symmetry, i.e. the transition rule, when the proposed approach is to excite a single coupled cluster, only two transition states, the electron excitation on q0 to q2 and the electron excitation on q1 to q3, need to be considered. Thus, in the present application, based on spin symmetry, when the proposed approach is to singly excite a coupled cluster:

that is, when the proposed mode is single excitation coupled cluster, the fermi-form cluster operator for calculating hydrogen molecules of the present application includes only two excitation terms after considering the spin symmetry, while the fermi-form cluster operator for calculating hydrogen molecules of the prior art includes four excitation terms.

Next, consider the case of equivalent particle characteristics. It is known that in the microscopic world, identical particles are not distinguishable, which is in stark contrast to our classical mechanics. In classical mechanics, even if the intrinsic properties of individual objects are the same, we can still distinguish them according to their trajectory of motion, numbering them: pellet 1, pellet 2, etc. However, in quantum mechanics, the wave functions are scattered in space, that is, the wave functions of the particles in the same region overlap, and there is no definite orbital concept, and the particles cannot be identified by number. A multi-particle system composed of homogeneous particles is called an isotactic particle system. But for the convenience of calculation, the numbering is carried out artificially, but the numbering cannot be realized in practice. That is, the individual orbitals at the same energy level are equivalent, and the probability of a particle transitioning between two energy levels does not depend on the particular orbit it is in, but rather on the energy difference of the energy levels between the two energy levels.

Taking hydrogen molecules as an example, the equivalent particle characteristics are: the excitation of an electron on q0 to q2 is equivalent to the excitation of an electron on q1 to q3, and the excitation of an electron on q0 to q3 is equivalent to the excitation of an electron on q1 to q 2. We can get: t is t₂₀＝t₃₁And t₃₀＝t₂₁. That is, as long as the energy levels before and after excitation are the same, the same process can be considered, the excitation probability is the same, the amplitude values of the cluster operators corresponding to the excitation terms are also the same, and the cluster operators can be combined, so that the number of parameters is reduced, wherein the amplitude value of the cluster operator corresponding to the combined excitation term is approximately twice as large as the amplitude value of the original cluster operator.

The application combines the characteristics of equivalent particles, and when the proposed mode is a single excitation coupling cluster:

wherein, t'₂₀Is t₂₀Is approximately twice, t'₃₀Is t₃₀Approximately twice, it can be considered that:

t′₂₀＝2t₂₀

t′₃₀＝2t₃₀

next, both spin symmetry and equivalent particle properties are combined. Due to the spin symmetry, when the proposed mode is single-shot coupled cluster, T ═ T₁＝H₁+H₄In combination with equivalent particle characteristics, the excitation of an electron at q0 to q2 is equivalent to the excitation of an electron at q1 to q3, H₁And H₄The method can be regarded as the same process, has the same excitation probability, has the same amplitude value of the cluster operator corresponding to the excitation item, and can be combined.

Thus, the present application combines spin symmetry and equivalent particle properties when the proposed approach is single-shot coupled cluster:

wherein, t'₂₀Is t₂₀Approximately twice, it can be considered that:

t′₂₀＝2t₂₀

that is, when the proposed mode is a single excitation coupled cluster, the fermi-form cluster operator for calculating hydrogen molecules of the present application includes only one excitation term number, while the fermi-form cluster operator for calculating hydrogen molecules of the prior art includes four excitation terms, after considering spin symmetry and equivalent particle characteristics.

When the proposed mode is single-double excitation coupled cluster, the Fermi-form cluster operator of the system includes the number of single excitation terms and the number of double excitation terms, i.e. |0011 for describing hydrogen molecule>_Hartree-FockStates, regardless of spin symmetry and equivalent particle properties:

the method combines spin symmetry and equivalent particle characteristics, and when the proposed mode is single-double excitation coupling cluster:

wherein, t'₂₀Is t₂₀Approximately twice, it can be considered that:

t′₂₀＝2t₂₀

that is, when the proposed mode is a single-double excitation coupled cluster in combination with spin symmetry and equivalent particle characteristics, the fermi-form cluster operator for calculating hydrogen molecules of the present application includes only two excitation terms, while the fermi-form cluster operator for calculating hydrogen molecules of the prior art includes five excitation terms.

It is emphasized that the present application, in combination with equivalent particle properties, determines the number of excitation terms and the coefficients corresponding to the excitation terms, is equally effective for dual excitation processes, which cannot be visualized due to the simple hydrogen molecular system. However, as long as the energy levels before and after excitation are the same, the method can be regarded as the same process, has the same excitation probability, and the amplitude values of the cluster operators corresponding to the excitation terms are also the same, and can be combined, so that the number of parameters is reduced, wherein the amplitude value of the cluster operator corresponding to the combined excitation term is approximately twice of the amplitude value of the original cluster operator.

In addition, the above proposed design-simulating method is only an example and does not constitute a limitation to the present invention, for example, the design-simulating method may further include HE (Hardware Efficient), SP (Symmetry Preserved), and the like.

After the number of excitation terms included in the fermi-form cluster operator of the hierarchy and the coefficients corresponding to the excitation terms are determined, step S23 is performed.

And S23, calculating the Fermi form cluster operator of the system according to the number of the excitation terms and the coefficients corresponding to the excitation terms.

In step S22, a fermi form cluster operator corresponding to the hydrogen molecule is given, and similarly, for other systems, after the number of excitation terms and the coefficients corresponding to the excitation terms included in the fermi form cluster operator are determined, the fermi form cluster operator of the system can be calculated according to the corresponding algorithm of the system.

After the cluster operator in the fermi form of the hierarchy is calculated, step S24 is executed.

And S24, solving the experimental state of the system based on the Fermi form cluster operator of the system.

The test state of the system is an important intermediate parameter in calculating the ground state energy of the system. For any one trial state | ψ>(which is a product wave function) and when a Hamiltonian H of a system is applied to the system, the average energy E of the system in the state can be obtained, and the average energy is more than or equal to the ground state energy E of the system₀The expression is as follows:

from this expression canIt can be seen that by continuously adjusting the test state, if the adjusted test state | ψ>Is the ground state of the system | /)₀>When the equal sign in the inequality is true, the ground state energy E of the system can be obtained₀。

Alternatively, solving the trial state of the system based on the fermi form of the system's cluster operators may comprise the steps of:

s241, transforming the fermi operator form of the system into a pauli operator form of the cluster operator according to the pre-selected mapping method.

The mapping method may include: a Jordan-Wigner transform (J-W transform), a Parity transform, a Bravyi-Kitaev transform (B-K transform), an MSP (Multi layer Segmented Parity) transform, and so on.

As can be understood by those skilled in the art, the mapping principle corresponding to each mapping mode may include: the principle of state mapping and the principle of operator mapping.

For example, for a J-W transformation, the displayed state mapping is:

wherein the content of the first and second substances,

represents the computational state of the qubit and,

a transformation matrix is represented that is,

representing the occupation state of the fermi system. The displayed operator map is:

wherein the content of the first and second substances,

representing lifting operator, j representing qubit number, P representing parity set, Z_P(j)A set of pauli Z matrices acting on the qubits belonging to the parity set P is represented, X representing the pauli X matrix and Y representing the pauli Y matrix.

Equally, the operator mapping can also be shown as:

wherein the content of the first and second substances,

a representation generation operator, a_jWhich represents the annihilation operator, is,

and a_jCollectively called the lifting operator of the fermi system,

representing the generation operator/annihilation operator on the qubit,

representing an astronomical operator and n representing the number of quantum bits.

The state mapping and operator mapping display modes of other transformations are the same as those of J-W transformation.

Wherein the Fermi-form cluster operator is transformed into the Paglie operator-form cluster operator according to a preselected mapping manner. For example, for the design of UCCS

T is a Fermi form cluster operator which needs to be transformed into the Paglie operator form so as to be based onThe Pally operator generates a unitary operator, which is the basis for constructing a specific quantum line to which the construction is supposed to correspond.

After converting the fermi-form cluster operator into the pauli-form cluster operator, step S242 is executed.

S242, decomposing the cluster operator in the Pagli operator form into a corresponding unitary operator form and carrying out evolution to obtain an evolved quantum state; wherein the evolved quantum state is a test state of the system.

Optionally, decomposing the cluster operator in the form of the bubble operator into a corresponding unitary operator and evolving to obtain an evolved quantum state, may include the following steps:

and S2421, constructing a quantum simulation circuit based on the corresponding unitary operator after the cluster operator in the form of the Pally operator is decomposed.

And S2422, carrying out analog evolution according to the quantum analog circuit to obtain an evolved quantum state.

Next, please refer to fig. 5-9. Assuming that after J-W transformation of a Fermi sub-cluster operator containing five sub-terms, the Paglie operator form of the cluster operator T is as follows:

first, H is calculated₁The corresponding unitary operator:

FIG. 5 is a drawing H provided in the examples of the present application₁Corresponding quantum wire schematic. As shown in fig. 5, by H₁As can be seen from the corresponding unitary operator, RZ (2 θ) is added to q0₁) Door, namely H can be obtained₁Corresponding quantum wires.

Then, H is calculated₂The corresponding unitary operator:

FIG. 6 is a drawing H provided in the examples of the present application₁And H₂Corresponding quantum wire schematic. As shown in fig. 6, by H₂The corresponding unitary operator can know that q0 is used as a control bit, q1 is used as a target bit, and a CNOT gate is added; then, RZ (2 θ) is added to q1₂) A door; then, q0 bit is used as control bit, q1 is used as target bit, and CNOT gate is added to obtain H₂A corresponding quantum wire.

Then, H is calculated₃The corresponding unitary operator:

FIG. 7 is a drawing H provided in the examples of the present application₁、H₂And H₃Corresponding quantum wire schematic. As shown in FIG. 7, by H₃The corresponding unitary operator can know that two CNOT gates are required to be added in sequence by taking q0 as a control bit, q1 as a target bit, q1 as a control bit and q2 as a target bit; then, RZ (2,2 θ) is added to q2₃) A door; then, using q0 bit as control bit and q1 as target bit, adding CNOT gate to obtain H₃Corresponding quantum wires.

Then, H is calculated₄The corresponding unitary operator:

FIG. 8 is a drawing showing a schematic diagram of H according to an embodiment of the present application₁、H₂、H₃And H₄Corresponding quantum wire schematic. As shown in FIG. 8, by H₄The corresponding unitary operator can know that a Hadamard gate is required to be added on q 0; adding a first CNOT gate by using q0 as a control bit and q1 as a target bit; then, RZ (2 θ) is added to q1₄) A door; then, add a second CNOT gate with q0 as the control bit and q1 as the target bit; finally, at q0Adding a Hadamard gate to obtain H₄Corresponding quantum wires.

Then, H is calculated₅The corresponding unitary operator:

FIG. 9 is a drawing showing a schematic diagram of H according to an embodiment of the present application₁、H₂、H₃、H₄And H₅Corresponding quantum wire schematic. As shown in fig. 9, by H₅The corresponding unitary operator can know that q0 needs to be added first

A door; adding a first CNOT gate by using q0 as a control bit and q1 as a target bit; then, RZ (2 θ) is added to q1₅) A door; then, add a second CNOT gate with q0 as the control bit and q1 as the target bit; finally, add to q1

Door, i.e. obtaining the simulation H₅Corresponding quantum wires. That is to say that FIG. 9 includes H₁、H₂、H₃、H₄And H₅The corresponding quantum wire schematic, i.e., H-corresponding quantum wire, is shown in fig. 9.

In addition, H is assumed in combination with equivalent particle characteristics₁Equivalent to H₄Calculating a combination H₁And H₄The latter unitary operator should be:

θ′₁＝2θ₁

that is, merge H₁And H₄The quantum wires corresponding to the latter unitary operators are similar to the quantum wire schematic shown in fig. 5, except that θ is₁Is converted into theta'₁。

Fig. 5-9 illustrate how a fermi-form cluster operator containing five sub-entries constructs a quantum wire. [ 0011 ] for describing Hydrogen molecule>_Hartree-FockAnd under the conditions that the proposed mode is UCCSD, the mapping mode is J-W transformation, and the rotational symmetry and equivalent particle characteristics are not considered, the Fermi operator form cluster operator also comprises five subentries, namely when a quantum line is constructed, the five subentries of the Fermi operator form cluster operator are required to be converted into a Paglie operator form and decomposed into a corresponding unitary operator form. Then, the quantum wires corresponding to the five sub-items are constructed in time series. Then, the quantum circuit corresponding to the five sub-items is combined to form the quantum analog circuit. And finally, carrying out analog evolution according to the quantum analog circuit to obtain an evolved quantum state.

Whereas the present application is directed to |0011 describing hydrogen molecules due to consideration of spin symmetry and equivalent particle characteristics>_Hartree-FockAnd in the state, under the conditions that the proposed mode is single-double excitation coupling cluster and the mapping mode is J-W conversion, the Fermi form cluster operator has only two sub-items. When constructing a quantum line, only two subentries need to be converted into the Paglie operator form and decomposed into the corresponding unitary operator form. Then, quantum wires corresponding to the two sub-items are constructed in time series. Then, the quantum circuit corresponding to the two sub-items is combined to form the quantum analog circuit. And finally, carrying out analog evolution according to the quantum analog circuit to obtain an evolved quantum state.

In practical application, for any one experimental state | ψ>(it is a product-goodness function)When the Hamiltonian of a system (such as a multi-electron system) is acted on it, the average energy E of the system in the state can be obtained, and the average energy is more than or equal to the energy E of the system₀. Continuously adjusting the test state until the test state is | psi>Is the ground state of the system | /)₀>Then correspondingly obtaining the energy E of the system₀。

Therefore, further, after the system test state | ψ > is prepared by a method of calculating a system test state provided in the present application, the ground state energy of the system can be solved. For example, first, the average energy of the system in the trial state | ψ > is calculated; then, it is judged whether the average energy of the system in the test state | ψ > can be used as the ground state energy of the system. If so, obtaining the ground state energy of the system; otherwise, updating the test state and returning to the step of calculating the average energy of the system in the test state.

According to the method, when the Fermi-form cluster operator of the system is calculated, due to the fact that the spin symmetry and the equivalent particle characteristics are considered, the number of excitation terms needing to be calculated in the Fermi-form cluster operator is smaller than that when the spin symmetry is not considered in the prior art, complexity of the system is reduced, further when the energy of the system is solved, the calculated amount is reduced, the technical problem that complex molecules are difficult to simulate in the prior art is solved, calculation resources are saved, and the simulation efficiency of the complex molecules is improved.

Referring to fig. 10, fig. 10 is a schematic structural diagram of an apparatus for preparing a test state of a system based on spin symmetry and equivalent particle characteristics according to an embodiment of the present invention, and in accordance with the flow shown in fig. 2, the apparatus 110 for preparing a test state of a system based on spin symmetry and equivalent particle characteristics includes:

a first determining module 111, configured to determine a system and the number of tracks and the number of electrons of the system;

a second determining module 112, configured to determine, based on spin symmetry and equivalent particle characteristics, the number of excitation terms included in a fermi form cluster operator of the system and coefficients corresponding to the excitation terms according to the number of orbits and the number of electrons of the system;

a calculating module 113, configured to calculate a fermi form cluster operator of the system according to the number of the excitation terms and coefficients corresponding to the excitation terms;

and the solving module 114 is used for determining a cluster operator based on the Fermi form of the system and solving the experimental state of the system.

Optionally, the second determining module 112 includes:

and the determining unit is used for determining the number of excitation terms included by the fermi form cluster operator of the system and coefficients corresponding to the excitation terms based on spin symmetry, equivalent particle characteristics and the Hartree-Fock state of the system according to a pre-selected proposed mode.

Optionally, the determining unit is further configured to: when the proposed mode is a single excitation coupling cluster, confirming that the cluster operator in the fermi form of the system only comprises a single excitation item number; determining the number of the single excitation terms as excitation terms corresponding to other orbits with the same spin direction from the orbit of the original spin direction to the excitation terms corresponding to the orbits with the same spin direction of each electron in the system based on spin symmetry and Hartree-Fock state; and combining the cluster operators corresponding to the two single excitation terms with the same excitation probability in the determined number of the single excitation terms based on the equivalent particle characteristics, wherein the coefficient of the combined single excitation term is twice that of the single excitation term before combination.

Optionally, the determining unit is further configured to: when the pre-selected proposed mode is single-double excitation coupling cluster, confirming that the Fermi form cluster operator of the system only comprises single excitation item number and double excitation item number; determining the number of the single excitation terms as excitation terms corresponding to other orbits with the same spin direction from the orbit of the original spin direction to the excitation terms corresponding to the orbits with the same spin direction of each electron in the system based on spin symmetry and Hartree-Fock state; determining the number of the double excitation terms as an excitation term of each two electrons in the system which are excited from the original spin direction orbit to the other two orbits with the corresponding spin directions consistent together; based on the characteristics of equivalent particles, combining cluster operators corresponding to two single excitation terms with the same excitation probability in the determined number of the single excitation terms, wherein the coefficient of the combined single excitation term is twice that of the single excitation term before combination; and combining the cluster operators corresponding to the two double excitation terms with the same excitation probability in the determined number of the double excitation terms, wherein the coefficient of the combined double excitation terms is twice of the coefficient of the double excitation terms before combination.

Optionally, the second determining module 112 further includes:

a transformation unit for transforming the Fermi operator form of the system into a Paglie operator form of the cluster operator according to a preselected mapping manner;

In addition, the technical effect of the apparatus 110 for preparing the system test state based on the spin symmetry and the equivalent particle characteristics can refer to the technical effect of the method for calculating the system test state shown in fig. 2, and will not be described herein again.

An embodiment of the present invention further provides a storage medium, in which a computer program is stored, where the computer program is configured to execute the steps in any of the above method embodiments when running.

Specifically, in the present embodiment, the storage medium may be configured to store a computer program for executing the steps of:

s1, determining a system and the orbit number and the electron number of the system;

s2, determining the number of excitation terms included by the Fermi form cluster operator of the system and coefficients corresponding to the excitation terms according to the orbital number and the electron number of the system based on the spin symmetry and the equivalent particle characteristics;

s3, calculating the Fermi form cluster operator of the system according to the number of the excitation terms and the coefficients corresponding to the excitation terms;

and S4, solving the experimental state of the system based on the Fermi form cluster operator of the system.

Specifically, in this embodiment, the storage medium may include, but is not limited to: a U-disk, a Read-only Memory (ROM), a Random Access Memory (RAM), a removable hard disk, a magnetic disk, or an optical disk, which can store computer programs.

An embodiment of the present invention further provides an electronic apparatus, which includes a memory and a processor, where the memory stores a computer program, and the processor is configured to execute the computer program to perform the steps in any of the above method embodiments.

Specifically, the electronic apparatus may further include a transmission device and an input/output device, wherein the transmission device is connected to the processor, and the input/output device is connected to the processor.

Specifically, in this embodiment, the processor may be configured to execute the following steps by a computer program:

s3, calculating a Fermi form cluster operator of the system according to the number of the excitation terms and the coefficients corresponding to the excitation terms;

It should also be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.

The foregoing description has been directed to specific embodiments of this disclosure. Other embodiments are within the scope of the following claims. In some cases, the actions or steps recited in the claims may be performed in a different order than in the embodiments and still achieve desirable results. In addition, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results. In some embodiments, multitasking and parallel processing may also be possible or may be advantageous.

The terminology used in the description of the one or more embodiments is for the purpose of describing the particular embodiments only and is not intended to be limiting of the description of the one or more embodiments. As used in one or more embodiments of the present specification and the appended claims, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It should also be understood that the term "and/or" as used herein refers to and encompasses any and all possible combinations of one or more of the associated listed items.

It should be understood that although the terms first, second, third, etc. may be used in one or more embodiments of the present description to describe various information, such information should not be limited to these terms. These terms are only used to distinguish one type of information from another. For example, first information may also be referred to as second information, and similarly, second information may also be referred to as first information, without departing from the scope of one or more embodiments herein. The word "if," as used herein, may be interpreted as "at … …" or "when … …" or "in response to a determination," depending on the context. The above description is only for the purpose of illustrating the preferred embodiments of the one or more embodiments of the present disclosure, and is not intended to limit the scope of the one or more embodiments of the present disclosure, and any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the one or more embodiments of the present disclosure should be included in the scope of the one or more embodiments of the present disclosure.

The construction, features and functions of the present application are described in detail in the embodiments illustrated in the drawings, which are only preferred embodiments of the present application, but the present application is not limited by the drawings, and all changes that can be made and equivalents modified according to the idea of the present application are intended to be covered by the scope of the present application.

Claims

1. A method for preparing a system test state based on spin symmetry and equivalent particle characteristics, comprising:

determining a system and the number of orbits and electrons of the system;

2. The method according to claim 1, wherein the determining the number of excitation terms included in the fermi form of the system and the coefficients corresponding to the excitation terms according to the number of orbitals and the number of electrons of the system based on the spin symmetry and the equivalent particle characteristics comprises:

3. The method of claim 2, wherein determining the number of excitation terms included by the fermi-form cluster operator of the system based on spin symmetry, equivalent particle characteristics, and the Hartree-focus state of the system according to a preselected proposed approach comprises:

4. The method of claim 2, wherein determining the number of excitation terms included by the fermi-form cluster operator of the system based on spin symmetry, equivalent particle characteristics, and the Hartree-focus state of the system according to a preselected proposed approach comprises:

based on the characteristics of equivalent particles, combining cluster operators corresponding to two single excitation terms with the same excitation probability in the determined number of the single excitation terms, wherein the coefficient of the combined single excitation term is twice that of the single excitation term before combination; and combining the cluster operators corresponding to the two double-excitation terms with the same excitation probability in the determined double-excitation term number, wherein the coefficient of the combined double-excitation term is twice of the coefficient of the double-excitation term before combination.

5. The method of claim 2, wherein solving the trial state of the system based on the cluster operator of the fermi form of the system comprises:

6. The method of claim 5, wherein decomposing the Pally operator form of cluster operators into corresponding unitary operator forms and evolving to obtain evolved quantum states comprises:

7. The method of claim 5 or 6, wherein the mapping is one of a Jordan-Wigner transform, a Party transform, a Bravyi-Kitaev transform, and a SegmentParty transform.

8. An apparatus for preparing a system test state based on spin symmetry and equivalent particle characteristics, comprising:

9. An electronic device, comprising:

a processor;

a memory for storing processor-executable instructions;

wherein the processor implements the method of any one of claims 1-7 by executing the executable instructions.

10. A computer storage medium having stored thereon computer instructions which, when executed by a processor, carry out the steps of the method according to any one of claims 1 to 7.