Method for calculating ground state energy of target system and related device

Abstract

The embodiment of the application discloses a target system ground state energy calculation method and related device, the method comprises calculating the commutator of the Hamiltonian of a to-be-solved target system and an operator in a predefined operator pool; the commutator is randomized by a shadow tomography method, and an optimized commutator is obtained, the optimized commutator comprises fewer components than the commutator before optimization; and the ground state energy of the to-be-solved system is determined according to the size of the expected value of the optimized commutator. The embodiment of the application is beneficial to improving the calculation speed of the ground state energy of the target system and reducing the consumption of hardware resources.

Description

Technical Field

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

[0002] The variational quantum eigensolver (VQE) is an algorithm that uses a classical optimizer to train a parameterized quantum circuit to solve for the eigenvalues ​​and eigenvectors of a matrix. It is the earliest variational quantum algorithm. While representing and computing these eigenvalues ​​and eigenvectors on a classical computer requires storage space that increases exponentially with the size of the physical system, the computational resources consumed on a quantum computer increase polynomially with the size of the physical system. Due to this property, VQE is widely used to solve problems related to the ground state and low excitations of quantum systems in quantum chemistry.

[0003] Current variational quantum algorithms update the parameters in quantum circuits by solving for the gradient of the loss function (i.e., energy). This method requires precise energy calculation, which is the most time-consuming and hardware-intensive step in calculating the ground state energy of the target system. Summary of the Invention

[0004] This application provides a method and related apparatus for calculating the ground state energy of a target system, which helps to improve the calculation speed of the ground state energy of the target system and reduce the consumption of hardware resources.

[0005] The first aspect of this 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 and the operators in the predefined operator pool;

[0007] The commutator is derandomized using the shadow tomography method to obtain an optimized commutator, which contains fewer components than the unoptimized commutator.

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

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

[0010] The single-electron integral and two-electron integral are determined based on the molecular structure of the target system to be solved;

[0011] The coefficients of the monomer operator and the two-body operator in the Fermi-Hamiltonian are determined based on the single-electron integral and the two-electron integral, and the Fermi-Hamiltonian of the target system to be solved is obtained. 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 into the Pauli Hamiltonian.

[0013] Optionally, before calculating the Hamiltonian of the target system to be solved and the commutators of 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 the predefined operator pool;

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

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

[0017] Run the variable 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 based on the optimized commutator and the quantum state at the current moment.

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

[0020] Add the operator corresponding to the largest expected value to the variable quantum circuit at the current time step to obtain the variable quantum circuit at the next time step.

[0021] Using the next moment as the current moment, and executing the variable quantum circuit described in the steps for the current moment, the quantum state at the current moment is measured;

[0022] If the energy at the current moment, determined based on the quantum state at the current moment, converges, then the energy at the current moment is taken 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 based on the quantum state at the current moment, does not converge, then the step of determining the expected value of the optimized commutator based on the optimized commutator and the quantum state at the current moment is executed.

[0025] Optionally, the method further includes:

[0026] Determine the Hartley-Fock ground state of the target system to be solved;

[0027] Construct a coded quantum circuit for evolving a quantum state from state 0 to the Hartley-Fock ground state;

[0028] The encoded quantum circuit is used as a variable quantum circuit at the initial moment.

[0029] The second aspect of this application provides a device for calculating the ground state energy of a target system, comprising:

[0030] The commutator computation unit is used to calculate the commutator between the Hamiltonian of the target system and the operators in the predefined operator pool;

[0031] The randomization unit is used to derandomize the commutator using the shadow tomography method to obtain an optimized commutator, wherein the optimized commutator contains fewer components than the unoptimized commutator.

[0032] An energy calculation unit is used to determine the ground state energy of the system to be solved based on the magnitude of the expected value of the optimized commutator.

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

[0034] The processor is connected to a memory, wherein the memory is used to store computer programs and the processor is used to invoke the computer programs to execute the methods as described in the second aspect of the embodiments of this application.

[0035] A fourth aspect of this application provides a computer-readable storage medium storing a computer program, the computer program including program instructions, which, when executed by a processor, perform the method as described in the first aspect of this application.

[0036] As can be seen, the method and related apparatus for calculating the ground state energy of a target system provided in this application calculate the commutators of the Hamiltonian of the target system and the operators in a predefined operator pool. The ground state energy of the system is determined based on the expected value of the commutators. This transforms the existing method of updating parameters in a quantum circuit through precise calculation of the loss function into updating the quantum circuit structure and parameters by comparing the expected values ​​of the commutators. Since comparing the expected values ​​of the commutators does not require precise calculation, only knowing their magnitude is sufficient. Therefore, the commutators are derandomized using the shadow tomography method to obtain optimized commutators. The optimized commutators contain fewer components than the unoptimized commutators, thus omitting smaller contributing commutator components and enabling rapid comparison of commutator expected values, thereby improving the calculation speed of the target system's ground state energy. Similarly, omitting smaller contributing commutator components saves storage capacity during calculation and representation. Attached Figure Description

[0037] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0038] Figure 1 An example system block diagram is shown, illustrating a method for calculating the ground-state energy of a target system according to an embodiment of this application;

[0039] Figure 2 A flowchart illustrating a method for calculating the ground-state energy of a target system according to an embodiment of this application is shown.

[0040] Figure 3 A schematic diagram of the structure of a calculation device for the ground state energy of a target system provided in one embodiment of this application is shown;

[0041] Figure 4 A schematic diagram of the structure of a computer device provided in one embodiment of this application is shown. Detailed Implementation

[0042] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort 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 to drive the functions of a classical computer. If there are n bits of data, there are 2^n possible classical states, and one state is represented at a time.

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

[0045] Please refer to Figure 1 This illustrates an example system block diagram of a method for calculating the ground-state energy of a target system according to an embodiment of this application. System 100 may be a hybrid computing system comprising 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 implementation, the quantum system 110 and the classical computer 120 may be configured to communicate via one or more wired and / or wireless connections (e.g., wireless networks). The quantum system 110 may include a quantum chipset consisting of one or more quantum chips, comprising various hardware components for processing data encoded in qubits. The quantum chipset may be a quantum computing core surrounded by infrastructure to protect the quantum chips from electromagnetic noise sources, mechanical vibration sources, heat sources, and other noise sources that can degrade the performance of the quantum chips. The classical computer 120 may be electronically integrated with the 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 qubits to evolve and / or become entangled. Figure 1In the illustrated example embodiment, the quantum system 110 may include a measurement and control unit 111, an interface 112, and a quantum chip 113. In some embodiments, all or part of each of the measurement and control unit 111, interface 112, and quantum chip 113 may be located in a cryogenic environment to facilitate the performance of quantum operations. The quantum chip 113 may be any hardware capable of processing information using quantum states. This hardware may include multiple qubits and means for coupling or entanglement of the qubits 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 the qubits stored in a quantum register. The quantum gates may include one or more single-qubit gates, two-qubit gates, and / or other multi-qubit gates.

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

[0048] Interface 112 may be a classical-quantum interface, comprising a combination of devices capable of receiving instructions from the integrated measurement and control unit 111 and converting those instructions into a means for implementing quantum operations. In one embodiment, interface 112 may convert instructions from the integrated measurement and control unit 111 into drive signals capable of driving or manipulating qubits, and / or applying quantum gates to qubits. Additionally, interface 112 may be configured to convert signals received from the quantum chip 113 into digital signals capable of being processed and transmitted by the integrated measurement and control unit 111. Devices included in interface 112 may include, but are not limited to, digital-to-analog converters, analog-to-digital converters, waveform generators, attenuators, amplifiers, optical fibers, lasers, and filters. Interface 112 may further include circuitry configured to measure multiple qubits after the application of quantum gates, wherein the measurements may produce results represented in classical bits. Each measurement performed by interface 112 may be read out to a device connected to the quantum system 110, such as a classical computer 120. The multiple measurement results provided by interface 112 may represent probabilistic results.

[0049] The classical computer 120 can include hardware components such as a processor and storage devices (e.g., including memory devices and classical registers) for processing data encoded in classical bits. In one embodiment, the classical computer 120 can be configured to provide the quantum system 110 with various control signals, instructions, and data encoded in classical bits. Further, quantum states 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 states as classical bits in classical registers. In one embodiment, the classical computer 120 can be any suitable combination of computer-executable hardware and / or computer-executable software capable of executing the preparation module 121 to perform quantum computation using data stored in the data storage module 122 as part of the construction and computation. The data storage module 122 can be a repository for data to be analyzed using quantum computing algorithms and the results of that 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. Preparation module 121 can be instantiated as part of a larger algorithm, such as an application programming interface (API) function call, or by resolving hybrid classical-quantum computing into aspects of quantum and classical computing. For example, preparation module 121 can generate instructions for creating quantum circuits using quantum gates. In an embodiment, such instructions can be stored by the measurement and control unit 111 and can be instantiated by components of interface 112 to execute, enabling quantum operations of quantum gates to be performed on quantum chip 113.

[0050] The classic computer 120 may be a laptop computer, desktop computer, vehicle-integrated computer, smart mobile device, tablet device, and / or any other suitable classic computing device. Additionally or alternatively, the classic computer 120 may also operate 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 classic computer 120 may also reside in a cloud computing deployment model, such as a private cloud, community cloud, public cloud, or hybrid cloud.

[0051] Please refer to Figure 2 This document illustrates a flowchart of a method for calculating the ground-state energy of a target system according to an embodiment of this application. This method can be applied to computer devices, which refer to electronic devices capable of data calculation and processing. The method may include the following steps:

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

[0053] The Hamiltonian is a functional representation of the total energy of a system, with the system's generalized coordinates and generalized momentum as independent variables. The Hamiltonian operator acts on the wave function, as shown in the Schrödinger equation. The Schrödinger equation describes the change of the wave function over time. By solving the Schrödinger equation, we can obtain the specific form of the wave function and its corresponding energy, thus understanding the properties of the microscopic system.

[0054] The core problem in quantum chemistry lies in solving the Schrödinger equation. Generally, solving time-dependent Schrödinger equations is quite complex, hence the Born-Oppenheimer approximation (BO approximation) is introduced. The BO approximation assumes that the atomic nucleus has a much larger mass than the electron and a much lower velocity, thus allowing for the separation of these two variables. This leads to the following time-independent equation of electron motion, also known as the time-independent Schrödinger equation, with the following Hamiltonian:

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

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

[0057] The operator pool refers to a collection of candidate quantum gate operations used to construct quantum circuits. These operations are typically selected based on the specific requirements of the problem and may include, but are not limited to, single-qubit gates and two-qubit gates. During algorithm execution, elements from the operator pool may be added to or removed from the quantum circuit to adjust its structure and 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 Hamiltonian of the target system to be solved and the commutators of operators in the predefined operator pool, the method further includes:

[0060] The single-electron integral and two-electron integral are determined based on the molecular structure of the target system to be solved;

[0061] The coefficients of the monomer operator and the two-body operator in the Fermi-Hamiltonian are determined based on the single-electron integral and the two-electron integral, and the Fermi-Hamiltonian of the target system to be solved is obtained. 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 into the Pauli Hamiltonian.

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

[0064]

[0065] Generally, the Fermi-Hamiltonian of a molecular system consists of a monomer operator (in the form of "i+j") and a two-body operator (in the form of "i1+i2+j1j2"), where i, j, i1, i2, j1, and j2 are all orbital numbers. For example:

[0066] fermion={

[0067] 0+0:a

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

[0070] }

[0071] The above electronic integral results determine the coefficients a and b in the Fermi-Hamiltonian of the molecular system.

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

[0073]

[0074] Finally, the Fermi-Hamiltonian of this 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 Fermi Hamiltonian can be transformed into a Pauli Hamiltonian using methods such as the Jordan-Wigner transform, Parity transform, and Bravii-Kitaev transform. For example, using the Jordan-Wigner transform, the Pauli Hamiltonian of the above system takes the following form:

[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 Hamiltonian of the target system to be solved and the commutators of 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 the predefined operator pool;

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

[0113] Coupled cluster operators are an important method in quantum chemical calculations used to describe the wavefunctions 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 hydrogen molecule system mentioned above as an example, it has four spin orbitals: 0 and 1 (bonding orbitals) and 2 and 3 (antibonding orbitals). In the ground state, two electrons occupy the bonding orbitals 0 and 1. Since excitation does not change the electron spin state, 0 can only be excited to 2, and 1 can only be excited to 3. The corresponding singlet and doublet excitation operators are:

[0115]

[0116] in, The coefficients to be solved are... For generating and annihilating operators.

[0117] Will This constitutes an operator pool. This is only one embodiment provided in this application; it is conceivable that corresponding operators can also be obtained through decomposition using other operator theories.

[0118] Similarly, operators in the operator pool also need to be converted to Pauli operators, which can be done using the transformations described above. For example, consider only the double-excitation operator. Under this premise, 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 commutator coefficients mentioned above are all imaginary numbers. In actual calculations, we only take the imaginary part of the coefficients, that is:

[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: The commutator is derandomized using the shadow tomography method to obtain an optimized commutator, wherein the optimized commutator contains fewer components than the unoptimized commutator.

[0156] Shadow tomography is a novel technique in quantum information processing that allows us to efficiently estimate the output probability distribution of a quantum state under certain measurement settings without completely reconstructing the quantum state. Compared to traditional quantum state tomography, shadow tomography requires fewer copies of the quantum state and less time to obtain partial information about the quantum state. Specifically, the derandomization of the commutators using shadow tomography can be found in the paper "Efficient estimation of Pauli observables by derandomization" (Phys. Rev. Lett. 127, 030503 (2021)).

[0157] Take a two-bit Hamiltonian as an example:

[0158] P1 = {

[0159] "":1,

[0160] "X0 X1":1,

[0161] "X1":1,

[0162] "Z1":1,

[0163] "X0 Z1":,1

[0164] }

[0165] With the number of observations set to 200, after a derandomization process, a new Hamiltonian P2 can be obtained.

[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 based on the magnitude of the expected value of the optimized commutator.

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

[0172] Run the variable 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 based on the optimized commutator and the quantum state at the current moment.

[0174] Specifically, if the Hamiltonian of the target system is denoted by H, and the operators in the predefined operator pool are denoted by K... i If we represent that the commutative element is [H,K], then the commutative element is [H,K]. i ]; Run the variable quantum circuit at the current moment and measure the quantum state ψ at the current moment. (n) Then the expected value of the Yi Zi is <ψ (n) |[H,K i ]|ψ (n) >

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

[0176] Add the operator corresponding to the largest expected value to the variable quantum circuit at the current time step to obtain the variable quantum circuit at the next time step.

[0177] Using the next moment as the current moment, and executing the variable quantum circuit described in the steps for the current moment, the quantum state at the current moment is measured;

[0178] If the energy at the current moment, determined based on the quantum state at the current moment, converges, then the energy at the current moment is taken as the ground state energy of the system to be solved.

[0179] If the energy at the current moment, determined based on the quantum state at the current moment, does not converge, then the step of determining the expected value of the optimized commutator based on the optimized commutator and the quantum state at the current moment is executed.

[0180] Specifically, the energy at the current moment is determined based on the quantum state at the current moment, and the energy at the current moment is equal to the Hamiltonian acting on the quantum state at the current moment. Energy convergence refers to the process of energy gradually decreasing and tending to stabilize, which can be measured, for example, by precision or error.

[0181] Taking the operator {"X0 X1 X2 Y3":-0.125000} as an example, with an evolution time of 1 and a layer number of 1, the proposed circuit built based on this operator is as follows:

[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 also includes:

[0198] Determine the Hartley-Fock ground state of the target system to be solved;

[0199] Construct a coded quantum circuit for evolving a quantum state from state 0 to the Hartley-Fock ground state;

[0200] The encoded quantum circuit is used as a variable quantum circuit at the initial moment.

[0201] The initial quantum state is |ψ (0) > represents the Hartley-Fock ground state of the target system to be solved |ψ (HF) Therefore, the variable quantum circuit at the initial moment is encoded as |ψ (HF) The quantum circuit U(θ) initially does not include the variational parameter θ. Then, during the optimization iteration process, the variational quantum circuit U(θ) adaptively adds an operator, namely the aforementioned maximum expected value <ψ. (n) |[H,Ki ]|ψ (n) The corresponding operator K i During iteration, the energy decreases the fastest, meaning the derivative of energy with respect to θ is maximized. The derivative of energy with respect to θ is equal to... If the current time is k, then the quantum state at time k is...

[0202] in, Let |0> represent unoccupied orbitals, |1> represent occupied orbitals, and N be the number of electrons. A hydrogen molecule includes two occupied electrons; therefore, under the Jordan-Wigner transform, this is equivalent to applying two X gates to |00>.

[0203] As can be seen, the method and related apparatus for calculating the ground state energy of a target system provided in this application calculate the commutators of the Hamiltonian of the target system and the operators in a predefined operator pool. The ground state energy of the system is determined based on the expected value of the commutators. This transforms the existing method of updating parameters in a quantum circuit through precise calculation of the loss function into updating the quantum circuit structure and parameters by comparing the expected values ​​of the commutators. Since comparing the expected values ​​of the commutators does not require precise calculation, only knowing their magnitude is sufficient. Therefore, the commutators are derandomized using the shadow tomography method to obtain optimized commutators. The optimized commutators contain fewer components than the unoptimized commutators, thus omitting smaller contributing commutator components and enabling rapid comparison of commutator expected values, thereby improving the calculation speed of the target system's ground state energy. Similarly, omitting smaller contributing commutator components saves storage capacity during calculation and representation.

[0204] Figure 3 A schematic diagram of a device for calculating the ground-state energy of a target system according to an embodiment of this application is shown. The device includes:

[0205] The 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] Randomization unit 302 is used to derandomize the commutator using the shadow tomography method to obtain an optimized commutator, wherein the optimized commutator contains fewer components than the unoptimized commutator.

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

[0208] Figure 4The diagram illustrates the structure of a computer device according to an embodiment of this application, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the computer system function of the method for calculating the ground state energy of the target system in any of the above embodiments.

[0209] This application also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a computer, causes the computer to perform the functions of a computer system for calculating the ground-state energy of the target system in any of the above embodiments.

[0210] This application also provides a computer program product containing instructions that, when executed by a computer, cause the computer to perform the functions of the computer system of the method for calculating the ground state energy of the target system in any of the above embodiments.

[0211] It is understood that the specific examples in this application are only intended to help those skilled in the art better understand the implementation methods of this application, and are not intended to limit the scope of the invention.

[0212] It is understood that in the various embodiments of this application, the sequence number of each process does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not limit the implementation process of the embodiments of this application in any way.

[0213] It is understood that the various implementation methods described in this application can be implemented individually or in combination, and the implementation methods in this application are not limited in this respect.

[0214] Unless otherwise stated, all technical and scientific terms used in the embodiments of this application have the same meaning as commonly understood by one of ordinary skill in the art. The terminology used in this application is for the purpose of describing particular embodiments only and is not intended to limit the scope of this application. The term "and / or" as used in this application includes any and all combinations of one or more of the associated listed items. The singular forms "a," "the," and "the" as used in the embodiments of this application and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise.

[0215] It is understood that the processor in the embodiments of this application can be an integrated circuit chip with signal processing capabilities. During implementation, each step of the above method embodiments can be completed by the integrated logic circuits in the processor's hardware or by instructions in software form. The processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this application. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of this application can be directly embodied in the execution of a hardware decoding processor, or executed by a combination of hardware and software modules in the decoding processor. The software modules can be located in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory; the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method.

[0216] It is understood that the memory in the embodiments of this application may be volatile memory or non-volatile memory, or may include both volatile and non-volatile memory. Specifically, non-volatile memory may be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. Volatile memory may be random access memory (RAM). It should be noted that the memory in 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 skilled in the art will recognize that the units and algorithm steps of the various examples 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 implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

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

[0219] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the mutual coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.

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

[0221] In addition, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0222] If a function is implemented as 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 this application, in essence, or the part that contributes to the prior art, or 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 and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0223] The above are merely specific embodiments of this application, but the scope of protection of this invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this invention should be determined by the scope of the claims.

Claims

1. A method for calculating the ground state energy of a target system, characterized in that, The method includes: Calculate the commutator between the Hamiltonian of the target system and the operators in the predefined operator pool; The commutator is derandomized using the shadow tomography method to obtain an optimized commutator, which contains fewer components than the unoptimized commutator. Run the variable quantum circuit at the current moment and measure the quantum state at the current moment; The expected value of the optimized commutator is determined based on the optimized commutator and the quantum state at the current moment; Add the operator corresponding to the largest expected value to the variable quantum circuit at the current time step to obtain the variable quantum circuit at the next time step. Using the next moment as the current moment, and executing the variable quantum circuit described in the steps for the current moment, the quantum state at the current moment is measured; If the energy at the current moment, determined based on the quantum state at the current moment, converges, then the energy at the current moment is taken as the ground state energy of the system to be solved.

2. The method according to claim 1, characterized in that, Before calculating the Hamiltonian of the target system to be solved and the commutator of operators in the predefined operator pool, the method further includes: The single-electron integral and two-electron integral are determined based on the molecular structure of the target system to be solved; The coefficients of the monomer operator and the two-body operator in the Fermi-Hamiltonian are determined based on the single-electron integral and the two-electron integral, and the Fermi-Hamiltonian of the target system to be solved is obtained. 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 into the Pauli Hamiltonian.

3. The method according to claim 1, characterized in that, Before calculating the Hamiltonian of the target system to be solved and the commutator of 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 the predefined operator pool; Each operator in the predefined operator pool is converted into a Pauli operator to obtain the predefined Pauli operator pool.

4. The method according to claim 1, characterized in that, The method further includes: If the energy at the current moment, determined based on the quantum state at the current moment, does not converge, then the step of determining the expected value of the optimized commutator based on the optimized commutator and the quantum state at the current moment is executed.

5. The method according to any one of claims 1-4, characterized in that, The method further includes: Determine the Hartley-Fock ground state of the target system to be solved; Construct a coded quantum circuit for evolving a quantum state from state 0 to the Hartley-Fock ground state; The encoded quantum circuit is used as a variable quantum circuit at the initial moment.

6. A device for calculating the ground-state energy of a target system, characterized in that, include: The commutator computation unit is used to calculate the commutator between the Hamiltonian of the target system and the operators in the predefined operator pool; The randomization unit is used to derandomize the commutator using the shadow tomography method to obtain an optimized commutator, wherein the optimized commutator contains fewer components than the unoptimized commutator. An energy calculation unit is used to run the variable quantum circuit at the current moment, measure the quantum state at the current moment; determine the expected value of the optimized commutator based on the optimized commutator and the quantum state at the current moment; add the operator corresponding to the largest expected value to the variable quantum circuit at the current moment to obtain the variable quantum circuit at the next moment; take the next moment as the current moment, and execute the step of running the variable quantum circuit at the current moment to measure the quantum state at the current moment; if the energy at the current moment determined based on the quantum state at the current moment converges, then the energy at the current moment is taken as the ground state energy of the system to be solved.

7. 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 invoke the computer program to perform the method as described in any one of claims 1-5.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, the computer program including program instructions that, when executed by a processor, perform the method as described in any one of claims 1-5.

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