Calculation method of ground state energy of target system and related device

Abstract

Embodiments of the invention disclose a target system ground state energy calculation method and a related device. The method comprises the steps of calculating a Hamiltonian of a to-be-solved target system and an opinion of an operator in a predefined operator pool; performing de-randomization processing on the peer by using a shadow chromatography method to obtain an optimized peer, the component included in the optimized peer being less than the component included in the unoptimized peer; and determining the ground state energy of the to-be-solved system according to the size of the expected value of the optimized etenant. By adopting the embodiment of the invention, the calculation speed of the ground state energy of the target system is improved, and the consumption of hardware resources is reduced.

Description

Technical Field

[0001] The present invention relates to the field of quantum computing technology, and in particular to a method for calculating the ground state energy of a target system and a related device. Background Art

[0002] The variational quantum eigensolver (VQE) is an algorithm that uses a classical optimizer to train a parameterized quantum circuit to solve matrix eigenvalues ​​and eigenvectors. It is the earliest variational quantum algorithm. If the matrix eigenvalues ​​and eigenvectors are represented and calculated on a classical computer, the storage capacity consumed grows exponentially with the size of the physical system to be calculated, while the computing resources consumed on a quantum computer grow polynomially with the size of the physical system to be calculated. Due to this property, VQE is widely used to solve the ground state and low excitation problems of quantum systems in quantum chemistry.

[0003] In the current variational quantum algorithm, the parameters in the quantum circuit are updated by solving the gradient of the loss function (i.e., energy). This method requires precise solution of energy and is the most time-consuming and hardware-intensive step in calculating the ground state energy of the target system. Summary of the invention

[0004] The embodiments of the present application provide a method and a related device for calculating the ground state energy of a target system, which are beneficial to improving the calculation speed of the ground state energy of the target system and reducing the consumption of hardware resources.

[0005] A first aspect of an embodiment of the present application provides a method for calculating the ground state energy of a target system, the method comprising:

[0006] Calculate the commutator between the Hamiltonian of the target system to be solved and the operators in the predefined operator pool;

[0007] De-randomizing the commutator by a shadow tomography method to obtain an optimized commutator, wherein the optimized commutator includes fewer components than the components included in the commutator before optimization;

[0008] The ground state energy of the system to be solved is determined according to the expected value of the optimized commutator.

[0009] Optionally, before calculating the commutator between the Hamiltonian of the target system to be solved and the operators in the predefined operator pool, the method further includes:

[0010] Determining the single electron integral and the double electron integral according to the molecular structure of the target system to be solved;

[0011] Determining coefficients of a monomer operator and a two-body operator in the Fermi Hamiltonian according to the single-electron integral and the two-electron integral to obtain the Fermi Hamiltonian of the target system to be solved, wherein the monomer operator and the two-body operator are determined according to the number of electron orbitals in the molecular structure;

[0012] The Fermi Hamiltonian is converted to the Pauli Hamiltonian.

[0013] Optionally, before calculating the commutator between the Hamiltonian of the target system to be solved and the operators in the predefined operator pool, the method further includes:

[0014] Each sub-operator obtained by decomposing the coupled cluster operator is placed into the operator pool to obtain a predefined operator pool;

[0015] Each operator in the predefined operator pool is converted into a Pauli operator to obtain a predefined Pauli operator pool.

[0016] Optionally, before determining the ground state energy of the system to be solved according to the expected value of the optimized commutator, the method further includes:

[0017] Run the variational quantum circuit at the current moment and measure the quantum state at the current moment;

[0018] The expected value of the optimized commutator is determined according to the optimized commutator and the quantum state at the current moment.

[0019] Optionally, determining the ground state energy of the system to be solved according to the expected value of the optimized commutator includes:

[0020] Adding the operator corresponding to the largest expected value to the variational quantum circuit at the current moment to obtain the variational quantum circuit at the next moment;

[0021] Taking the next moment as the current moment, and executing the step of running the variational quantum circuit at the current moment, and measuring the quantum state at the current moment;

[0022] If the energy at the current moment determined according to the quantum state at the current moment converges, the energy at the current moment is used as the ground state energy of the system to be solved.

[0023] Optionally, the method further includes:

[0024] If the energy at the current moment determined according to the quantum state at the current moment does not converge, the step of determining the expected value of the optimized commutator according to the optimized commutator and the quantum state at the current moment is performed.

[0025] Optionally, the method further includes:

[0026] Determining the Hartree-Fock ground state of the target system to be solved;

[0027] Constructing a coded quantum circuit for evolving a quantum state from a zero state to the Hartree-Fock ground state;

[0028] The coded quantum circuit is used as a variational quantum circuit at an initial moment.

[0029] A second aspect of an embodiment of the present application provides a device for calculating the ground state energy of a target system, comprising:

[0030] A commutator calculation unit, used to calculate the commutator between the Hamiltonian of the target system to be solved and the operators in the predefined operator pool;

[0031] A randomization unit, used for performing a de-randomization process on the commutator by a shadow tomography method to obtain an optimized commutator, wherein the optimized commutator includes fewer components than the components included in the commutator before optimization;

[0032] The energy calculation unit is used to determine the ground state energy of the system to be solved according to the expected value of the optimized commutator.

[0033] A third aspect of the embodiments of the present application provides an electronic device, including: a processor and a memory;

[0034] The processor is connected to the memory, wherein the memory is used to store the computer program, and the processor is used to call the computer program to execute the method in the first aspect of the embodiment of the present application.

[0035] A fourth aspect of an embodiment of the present application provides a computer-readable storage medium, which stores a computer program. The computer program includes program instructions. When the program instructions are executed by a processor, the method in the first aspect of the embodiment of the present application is executed.

[0036] It can be seen that the present application provides a method for calculating the ground state energy of a target system and a related device. By calculating the commutator of the Hamiltonian of the target system to be solved and the operator in the predefined operator pool, the ground state energy of the system to be solved is determined according to the size of the expected value of the commutator, thereby converting the updating of the parameters in the quantum circuit by the accurate calculation of the loss function in the existing method into the updating of the quantum circuit structure and parameters by comparing the size of the expected value of the commutator in the present application; and the comparison of the size of the expected value of the commutator does not require accurate calculation, only its size needs to be known, so the commutator is de-randomized by the shadow tomography method to obtain an optimized commutator, and the optimized commutator includes fewer components than the components included in the commutator before optimization, so that the commutator component terms with smaller contributions can be omitted, thereby realizing a fast comparison of the commutator expectation values ​​and improving the calculation speed of the ground state energy of the target system; similarly, since the commutator component terms with smaller contributions are omitted, the storage capacity consumed can be saved during calculation and representation. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0038] Figure 1 An exemplary system block diagram of a method for calculating the ground state energy of a target system provided by an embodiment of the present application is shown;

[0039] Figure 2 A schematic diagram showing a flow chart of a method for calculating the ground state energy of a target system provided by an embodiment of the present application;

[0040] Figure 3 A schematic diagram of the structure of a device for calculating the ground state energy of a target system provided by an embodiment of the present application is shown;

[0041] Figure 4 A schematic diagram of the structure of a computer device provided in one embodiment of the present application is shown. DETAILED DESCRIPTION

[0042] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0043] Classical computers use transistors to encode information in binary data, such as bits, where each bit can represent a value of 1 or 0. These 1s and 0s act as switches that drive the functions of a classical computer. If there are n bits of data, there are 2n possible classical states, and one state is represented at a time.

[0044] Quantum computers use quantum processors that operate on data represented by quantum bits, also known as qubits. A qubit can represent the classical binary state "0", "1", or a superposition of "0" and "1". Because it can represent a superposition of "0" and "1", a qubit can represent both the "0" and "1" states at the same time. For example, if there are n bits of data, then 2 n Quantum states can be represented simultaneously. Further, qubits in superposition can be related to each other, known as entanglement, where the state of one qubit (whether it is 1 or 0 or both) can depend on the state of another qubit, and more information can be encoded within the two entangled qubits. Based on the principles of superposition and entanglement, qubits can enable quantum computers to perform functions that may be relatively complex and time-consuming for classical computers.

[0045] Please refer to Figure 1 , which shows an example system block diagram of a method for calculating the ground state energy of a target system provided by an embodiment of the present application. System 100 may be a hybrid computing system including a combination of one or more quantum computers, quantum systems and / or classical computers. Figure 1 In the example shown, system 100 may include a quantum system 110 and a classical computer 120. In one embodiment, quantum system 110 and classical computer 120 may be configured to communicate via one or more of a wired connection and / or a wireless connection (e.g., a wireless network). Quantum system 110 may include a quantum chipset consisting of one or more quantum chips, which includes various hardware components for processing data encoded in quantum bits. The quantum chipset may be a quantum computing core surrounded by infrastructure to protect the quantum chip from electromagnetic noise sources, mechanical vibration sources, heat sources, and other noise sources that may degrade the performance of the quantum chip. Classical computer 120 may be electronically integrated with quantum system 110 via any suitable wired and / or wireless electronic connection.

[0046] exist Figure 1 In the example shown, quantum system 110 can be any suitable set of components capable of performing quantum operations on a physical system. Quantum operations, such as quantum gate operations, manipulate the quantum states of quantum bits to evolve and / or entangle. Figure 1In the example embodiment shown, the quantum system 110 may include a measurement and control integrated machine 111, an interface 112, and a quantum chip 113. In some embodiments, all or part of each of the measurement and control integrated machine 111, the interface 112, and the quantum chip 113 may be located in a cryogenic environment to help perform quantum operations. The quantum chip 113 may be any hardware capable of processing information using quantum states. The hardware may include a plurality of qubits and a device for coupling or entanglement of the qubits so as to process information using quantum states. Qubits may include, but are not limited to, charge qubits, flux qubits, phase qubits, spin qubits, and ion qubits. The quantum chip may include a set of quantum logic gates configured to perform quantum logic operations on qubits stored in a quantum register. The quantum gate may include one or more single-qubit gates, dual-qubit gates, and / or other multi-qubit gates.

[0047] The measurement and control integrated machine 111 can be any combination of digital computing devices capable of performing quantum computing (e.g., executing quantum circuits) in combination with the interface 112. The digital computing device may include a digital processor and memory for storing and executing quantum instructions using the interface 112. The digital computing device may also include a communication protocol device for receiving instructions and sending the results of the quantum computing performed to a classical computer. In addition, the digital computing device may also include a communication interface with an interface 112. In one embodiment, the measurement and control integrated machine 111 may be configured to receive classical instructions (e.g., from a classical computer 120) and convert the classical instructions into measurement and control instructions for the interface 112. The measurement and control instructions provided to the interface 112 by the measurement and control integrated machine 111 may be, for example, digital signals indicating which quantum gates in the quantum gate need to act on the quantum bit to perform a specific function. The interface 112 may be configured to convert these digital signals into analog signals (e.g., analog pulses of microwave pulses), which may be used to apply quantum gates on the quantum bit to manipulate the interaction between the quantum bits.

[0048] The interface 112 may be a classical-quantum interface, including a device combination capable of receiving instructions from the measurement and control integrated machine 111 and converting the instructions into a device for implementing quantum operations. In one embodiment, the interface 112 may convert instructions from the measurement and control integrated machine 111 into a drive signal that can drive or manipulate a quantum bit, and / or act on a quantum gate on the quantum bit. In addition, the interface 112 may be configured to convert a signal received from the quantum chip 113 into a digital signal that can be processed and transmitted by the measurement and control integrated machine 111. The devices included in the interface 112 may include, but are not limited to, a digital-to-analog converter, an analog-to-digital converter, a waveform generator, an attenuator, an amplifier, an optical fiber, a laser, and a filter. The interface 112 may further include a circuit component configured to measure a plurality of quantum bits after the quantum gate acts, wherein the measurement may produce a result represented by a classical bit. Each measurement performed by the interface 112 may be read out to a device connected to the quantum system 110, such as a classical computer 120. The plurality of measurement results provided by the interface 112 may represent a probabilistic result.

[0049] The classical computer 120 can include hardware components such as a processor and a storage device (e.g., including a memory device and a classical register) for processing data encoded in classical bits. In one embodiment, the classical computer 120 can be configured to provide various control signals, instructions, and data encoded in classical bits to the quantum system 110. Further, the quantum state measured by the quantum system 110 can be read out by the classical computer 120, and the classical computer 120 can store the measured quantum state as a classical bit in a classical register. In one embodiment, the classical computer 120 can be any suitable combination of computer executable hardware and / or computer executable software capable of executing a preparation module 121 to perform quantum computing using data stored in a data storage module 122 as part of the construction and calculation. The data storage module 122 can be a repository for data to be analyzed using a quantum computing algorithm and the results of the analysis. The preparation module 121 can be a program or module capable of preparing classical data from the data storage module 122 as part of a quantum circuit implementation. The preparation module 121 can be instantiated as part of a larger algorithm, such as a function call of an application programming interface (API), or by parsing hybrid classical-quantum computing into aspects of quantum and classical computing. For example, the preparation module 121 can generate instructions for creating a quantum circuit using quantum gates. In an embodiment, such instructions can be stored by the measurement and control integrated machine 111, and components of the interface 112 can be instantiated to execute, so that the quantum operation of the quantum gate can be performed on the quantum chip 113.

[0050] The classical computer 120 may be a laptop computer, a desktop computer, a vehicle integrated computer, a smart mobile device, a tablet device, and / or any other suitable classical computing device. Additionally or alternatively, the classical computer 120 may also be operated as part of a cloud computing service model, such as software as a service (SaaS), platform as a service (PaaS), or infrastructure as a service (IaaS). The classical computer 120 may also be located in a cloud computing deployment model, such as a private cloud, a community cloud, a public cloud, or a hybrid cloud.

[0051] Please refer to Figure 2 , which shows a flow chart of a method for calculating the ground state energy of a target system provided by an embodiment of the present application. The method can be applied to a computer device, which refers to an electronic device with data calculation and processing capabilities. The method may include the following steps:

[0052] Step 201: Calculate the commutator between the Hamiltonian of the target system to be solved and the operators in the predefined operator pool.

[0053] Among them, Hamiltonian is a functional representation of the total energy of a system, which takes the generalized coordinates and generalized momentum of the system as independent variables. The Hamiltonian operator corresponding to the Hamiltonian acts on the wave function, namely the Schrödinger equation. The Schrödinger equation describes the change of the wave function over time. By solving the Schrödinger equation, we can get the specific form of the wave function and the corresponding energy, so as to understand the properties of the microscopic system.

[0054] The core problem of quantum chemistry is to solve the Schrödinger equation. Generally speaking, solving the time-dependent Schrödinger equation is relatively complicated, so the Born-Oppenheimer approximation (BOapproximation) is introduced. The BO approximation believes that the mass of the nucleus is much greater than that of the electron and the movement speed is much lower than that of the electron, so the two can be separated into variables and the movement of the nucleus or the electron can be discussed separately. Then, the following time-independent electron motion equation can be obtained, also known as the steady-state Schrödinger equation, and its Hamiltonian is as follows:

[0055] H=K e +V ee +V Ne

[0056] Among them, K e is the electron kinetic energy, V ee is the electron-electron potential energy and V Ne is the electron-nuclear potential energy.

[0057] The operator pool refers to a collection of multiple candidate quantum gate operations that are used to construct quantum circuits. These operations are usually selected based on the specific requirements of the problem, and they may include but are not limited to single-qubit gates, double-qubit gates, etc. During the execution of the algorithm, elements in the operator pool may be added to or removed from the quantum circuit to adjust the structure of the quantum circuit to make it more suitable for solving the problem.

[0058] The commutator describes the interaction between two operators (or operations). Let F and G be two operators, then the commutator of F and G is [F, G] = FG-GF.

[0059] Furthermore, before calculating the commutator between the Hamiltonian of the target system to be solved and the operators in the predefined operator pool, the method further includes:

[0060] Determining the single electron integral and the double electron integral according to the molecular structure of the target system to be solved;

[0061] Determining coefficients of a monomer operator and a two-body operator in the Fermi Hamiltonian according to the single-electron integral and the two-electron integral to obtain the Fermi Hamiltonian of the target system to be solved, wherein the monomer operator and the two-body operator are determined according to the number of electron orbitals in the molecular structure;

[0062] The Fermi Hamiltonian is converted to the Pauli Hamiltonian.

[0063] For example, for the target system to be solved, a hydrogen molecule to be simulated with a bond length of 0.74, which contains four single-electron spin molecular orbitals and two electrons, the single-electron integral A (2*2 matrix form) and the double-electron integral G (2*2*2*2 tensor form) of the system are obtained by solving the classical quantum chemistry algorithm. The specific results are as follows:

[0064]

[0065] Generally speaking, the Fermi Hamiltonian of a molecular system consists of a single-body operator (in the form of "i+j") and a two-body operator (in the form of "i1+i2+j1 j2"), where i, j, i1, i2, j1, j2 are all orbital numbers. For example:

[0066] fermion={

[0067] 0+0:a

[0068] 1+0+1 0:b ....

[0070] }

[0071] The above electron integration results determine the coefficients a and b in the Fermi Hamiltonian of the molecular system.

[0072] The pseudo code for constructing the Fermi Hamiltonian is as follows:

[0073]

[0074] Finally, the Fermi Hamiltonian of the system is as follows:

[0075] { :0.715104

[0077] 0+0:-1.253310

[0078] 1+0+1 0:-0.674756

[0079] 1+0+3 2:-0.181210

[0080] 1+1:-1.253310

[0081] 2+0+2 0:-0.482501

[0082] 2+1+2 1:-0.663711

[0083] 2+1+3 0:0.181210

[0084] 2+2:-0.475069

[0085] 3+0+2 1:0.181210

[0086] 3+0+3 0:-0.663711

[0087] 3+1+3 1:-0.482501

[0088] 3+2+1 0:-0.181210

[0089] 3+2+3 2:-0.697652

[0090] 3+3:-0.475069

[0091] }

[0092] The conversion of the Fermi Hamiltonian into the Pauli Hamiltonian can be achieved by: Jordan-Wigner transformation, Parity transformation, Bravyi-Kitaev transformation, etc. For example, using the Jordan-Wigner transformation, the Pauli Hamiltonian of the above system is as follows:

[0093] {

[0094] "":-0.097066,

[0095] "X0 X1 Y2 Y3":-0.045303,

[0096] "X0 Y1 Y2 X3":0.045303,

[0097] "Y0 X1 X2 Y3":0.045303,

[0098] "Y0 Y1 X2 X3":-0.045303,

[0099] "Z0":0.171413,

[0100] "Z0 Z1":0.168689,

[0101] "Z0 Z2":0.120625,

[0102] "Z0 Z3":0.165928,

[0103] "Z1":0.171413,

[0104] "Z1 Z2":0.165928,

[0105] "Z1 Z3":0.120625,

[0106] "Z2":-0.223432,

[0107] "Z2 Z3":0.174413,

[0108] "Z3": -0.223432

[0109] }

[0110] Furthermore, before calculating the commutator between the Hamiltonian of the target system to be solved and the operators in the predefined operator pool, the method further includes:

[0111] Each sub-operator obtained by decomposing the coupled cluster operator is placed into the operator pool to obtain a predefined operator pool;

[0112] Each operator in the predefined operator pool is converted into a Pauli operator to obtain a predefined Pauli operator pool.

[0113] Among them, the coupled cluster operator is an important method in quantum chemical calculations, which is used to describe the wave function of multi-electron systems. Coupled cluster theory is a post-Hartree-Fock method that improves the description of electronic structure through exponential variational principles.

[0114] Taking the above hydrogen molecule system as an example, there are four spin orbitals, 0, 1 (bonding orbitals) and 2, 3 (antibonding orbitals). In the ground state, two electrons occupy bonding orbitals 0 and 1. By default, excitation does not change the electron spin state, so 0 can only be excited to 2, and 1 can only be excited to 3. The corresponding single and double excitation operators are:

[0115]

[0116] in, is the coefficient to be solved, is the creation and annihilation operator.

[0117] Will This is just one embodiment provided by the present application, and it is conceivable that the corresponding operator can also be obtained by decomposing through other operator theories.

[0118] Similarly, the operators in the operator pool also need to be converted into Pauli operators, which can be done by using the above transformation. For example, if we only consider the double excitation operator , its operator pool contains only one item, namely:

[0119] pool={

[0120] "3+2+1 0":1.0

[0121] }

[0122] After the Jordan-Wigner transformation, the operator pool becomes:

[0123] pauli_pool = {

[0124] "X0 X1 X2 Y3":-0.125000,

[0125] "X0 X1 Y2 X3":-0.125000,

[0126] "X0 Y1 X2 X3":0.125000,

[0127] "X0 Y1 Y2 Y3":-0.125000,

[0128] "Y0 X1 X2 X3":0.125000,

[0129] "Y0 X1 Y2 Y3":-0.125000,

[0130] "Y0 Y1 X2 Y3":0.125000,

[0131] "Y0 Y1 Y2 X3":0.125000

[0132] }

[0133] Taking the operator "X0 X1 X2 Y3":-0.125000 as an example, its commutator with the Hamiltonian of the molecular system is:

[0134] {

[0135] "X0 X1 X2 X3":0.055858i,

[0136] "X0 X1 Y2 Y3":-0.055858i,

[0137] "X0 Y1 X2 Y3":0.042853i,

[0138] "Y0 X1 X2 Y3":0.042853i,

[0139] "Z0":-0.011326i,

[0140] "Z0 Z1 Z3":0.011326i,

[0141] "Z1 Z2 Z3":-0.011326i,

[0142] "Z2":0.011326i

[0143] }

[0144] Note that the above commutation coefficients are all imaginary numbers. In actual calculations, we only take the imaginary part of the coefficients, namely:

[0145] {

[0146] "X0 X1 X2 X3":0.055858,

[0147] "X0 X1 Y2 Y3":-0.055858,

[0148] "X0 Y1 X2 Y3":0.042853,

[0149] "Y0 X1 X2 Y3":0.042853,

[0150] "Z0":-0.011326,

[0151] "Z0 Z1 Z3":0.011326,

[0152] "Z1 Z2 Z3":-0.011326,

[0153] "Z2":0.011326

[0154] }

[0155] Step 202: De-randomize the commutator by a shadow tomography method to obtain an optimized commutator, wherein the optimized commutator includes fewer components than the components included in the commutator before optimization.

[0156] Among them, Shadow Tomography is a new technology in quantum information processing, which allows us to efficiently estimate the output probability distribution of quantum states under certain measurement settings without completely reconstructing the quantum state. Compared with traditional quantum state tomography, shadow tomography only requires fewer copies of quantum states and a shorter time to obtain partial information about the quantum state. Specifically, the derandomization of the commutator by the shadow tomography method can be found in the document entitled "Efficient estimation of Pauli observables by derandomization" Phys. Rev. Lett. 127, 030503 (2021).

[0157] Take the two-qubit Hamiltonian as an example:

[0158] P1={

[0159] "":1,

[0160] "X0 X1":1,

[0161] "X1":1,

[0162] "Z1":1,

[0163] "X0 Z1":,1

[0164] }

[0165] The number of observations is set to 200. After a derandomization process, the above Hamiltonian can obtain a new Hamiltonian P2

[0166] P2={

[0167] "X0 X1":200,

[0168] "X0 Z0":200

[0169] }

[0170] Step 203: Determine the ground state energy of the system to be solved according to the expected value of the optimized commutator.

[0171] Furthermore, before determining the ground state energy of the system to be solved according to the expected value of the optimized commutator, the method further includes:

[0172] Run the variational quantum circuit at the current moment and measure the quantum state at the current moment;

[0173] The expected value of the optimized commutator is determined according to the optimized commutator and the quantum state at the current moment.

[0174] Specifically, if the Hamiltonian of the target system to be solved is represented by H, the operators in the predefined operator pool are represented by K i If it is represented, then the commutator is [H,K i ]; Run the variational quantum circuit at the current moment and measure the quantum state ψ at the current moment (n) ; then the expected value of the exchange is <ψ (n) |[H,K i ]|ψ (n) >.

[0175] Specifically, determining the ground state energy of the system to be solved according to the expected value of the optimized commutator includes:

[0176] Adding the operator corresponding to the largest expected value to the variational quantum circuit at the current moment to obtain the variational quantum circuit at the next moment;

[0177] Taking the next moment as the current moment, and executing the step of running the variational quantum circuit at the current moment, and measuring the quantum state at the current moment;

[0178] If the energy at the current moment determined according to the quantum state at the current moment converges, the energy at the current moment is used as the ground state energy of the system to be solved;

[0179] If the energy at the current moment determined according to the quantum state at the current moment does not converge, the step of determining the expected value of the optimized commutator according to the optimized commutator and the quantum state at the current moment is performed.

[0180] Specifically, the energy at the current moment is determined according to the quantum state at the current moment, and the energy at the current moment is equal to the quantum state of the Hamiltonian acting on the current moment. Energy convergence refers to the process in which energy gradually decreases and tends to be stable, which can be measured by accuracy or error, for example.

[0181] Taking the operator {"X0 X1 X2 Y3":-0.125000} as an example, the evolution time is set to 1, the number of layers is 1, and the proposed circuit constructed based on this operator is:

[0182] H(0)

[0183] H(1)

[0184] H(2)

[0185] RX(3,1.570796)

[0186] CNOT(0,3)

[0187] CNOT(1,3)

[0188] CNOT(2,3)

[0189] RZ(3,-0.125000)

[0190] CNOT(0,3)

[0191] CNOT(1,3)

[0192] CNOT(2,3)

[0193] H(0)

[0194] H(1)

[0195] H(2)

[0196] RX(3,-1.570796)

[0197] Furthermore, the method further comprises:

[0198] Determining the Hartree-Fock ground state of the target system to be solved;

[0199] Constructing a coded quantum circuit for evolving a quantum state from a zero state to the Hartree-Fock ground state;

[0200] The coded quantum circuit is used as a variational quantum circuit at an initial moment.

[0201] Among them, the quantum state at the initial moment is |ψ (0) > is the Hartree-Fock ground state of the target system to be solved |ψ (HF) >, so the variational quantum circuit at the initial moment is the encoding |ψ (HF) >The quantum circuit does not include the variational parameter θ at the initial moment. Then, the variational quantum circuit U(θ) adaptively adds an operator during the optimization iteration, which is the maximum expected value <ψ (n) |[H,Ki ]|ψ (n) >The corresponding operator K i , the energy decreases fastest during iteration, that is, the derivative of energy with respect to θ is the largest, and the derivative of energy with respect to θ is equal to The current time is k, then the quantum state at time k is

[0202] in, |0> represents an unoccupied orbital, |1> represents an occupied orbital, and N is the number of electrons. A hydrogen molecule includes two electrons in an occupied orbital, so under the Jordan-Wigner transformation, it is equivalent to applying two X gates to |00>.

[0203] It can be seen that the present application provides a method for calculating the ground state energy of a target system and a related device. By calculating the commutator of the Hamiltonian of the target system to be solved and the operator in the predefined operator pool, the ground state energy of the system to be solved is determined according to the size of the expected value of the commutator, thereby converting the updating of the parameters in the quantum circuit by the accurate calculation of the loss function in the existing method into the updating of the quantum circuit structure and parameters by comparing the size of the expected value of the commutator in the present application; and the comparison of the size of the expected value of the commutator does not require accurate calculation, only its size needs to be known, so the commutator is de-randomized by the shadow tomography method to obtain an optimized commutator, and the optimized commutator includes fewer components than the components included in the commutator before optimization, so that the commutator component terms with smaller contributions can be omitted, thereby realizing a fast comparison of the commutator expectation values ​​and improving the calculation speed of the ground state energy of the target system; similarly, since the commutator component terms with smaller contributions are omitted, the storage capacity consumed can be saved during calculation and representation.

[0204] Figure 3 A schematic diagram of the structure of a device for calculating the ground state energy of a target system provided by an embodiment of the present application is shown. The device includes:

[0205] A commutator calculation unit 301 is used to calculate the commutator between the Hamiltonian of the target system to be solved and the operators in the predefined operator pool;

[0206] A randomization unit 302 is used to perform a de-randomization process on the commutator by a shadow tomography method to obtain an optimized commutator, wherein the optimized commutator includes fewer components than the components included in the commutator before optimization;

[0207] The energy calculation unit 303 is used to determine the ground state energy of the system to be solved according to the expected value of the optimized commutator.

[0208] Figure 4A structural schematic diagram of a computer device provided by an embodiment of the present application is shown, including a memory and a processor, the memory stores a computer program, and the processor implements the functions of a computer system of a method for calculating the ground state energy of a target system in any of the above-mentioned embodiments when executing the computer program.

[0209] An embodiment of the present application further provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a computer, the computer executes the functions of a computer system of the method for calculating the ground state energy of a target system in any of the above embodiments.

[0210] The present application also provides a computer program product comprising instructions, which, when executed by a computer, enables the computer to perform the functions of a computer system of the method for calculating the ground state energy of a target system in any of the above-mentioned embodiments.

[0211] It should be understood that the specific examples in this application are only intended to help those skilled in the art to better understand the embodiments of the present application, rather than to limit the scope of the present invention.

[0212] It can be understood that in the various implementations of the present application, the size of the serial number of each process does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the implementation methods of the present application.

[0213] It can be understood that the various embodiments described in this application can be implemented individually or in combination, and the embodiments of this application are not limited to this.

[0214] Unless otherwise stated, all technical and scientific terms used in the embodiments of the present application have the same meaning as those generally understood by those skilled in the art of the technical field of the present application. The terms used in the present application are only for the purpose of describing specific embodiments and are not intended to limit the scope of the present application. The term "and / or" used in the present application includes any and all combinations of one or more related listed items. The singular forms of "a kind of", "above" and "the" used in the embodiments of the present application and the appended claims are also intended to include plural forms, unless the context clearly indicates other meanings.

[0215] It can be understood that the processor of the embodiment of the present application can be an integrated circuit chip with signal processing capabilities. In the implementation process, each step of the above method implementation can be completed by the hardware integrated logic circuit or software instructions in the processor. The above processor can be a general processor, a digital signal processor (DigitalSignal Processor, DSP), an application-specific integrated circuit (Application Specific Integrated Circuit, ASIC), a field programmable gate array (Field Programmable Gate Array, FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components. The methods, steps and logic block diagrams disclosed in the embodiment of the present application can be implemented or executed. The general processor can be a microprocessor or the processor can also be any conventional processor, etc. The steps of the method disclosed in the embodiment of the present application can be directly embodied as a hardware decoding processor to perform, or the hardware and software modules in the decoding processor are combined and executed. The software module can be located in a mature storage medium in the field such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory or an electrically erasable programmable memory, a register, etc. The storage medium is located in the memory, and the processor reads the information in the memory and completes the steps of the above method in combination with its hardware.

[0216] It is understood that the memory in the embodiments of the present application may be a volatile memory or a non-volatile memory, or may include both volatile and non-volatile memory. Among them, the non-volatile memory may be a read-only memory (ROM), a programmable read-only memory (programmable ROM, PROM), an erasable programmable read-only memory (erasable PROM, EPROM), an electrically erasable programmable read-only memory (EEPROM) or a flash memory. The volatile memory may be a random access memory (RAM). It should be noted that the memory of the systems and methods described herein is intended to include, but is not limited to, these and any other suitable types of memory.

[0217] Those of ordinary skill in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this application.

[0218] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the aforementioned method implementation methods and will not be repeated here.

[0219] In the several embodiments provided in the present application, it should be understood that the disclosed systems, devices and methods can be implemented in other ways. For example, the device implementation described above is only schematic. For example, the division of units is only a logical function division. There may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0220] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the present embodiment.

[0221] In addition, each functional unit in each embodiment of the present application may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit.

[0222] If the function is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium, including a number of instructions for a computer device (which can be a personal computer, server, or network device, etc.) to perform all or part of the steps of each implementation method of the present application. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM), random access memory (RAM), disk or optical disk, etc., various media that can store program codes.

[0223] The above are only specific embodiments of the present application, but the protection scope of the present invention is not limited thereto. Any person skilled in the art who is familiar with the present technical field can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A method for calculating the ground state energy of a target system, characterized in that: The method comprises: Calculate the commutator between the Hamiltonian of the target system to be solved and the operators in the predefined operator pool; De-randomizing the commutator by a shadow tomography method to obtain an optimized commutator, wherein the optimized commutator includes fewer components than the components included in the commutator before optimization; The ground state energy of the system to be solved is determined according to the expected value of the optimized commutator.

2. The method according to claim 1, characterized in that Before calculating the commutator between the Hamiltonian of the target system to be solved and the operators in the predefined operator pool, the method further includes: Determining the single electron integral and the double electron integral according to the molecular structure of the target system to be solved; Determining coefficients of a monomer operator and a two-body operator in the Fermi Hamiltonian according to the single-electron integral and the two-electron integral to obtain the Fermi Hamiltonian of the target system to be solved, wherein the monomer operator and the two-body operator are determined according to the number of electron orbitals in the molecular structure; The Fermi Hamiltonian is converted to the Pauli Hamiltonian.

3. The method according to claim 1, characterized in that Before calculating the commutator between the Hamiltonian of the target system to be solved and the operators in the predefined operator pool, the method further includes: Each sub-operator obtained by decomposing the coupled cluster operator is placed into the operator pool to obtain a predefined operator pool; Each operator in the predefined operator pool is converted into a Pauli operator to obtain a predefined Pauli operator pool.

4. The method according to claim 1, characterized in that Before determining the ground state energy of the system to be solved according to the expected value of the optimized commutator, the method further includes: Run the variational quantum circuit at the current moment and measure the quantum state at the current moment; The expected value of the optimized commutator is determined according to the optimized commutator and the quantum state at the current moment.

5. The method according to claim 2, characterized in that: Determining the ground state energy of the system to be solved according to the expected value of the optimized commutator includes: Adding the operator corresponding to the largest expected value to the variational quantum circuit at the current moment to obtain the variational quantum circuit at the next moment; Taking the next moment as the current moment, and executing the step of running the variational quantum circuit at the current moment, and measuring the quantum state at the current moment; If the energy at the current moment determined according to the quantum state at the current moment converges, the energy at the current moment is used as the ground state energy of the system to be solved.

6. The method according to claim 5, characterized in that The method further comprises: If the energy at the current moment determined according to the quantum state at the current moment does not converge, the step of determining the expected value of the optimized commutator according to the optimized commutator and the quantum state at the current moment is performed.

7. The method according to any one of claims 4 to 6, characterized in that: The method further comprises: Determining the Hartree-Fock ground state of the target system to be solved; Constructing a coded quantum circuit for evolving a quantum state from a zero state to the Hartree-Fock ground state; The coded quantum circuit is used as a variational quantum circuit at an initial moment.

8. A device for calculating the ground state energy of a target system, characterized in that: include: A commutator calculation unit, used to calculate the commutator between the Hamiltonian of the target system to be solved and the operators in the predefined operator pool; A randomization unit, used for performing a de-randomization process on the commutator by a shadow tomography method to obtain an optimized commutator, wherein the optimized commutator includes fewer components than the components included in the commutator before optimization; The energy calculation unit is used to determine the ground state energy of the system to be solved according to the expected value of the optimized commutator.

9. An electronic device, characterized in that: include: Processor and memory; The processor is connected to a memory, wherein the memory is used to store a computer program, and the processor is used to call the computer program to execute the method according to claim 7.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, wherein the computer program includes program instructions, and when the program instructions are executed by a processor, the method according to claim 7 is performed.

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