A method and device for determining a target system Hamiltonian

Abstract

The application discloses a method and device for determining a target system Hamiltonian, which comprises the following steps: firstly, determining a first Hamiltonian H of the target system, constructing a multi-bit quantum logic gate U, and generating a second Hamiltonian H' according to the first Hamiltonian H, wherein the second Hamiltonian H' satisfies the multi-bit quantum logic gate U, wherein j represents the number of quantum bits, X q(j) represents an operation operator acting on the jth quantum bit, τ j represents a Hamiltonian reduced in the conversion process from the first Hamiltonian to the second Hamiltonian, which can realize the representation of the Hamiltonian of the target system to be simulated by using a smaller number of quantum bits, thereby providing support for the calculation of the energy of the target system through quantum chemical simulation.

Description

Technical Field

[0001] This invention belongs to the field of quantum computing technology, specifically a method and apparatus for determining the Hamiltonian of a target system. Background Technology

[0002] A quantum computer is a physical device that performs high-speed mathematical and logical operations, stores and processes quantum information in accordance with the laws of quantum mechanics. When a device processes and calculates quantum information and runs quantum algorithms, it is a quantum computer. Because of its ability to process mathematical problems more efficiently than ordinary computers—for example, reducing the time to crack RSA keys from hundreds of years to hours—quantum computers have become a key technology under research.

[0003] Quantum computing simulation is a simulation program that uses numerical computation and computer science to simulate computations that follow the laws of quantum mechanics. As a simulation program, it uses the high-speed computing power of computers to characterize the spacetime evolution of quantum states based on the fundamental laws of quantum bits in quantum mechanics.

[0004] The Hamiltonian is a physical quantity related to the total energy of a target system. For some systems, time-evolution-based quantum circuits can be constructed to simulate them; previously, quantum circuits could be used to characterize the Hamiltonian in these systems. However, with the continuous improvement of quantum chemistry theory, the target systems to be simulated are becoming increasingly complex. For complex target systems that need to be studied, how to characterize the Hamiltonian of the target system using a relatively small number of qubits is particularly important for subsequent operations to determine the energy of the target system, and this has become an urgent problem to be solved. Summary of the Invention

[0005] The purpose of this invention is to provide a method and apparatus for determining the Hamiltonian of a target system, thereby overcoming the shortcomings of the prior art. It enables the characterization of the Hamiltonian of the target system to be simulated using a smaller number of qubits, providing support for calculating the energy of the target system through quantum chemical simulation, improving the calculation speed and accuracy, and promoting the further development of quantum chemical simulation applications.

[0006] One embodiment of this application provides a method for determining the Hamiltonian of a target system, the method comprising:

[0007] Determine the first Hamiltonian H of the target system;

[0008] Construct a multi-qubit quantum logic gate U, and generate a second Hamiltonian H′ based on the first Hamiltonian H, wherein the second Hamiltonian H′ satisfies The multi-bit quantum logic gate U satisfies Where j represents the number of the qubit, Xq(j) Let τ represent the operation operator performed on the j-th qubit. j This represents the Hamiltonian reduction during the transition from the first Hamiltonian to the second Hamiltonian.

[0009] Optionally, constructing the multi-bit quantum logic gate U includes:

[0010] A control pulse is generated based on the pulse parameters, the control pulse is adjusted iteratively through the pulse parameters, and the multi-bit quantum logic gate U is determined based on the adjusted control pulse.

[0011] One embodiment of this application provides a method for determining the energy of a target system based on Hamiltonian, the method comprising:

[0012] Obtain target system information, which includes electronic information and electron spin orbital information;

[0013] Based on the electronic information and electron spin orbital information, the Hartree Fock state in fermion form of the target system is obtained;

[0014] By using a pre-set encoding method, the Hartree Fock state in fermion form is encoded onto a qubit to obtain a quantum state in Pauli operator form;

[0015] The energy of the target system is calculated using the second Hamiltonian as described in the preceding claims, the quantum state in the form of the Pauli operator, and the evolution wave function.

[0016] Optionally, if the number of spin orbitals of the target system is N, the dimension of the second Hamiltonian matrix is ​​(2^N). N -2), and the number of qubits used for encoding is (N-2).

[0017] Optionally, after obtaining the Hartree Fock state in fermionic form of the target system, the method further includes:

[0018] The experimental state of the target system is obtained based on the Hartree Fock state in the fermionic form of the target system.

[0019] Optionally, obtaining the experimental state of the target system based on the Hartree Fock state of the fermionic form of the target system includes:

[0020] According to the pre-selected scheme, the Hartree Fock state is evolved to obtain the evolved quantum state as the test state of the target system.

[0021] Optionally, the step of evolving the Hartree Fock state according to a pre-selected hypothetical method to obtain the evolved quantum state as the experimental state of the target system includes:

[0022] Based on the pre-selected scheme and the Hartree Fock state, calculate the cluster operator in fermionic form of the target system;

[0023] Select a mapping method and transform the target system's fermion-form cluster operators into Pauli-form cluster operators;

[0024] The cluster operator in the form of the Pauli operator is decomposed into the corresponding unitary operator and evolved to obtain the evolved quantum state as the test state of the target system to be solved.

[0025] Another embodiment of this application provides a device for determining the Hamiltonian of a target system, the device comprising:

[0026] The determination module is used to determine the first Hamiltonian H of the target system;

[0027] The generation module is used to construct a multi-bit quantum logic gate U, and generate a second Hamiltonian H′ based on the first Hamiltonian H, wherein the second Hamiltonian H′ satisfies The multi-bit quantum logic gate U satisfies Where j represents the number of the qubit, X q(j) Let τ represent the operation operator performed on the j-th qubit. j This represents the Hamiltonian reduction during the transition from the first Hamiltonian to the second Hamiltonian.

[0028] Optionally, the generation module includes:

[0029] An adjustment unit is used to generate control pulses based on pulse parameters, adjust the control pulses iteratively through the pulse parameters, and determine the multi-bit quantum logic gate U based on the adjusted control pulses.

[0030] One embodiment of this application provides a device for determining the energy of a target system based on Hamiltonian, the device comprising:

[0031] The first acquisition module is used to acquire target system information, which includes electronic information and electron spin orbital information.

[0032] The second acquisition module is used to obtain the Hartree Fock state of the fermion form of the target system based on the electronic information and the electron spin orbital information;

[0033] The encoding module is used to encode the Hartree Fock state in fermion form onto a quantum bit using a pre-set encoding method, so as to obtain a quantum state in Pauli operator form;

[0034] The computation module is used to calculate the energy of the target system using the second Hamiltonian as described in the preceding claims, the quantum state in the form of the Pauli operator, and the evolution wave function.

[0035] Optionally, after the second obtaining module, the device further includes:

[0036] The third acquisition module is used to obtain the experimental state of the target system based on the Hartree Fock state in the fermionic form of the target system.

[0037] Optionally, the third obtaining module includes:

[0038] An evolution unit is used to evolve the Hartree Fock state according to a pre-selected scheme, and obtain the evolved quantum state as the test state of the target system.

[0039] Optionally, the evolutionary unit includes:

[0040] The computational subunit is used to calculate the cluster operator in the fermion form of the target system according to the pre-selected scheme and the Hartree Fock state;

[0041] The transformation subunit is used to select the mapping method and transform the cluster operator in the form of fermions of the target system into a cluster operator in the form of Pauli operators;

[0042] The decomposition subunit is used to decompose the cluster operator in the form of the Pauli operator into the corresponding unitary operator form and evolve it to obtain the evolved quantum state as the test state of the target system to be solved.

[0043] One embodiment of this application provides a storage medium storing a computer program, wherein the computer program is configured to execute the method described in any of the above descriptions when it is run.

[0044] One embodiment of this application provides an electronic device including a memory and a processor, wherein the memory stores a computer program and the processor is configured to run the computer program to perform the method described in any of the above-described embodiments.

[0045] Compared with existing technologies, this invention first constructs a multi-qubit quantum logic gate and generates a second Hamiltonian based on the first Hamiltonian of the target system. Then, based on the electronic information and electron spin orbital information of the target system, it obtains the Hartree Fock state in fermion form. Through a pre-set encoding method, the Hartree Fock state in fermion form is encoded onto the qubits to obtain the quantum state in Pauli operator form. Finally, the energy of the target system is calculated using the second Hamiltonian, the quantum state in Pauli operator form, and the evolution wave function. It can characterize the Hamiltonian of the target system to be simulated using a smaller number of qubits, providing support for calculating the energy of the target system through quantum chemical simulation, improving the calculation speed and accuracy, and promoting the further development of quantum chemical simulation applications. Attached Figure Description

[0046] Figure 1 This is a system network diagram of a method for determining the Hamiltonian of a target system provided in an embodiment of the present invention;

[0047] Figure 2 This is a flowchart illustrating a method for determining the Hamiltonian of a target system provided in an embodiment of the present invention;

[0048] Figure 3 This is a flowchart illustrating a method for determining the energy of a target system based on Hamiltonian, provided in an embodiment of the present invention.

[0049] Figure 4 This is a schematic diagram of a quantum circuit for constructing a Hartree Fock state provided in an embodiment of the present invention;

[0050] Figure 5 This is a schematic diagram of a quantum circuit structure corresponding to a proposed method;

[0051] Figure 6 This is a schematic diagram of the structure of a device for determining the Hamiltonian of a target system provided in an embodiment of the present invention;

[0052] Figure 7 This is a schematic diagram of a device for determining the energy of a target system based on Hamiltonian, provided in an embodiment of the present invention. Detailed Implementation

[0053] The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0054] The present invention first provides a method for determining the Hamiltonian of a target system. This method can be applied to electronic devices, such as computer terminals, specifically ordinary computers, quantum computers, etc.

[0055] The following detailed explanation uses a computer terminal as an example. Figure 1 This is a system network block diagram of a method for determining the Hamiltonian of a target system provided in an embodiment of the present invention. The system applied to the method for determining the Hamiltonian of a target system may include a network 110, a server 120, a wireless device 130, a client 140, a storage unit 150, a classical processing system 160, a quantum processing system 170, and may also include additional memory, a classical processor, a quantum processor, and other devices not shown.

[0056] Network 110 is a medium that provides communication links between various devices and computers connected together in a system network for the determination method of the Hamiltonian of the target system. It includes, but is not limited to, the Internet, corporate intranets, local area networks, mobile communication networks and combinations thereof. The connection method can be wired, wireless communication links or fiber optic cables, etc.

[0057] Server 120 and client 140 are conventional data processing systems that may contain data and applications or software tools that perform conventional computational processes. Client 140 may be a personal computer or a network computer, so the data may also be provided by server 120. Wireless device 130 may be a smartphone, tablet, laptop, smart wearable device, etc. Storage unit 150 may include database 151, which can be configured to store data such as qubit parameters, quantum logic gate parameters, quantum circuits, and quantum programs.

[0058] The classical processing system 160 (quantum processing system 170) may include a classical processor 161 (quantum processor 171) for processing classical data (quantum data) and a memory 163 (memory 172) for storing classical data (quantum data). The classical data (quantum data) may be a boot file, an operating system image, and an application program 162 (application program 173). The application program 162 (application program 173) may be used to implement a quantum algorithm compiled according to the method for determining the target system Hamiltonian provided in the embodiments of the present invention.

[0059] Any data or information stored or generated in the classical processing system 160 (quantum processing system 170) can also be configured to be stored or generated in another classical (quantum) processing system in a similar manner, and any application executed therein can also be configured to be executed in another classical (quantum) processing system in a similar manner.

[0060] It should be noted that a true quantum computer has a hybrid structure, which includes at least... Figure 1 The system consists of two main parts: the classical processing system 160, which is responsible for performing classical calculations and control; and the quantum processing system 170, which is responsible for running quantum programs and thus realizing quantum computing.

[0061] The aforementioned classical processing system 160 and quantum processing system 170 can be integrated into a single device or distributed across two different devices. For example, the first device, including the classical processing system 160, runs a classical computer operating system that provides quantum application development tools and services, as well as the storage and network services required for quantum applications. Users develop quantum applications using the quantum application development tools and services on the second device and send the quantum program to the second device, including the quantum processing system 170, via the network services. The second device runs a quantum computer operating system, which parses the code of the quantum program and compiles it into instructions that can be recognized and executed by the quantum computer control system. The quantum processor 170 then implements the quantum algorithm corresponding to the quantum program based on these instructions.

[0062] In the classic silicon-based processing system 160, the units of the classic processor 161 are CMOS transistors. These computing units are not limited by time or coherence; that is, they are available at any time without time constraints. Furthermore, the number of these computing units in a silicon chip is sufficient; currently, a classic processor contains tens of thousands of computing units. The sufficient number of computing units and the fixed selectable computing logic of the CMOS transistors, such as AND logic, allow for computational efficiency through a combination of numerous CMOS transistors and limited logic functions.

[0063] Unlike the logic units in the classical processing system 160, the basic computational unit of the quantum processor 171 in the quantum processing system 170 is the qubit. The input of a qubit is limited by coherence and coherence time; that is, a qubit is limited by its available usage time and is not always readily available. Making full use of qubits within their available usage time is a key challenge in quantum computing. Furthermore, the number of qubits in a quantum computer is one of the representative indicators of its performance. Each qubit performs computational functions through on-demand configured logic functions. Given the limited number of qubits and the diverse logic functions available in quantum computing, such as Hadamard gates (H gates), Pauli-X gates (X gates), Pauli-Y gates (Y gates), Pauli-Z gates (Z gates), X gates, RY gates, RZ gates, CNOT gates, CR gates, iSWAP gates, Tofoli gates, etc., quantum computing requires combining a limited number of qubits with diverse combinations of logic functions to achieve computational effects.

[0064] Based on these differences, the design of logical functions applied to qubits (including the design of whether qubits are used and the design of the efficiency of each qubit) is crucial to improving the computational performance of quantum computers and requires specialized design. The aforementioned design of qubits is a technical problem that ordinary computing devices do not need to consider or address. In this application, as quantum chemistry theory continues to improve, the target systems to be simulated are becoming increasingly complex. For complex target systems to be studied, how to characterize the Hamiltonian of the target system using a smaller number of qubits is particularly important for subsequent operations to determine the energy of the target system, which has become a problem urgently needing to be solved. This application provides a method and apparatus for determining the Hamiltonian of a target system to overcome the shortcomings of existing technologies. It enables the characterization of the Hamiltonian of the target system using a smaller number of qubits, providing support for calculating the energy of the target system through quantum chemical simulation, improving computational speed and accuracy, and promoting the further development of quantum chemical simulation applications.

[0065] See Figure 2 , Figure 2 This is a flowchart illustrating a method for determining the Hamiltonian of a target system provided in an embodiment of the present invention.

[0066] This embodiment provides an example of a method for determining the Hamiltonian of a target system, the method of which may include:

[0067] S201: Determine the first Hamiltonian H of the target system.

[0068] Specifically, the target system can be considered as the molecular structure model that the user wants to simulate the ground state energy of, including, for example, the number of electrons that make up the molecule, the type of electrons, and the spin orbital information of the electrons.

[0069] The Hamiltonian is a physical concept in classical mechanics. In quantum mechanics, classical physical quantities are transformed into corresponding operators, and the Hamiltonian corresponds precisely to the Hamiltonian operator. The Hamiltonian can be understood as the sum of the kinetic energies of all particles in a target system plus the potential energy of particles associated with the target system. The Hamiltonian differs for different situations or numbers of particles because it includes the sum of the particle kinetic energies and the potential energy function corresponding to that situation, generally denoted by H.

[0070] In quantum mechanics, all measurable mechanical quantities can be described by a Hermitian matrix. A Hermitian matrix is ​​defined as the matrix itself, where its transpose and conjugate are equal.

[0071]

[0072] Such matrices are usually called measurement operators. Non-zero operators will have at least one non-zero eigenvalue λ and a corresponding eigenstate |ψ>.

[0073] H|ψ>=λ|ψ>

[0074] If the eigenvalues ​​of the operator H correspond to the energy level distribution of a certain system, then such an operator can also be called a Hamiltonian, that is, the first Hamiltonian described in this application.

[0075] S202: Construct a multi-qubit quantum logic gate U, and generate a second Hamiltonian H′ based on the first Hamiltonian H, wherein the second Hamiltonian H′ satisfies The multi-bit quantum logic gate U satisfies Where j represents the number of the qubit, X q(j) Let τ represent the operation operator performed on the j-th qubit. j This represents the Hamiltonian reduction during the transition from the first Hamiltonian to the second Hamiltonian.

[0076] Specifically, constructing the multi-bit quantum logic gate U may include:

[0077] A control pulse is generated based on the pulse parameters, the control pulse is adjusted iteratively through the pulse parameters, and the multi-bit quantum logic gate U is determined based on the adjusted control pulse.

[0078] In one optional implementation, a corresponding control pulse can be generated based on the set pulse parameters, and the entanglement capacity of a multi-bit quantum gate can be generated by applying the control pulse. Therefore, a multi-bit quantum gate with high entanglement capacity can be obtained by iteratively adjusting the pulse parameters. Furthermore, based on the pulse parameters, the entanglement capacity of the multi-bit quantum gate can be transformed into an optimizable objective function. By iteratively optimizing the pulse parameters, a control pulse capable of generating a multi-bit quantum gate with high entanglement capacity can be obtained, thereby obtaining a multi-bit quantum logic gate U with high entanglement capacity.

[0079] The generation of the second Hamiltonian H′ based on the first Hamiltonian H mainly utilizes a symmetric qubit reduction method. The main idea is to find v multi-qubit quantum logic gates U to convert the first Hamiltonian H into the second Hamiltonian H′. The second Hamiltonian H′ has the same eigenvalues ​​as the first Hamiltonian H, and the second Hamiltonian H′ satisfies... Make each μ in the second Hamiltonian i The terms are negligible across a set of qubits, thus allowing the number of qubits to be gradually reduced from the second Hamiltonian, where, It is the transpose conjugate of the multi-bit quantum logic gate U.

[0080] For example, when H′=Z0X1-X1+Y0X1, all terms in the second Hamiltonian H′ can act on the second qubit (the qubit with subscript 1 in the above formula). This proves that each term in the second Hamiltonian H′ is commutative with I0X1, and the ground state eigenvector of the second Hamiltonian H′ is also the eigenvector of I0X1, with eigenvalues ​​of ±1. Therefore, the second Hamiltonian H′ can be expressed as:

[0081] H′=(Z0I1-I0I1+Y0I1)I0X1

[0082]

[0083] in, It can be understood as the eigenvector of the second Hamiltonian H′.

[0084] In another alternative implementation, by constructing a multi-qubit quantum logic gate U, each μ... i The terms and Pauli-X gates act together on qubit j to ensure that each term of the resulting second Hamiltonian H′ is exchanged with each Pauli-X quantum logic gate applied to the j-th qubit, satisfying [H′, X... q(j) Since ] = 0, the eigenvector of the second Hamiltonian H′ obtained after the transformation is also the eigenvector of each X. q(j) The eigenvectors of the operator. It should be noted that the operator can be understood as an operator composed of matrix gates.

[0085] As can be seen, this application first determines the first Hamiltonian H of the target system, then constructs a multi-qubit quantum logic gate U, and finally generates the second Hamiltonian H′ based on the first Hamiltonian H. The second Hamiltonian H′ satisfies The multi-bit quantum logic gate U satisfies Where j represents the number of the qubit, X q(j) Let τ represent the operation operator performed on the j-th qubit. j This represents the reduced Hamiltonian during the transition from the first Hamiltonian to the second Hamiltonian. It enables the characterization of the Hamiltonian of the target system to be simulated using a smaller number of qubits, providing support for calculating the energy of the target system through quantum chemical simulation.

[0086] See Figure 3 , Figure 3 This is a flowchart illustrating a method for determining the energy of a target system based on Hamiltonian, provided in an embodiment of the present invention.

[0087] This embodiment provides an example of a method for determining the energy of a target system based on Hamiltonian. The method for determining the energy of a target system based on Hamiltonian may include:

[0088] S301: Obtain target system information, which includes electronic information and electron spin orbital information.

[0089] Specifically, an electron is a fundamental particle, generally referring to the number of electrons outside the nucleus in a target system; electron spin orbital information is a mathematical description of the probability of finding an electron in a specific space outside the atomic nucleus in the target system, and indicates the possible position of the electron in three-dimensional space. It should be noted that the electron information of the target system can include alpha and beta electrons, and the number of spin orbitals in the target system is N.

[0090] S302: Based on the electronic information and electron spin orbital information, obtain the Hartree Fock state in the fermion form of the target system.

[0091] For example, see Figure 4 , Figure 4 This is a schematic diagram of a quantum circuit for constructing a Hartree Fock state according to an embodiment of the present invention. For the hydrogen molecule target system, it is only necessary to add a NOT gate to each of the two qubits to initialize |0000> to |0101> in the quantum circuit.

[0092] Taking the target system as a hydrogen molecule as an example, it contains four single-electron spin molecular orbitals and two electrons. Based on the number of electrons and electron spin orbital information of the hydrogen molecule, if one quantum bit represents one electron spin orbital, that is, 0 represents an empty orbital and 1 represents an occupied orbital, the Hartree-Fock state of the hydrogen molecule target system can be represented by the quantum state |0101>.

[0093] In an optional implementation, after obtaining the Hartree Fock state in the fermionic form of the target system, the method may further include:

[0094] The experimental state of the target system is obtained based on the Hartree Fock state in the fermionic form of the target system.

[0095] Specifically, the experimental state of the target system can be obtained by evolving the HartreeFock state according to a pre-selected simulation method, and the evolved quantum state can be used as the experimental state of the target system.

[0096] Step 1: Calculate the cluster operator in fermionic form of the target system according to the pre-selected scheme and the Hartree Fock state.

[0097] Specifically, cluster operators can be understood as a type of artificially defined operator used to represent the jumping of electrons in orbitals. Let's assume a pre-prepared initial molecular state, such as |ψ> Hartree-Fock The method for evolving to quantum circuits can be pre-selected as the coupled cluster (CC) approach. This is a method that starts from Hartree Fock molecular orbitals and obtains the experimental state |ψ> through simulation. Here, the simulation is the exponential coupled cluster operator e. T Satisfying: |ψ>=e T |ψ> Hartree-Fock In this hypothesis, T represents the N-electron cluster operator, defined as the sum of several excitation operators, i.e.:

[0098] T = T1 + T2 + ... + T N

[0099] Where T1 is the single-particle excitation operator, T2 is the two-particle excitation operator, and the remaining terms follow the same pattern. Since the probability of triple and quadruple excitations occurring in a multi-electron system is very small, a "truncation" is usually performed at the double excitation point, ultimately leaving only the T1 and T2 terms, i.e.:

[0100] T = T1 + T2

[0101] in, To create an operator, a r a s Here, p, q, r, and s represent annihilation operators, and the undetermined coefficient t represents the orbital. pq t pqrs Parameters that need to be found by the optimizer satisfy

[0102] It is important to note that after transforming the initial state of the target system into a cluster operator in fermionic form through a hypothetical method, due to e T Exponentially coupled cluster operators are not unitary operators, therefore e cannot be directly used. T The exponentially coupled cluster operator is mapped onto the qubit using a predefined mapping method, but it cannot construct the corresponding quantum circuit. Therefore, it is necessary to construct a unitary operator version of the exponentially coupled cluster operator, namely the unitary coupled cluster (UCC) operator.

[0103] For example, it can first be defined Where T = ∑ i T i ,and It should be noted that if the cluster operator T in UCC contains only the term T1, then this is called a single-excitation coupled cluster (UCCS); if the cluster operator T in UCC contains both T1 and T2, then this is called a single-double-excitation coupled cluster (UCCSD).

[0104] Correspondingly, for UCCS and UCCSD, it is assumed that the corresponding quantum circuits are the same, for example, as follows: Figure 5 As shown, Figure 5 This is a schematic diagram of a quantum circuit structure corresponding to a proposed method, specifically a four-qubit quantum circuit diagram corresponding to the UCC method. The diagram shows a quantum circuit diagram of 4 qubits q0, q1, q2, and q3, where X -π / 2 X π / 2 This represents the X gate and Y gate with parameters of -π / 2 and π / 2 respectively. Similarly, icon ① and its connection to the solid line represent the CNOT gate and Z gate. θ This represents a Z-gate with parameter θ. The proposed principle can include: a proposed formula, for example, the matrix operator U(θ) corresponding to a quantum circuit. For UCC, the corresponding proposed formula is:

[0105]

[0106] in, This is the hypothetical scenario, where Pi is the generator.

[0107] For example, for describing the hydrogen molecule, |0011> Hartree-Fock State, that is

[0108] When T = T1, it is the Hamiltonian constructed by the first four single excitations; when T = T1 + T2, it is the Hamiltonian constructed by the single excitation and double excitation.

[0109] Step 2: Select the mapping method and transform the cluster operator in the form of fermions of the target system into a cluster operator in the form of Pauli operators.

[0110] Step 3: Decompose the cluster operator in the form of the Pauli operator into the corresponding unitary operator and evolve it to obtain the evolved quantum state as the experimental state of the target system to be solved.

[0111] For example, when transforming fermionic cluster operators into Pauli operator forms using the Jordan-Wigner transform, it is necessary to introduce the asymptotic approximation theorem, namely the Trotter formula, which is the core of quantum simulation algorithms: lim n→∞ (e iAt / n e iBt / n )n=e i(A+B)t, where A and B are Hermitian operators, t is a real number, and n is a positive integer.

[0112] It should be noted that, using Todd's formula, an exponential function can be decomposed into several sub-exponential function terms. Todd's decomposition emphasizes the tendency for the larger n is, the closer it is to the original expression, rather than considering the specific value of n.

[0113] For example, suppose After the Jordan-Wigner transform, we can see that:

[0114]

[0115]

[0116]

[0117] Where X represents the Pauli-X gate, Y represents the Pauli-Y gate, Z represents the Pauli-Z gate, and the subscripts indicate the qubit numbers of each quantum logic gate.

[0118] S303: The Hartree Fock state in fermion form is encoded onto a qubit using a pre-set encoding method to obtain a quantum state in Pauli operator form.

[0119] Specifically, we can first determine N qubits and then use a pre-set encoding method to transform the Hartree Fock state in fermion form into the Hilbert space in Pauli operator form, so that each fermion state can be represented by a quantum state.

[0120] The electronic information of the target system includes α electrons and β electrons, and the quantum state in the form of the Pauli operator can be represented in the following form:

[0121]

[0122] p is the spin orbital number of the α or β electron, and M is the number of spin orbitals of the α or β electron.

[0123] For example, from the Jordan-Wigner mapping to the Parity transform or the Bravyi-Kitaev mapping, because the number of electrons and spin electrons in the target system are conserved—and this is true for any Slater determinant that preserves the number of α electrons—it is clear that the ground state is simply a linear combination of Slater determinants. Furthermore, since calculating the ground state energy can essentially be viewed as a problem of electron distribution among orbitals, this information can be used to simplify the calculation. Specifically, if the expected occupancy of an orbital is close to 0 or 1, it can be removed from the calculation. Therefore, the calculation is simplified to include only the most important orbitals; this is known as performing the calculation of the target system's energy in a reduced active space.

[0124] For example, the Slater determinant of the Jordan-Wigner transform can be expressed as:

[0125]

[0126]

[0127] In one alternative implementation, the pre-set encoding method can be one of Jordan-Wigner transform, Parity transform, Bravyi-Kitaev transform, and SegmentParity transform.

[0128] S304: Calculate the energy of the target system using the second Hamiltonian, the quantum state in the form of the Pauli operator, and the evolution wave function.

[0129] In quantum computing, the selection of the wavefunction requires a reference wavefunction as a basis vector. For example, in quantum chemistry, the Hartree Fock state vector is generally used as the reference wavefunction to satisfy:

[0130] ψ(θ)=U(θ)|ψ> Hartree-Fock

[0131] Where ψ(θ) represents the wavefunction corresponding to a set of parameters θ, and U(θ) represents the matrix operator corresponding to a set of parameters θ. (Refer to the wavefunction |ψ>) Hartree-Fock In chemistry, this corresponds to the Hartree Fock ground state, which means that all the electrons in the molecule are in their lowest orbitals.

[0132] In one alternative implementation, when the wavefunction is generated, it is necessary to measure the expected value of the second Hamiltonian. The target system's second Hamiltonian in the quadratic quantization method can be mapped to a linear combination of local Pauli operator products through a predetermined transformation. The expected value of the quadratic quantization operator must be equivalent to the expected value of the corresponding first-order quantization operator. Since the first-order quantization operator maintains the same number of electrons, the quadratic quantization operator must contain an equal number of production and annihilation operators. Thus, the quadratic quantization form of the electronic second Hamiltonian can be obtained using these requirements:

[0133]

[0134] It should be noted that the existence of symmetry allows users to restrict the simulation to the characteristic space of symmetric operators, thereby reducing the number of qubits required to encode the fermionic system. In the JW and BK encoding methods, the number of qubits is equal to the number of spin orbitals N considered. However, due to the symmetry of the molecular Hamiltonian, the wavefunction can be stored in a smaller Hilbert space, thus achieving simplification. Therefore, by using a pre-defined encoding method, the dimension of the Hamiltonian matrix of the target system can be reduced to 2. N -2, and the number of qubits used for encoding can also be reduced to N-2.

[0135] In one alternative implementation, calculating the energy of the target system using the second Hamiltonian, the quantum state in the form of the Pauli operator, and the evolution wave function may include:

[0136] Step a: Obtain the fermion Hamiltonian corresponding to the target system, and transform the fermion Hamiltonian corresponding to the target system into the Pauli Hamiltonian of the target system.

[0137] Specifically, based on the second Hamiltonian, obtaining the fermion Hamiltonian corresponding to the target system requires the use of a creation operator. and annihilation operator a q To achieve this, they satisfy the opposition to easy relations.

[0138] For example, for the hydrogen molecule system, the corresponding fermion Hamiltonian is:

[0139]

[0140] It's important to note that in quantum computing, the fermionic form of the Hamiltonian cannot be directly derived in a circuit. Therefore, a process is needed to convert the integral expectation value into a form readable by the quantum circuit; this process is called mapping. It's crucial to understand that mapping merely changes the form of the Hamiltonian; the system energy information represented by different types of Hamiltonians is equivalent. Furthermore, for a quantum simulation circuit or a real quantum chip, Pauli operators are easier to manipulate and generate. Therefore, the fermionic Hamiltonian corresponding to the target system can be transformed into the Pauli Hamiltonian of the target system, facilitating subsequent simulation operations.

[0141] Following the example above, for the hydrogen molecule system, its corresponding fermion Hamiltonian is transformed into the Pauli Hamiltonian as follows:

[0142]

[0143] Step b: Based on the sub-terms of the Pauli Hamiltonian decomposition of the target system, construct the quantum circuits corresponding to each sub-term of the Pauli Hamiltonian of the target system.

[0144] Specifically, obtain the experimental state |ψ of the target system. n After that, it is necessary to start using the quantum expectation estimation algorithm to calculate the experimental state |ψ n >Expectation on the molecular Hamiltonian. The so-called quantum expectation estimate refers to the fact that the Hamiltonian H′ of multi-electron systems, Heisenberg models, and Iesing models can be expanded into a sum of multiple sub-terms, i.e.:

[0145]

[0146] Where h is a real number, σ is the Pauli operator, α, β and γ ∈ (X, Y, Z, I), and i, j and k represent the subspaces in which the Hamiltonian quantum terms operate.

[0147] Since the observables are linear, the average energy of the system can be calculated using the following formula:

[0148] E = <ψ * |H′|ψ>

[0149] Where, ψ * Since ψ is orthogonal and uniform, the right side of the equation can also be expanded into this form:

[0150]

[0151] Therefore, we can obtain the average energy E of the system by first calculating the expectation of each sub-term and then summing the expectations. It should be noted that the measurement of the expectation of each sub-term can be performed on a quantum processor, while a classical processor can handle the summation of the expectations.

[0152] For example, the Hamiltonian of a certain system is H′, which can ultimately be expanded into this form:

[0153]

[0154] In this formula, all sub-term coefficients h are 1, and it is assumed that the obtained experimental state is of the following form:

[0155] |ψ>=a|00>+b|01>+c|10>+d|11>

[0156] Among them, a 2 b 2 c 2 d 2 These refer to the probabilities P of collapsing to |00>, |01>, |10>, and |11> when measuring the experimental state. S By applying the Hamiltonian's sub-terms H′1, H′2, and H′3 to the experimental state, we can obtain the expected values ​​E1, E2, and E3 in sequence, specifically:

[0157] E1=<ψ * |H′1|ψ>

[0158] E2=<ψ * |H′2|ψ>

[0159] E3=<ψ * |H′3|ψ>

[0160] Taking E1, E2, and E3 as examples, for the desired E1, the coefficient h is the desired value, and there is no need to construct a circuit for measurement. For the expected value E2, its Hamiltonian is Because the measurement operation is in σ Z Above (with σ) Z The measurement is performed on the eigenvectors of the qubits (which are subspaces formed by the basis vectors), so it is only necessary to add a measurement gate to the qubits and then pass the measurement results to a classical processor for summation.

[0161] Step c: Measure the energy expectation of the experimental state using the quantum circuits corresponding to each subterm of the Pauli Hamiltonian of the target system.

[0162] Specifically, by expanding the measurement circuit of each sub-term expectation of the Pauli Hamiltonian of the target system, the measurement circuit of each sub-term expectation E(i) can be obtained. Then, the quantum processor transmits E(i) to the classical processor in sequence for summation, and the energy expectation of the target system in the experimental state is obtained.

[0163] It should be noted that, since the measurement operation is performed at σ Z The above is performed, for those containing σ x σ y The Hamiltonian cannot be directly measured at this point; it requires the determination of σ. x and σ y Performing a basis change operation, that is, letting the experimental state evolve again, due to σ x =H′×σ Z ×H′, That is, for σ x and σ y Before measurement, Hadamard gates and gates need to be added to the corresponding qubits respectively. The gate is then used to sum the measurement results, which are then passed to a classical processor.

[0164] It should be emphasized that the above-mentioned design methods, mapping methods and optimization methods are merely examples and do not constitute a limitation on the present invention. For example, design methods also include HE (Hardware Efficient) and SP (Symmetry Preserved) methods.

[0165] As can be seen, this embodiment first obtains the target system information. Based on the electronic information and electron spin orbital information in the target system information, the Hartree Fock state in fermion form of the target system is obtained. Through a pre-set encoding method, the Hartree Fock state in fermion form is encoded onto a qubit to obtain the quantum state in Pauli operator form. Finally, the energy of the target system is calculated using the second Hamiltonian, the quantum state in Pauli operator form, and the evolution wave function. This can provide support for the realization of quantum chemical simulation calculation of the energy of the target system, improve the calculation speed and accuracy, and promote the further development of quantum chemical simulation applications.

[0166] See Figure 6 , Figure 6 This is a schematic diagram of the structure of a device for determining the Hamiltonian of a target system provided in an embodiment of the present invention. Figure 2 Corresponding to the process shown, the apparatus includes:

[0167] Module 601 is used to determine the first Hamiltonian H of the target system;

[0168] Generation module 602 is used to construct a multi-bit quantum logic gate U, and generate a second Hamiltonian H′ based on the first Hamiltonian H, wherein the second Hamiltonian H′ satisfies The multi-bit quantum logic gate U satisfies Where j represents the number of the qubit, X q(j) Let τ represent the operation operator performed on the j-th qubit. j This represents the Hamiltonian reduction during the transition from the first Hamiltonian to the second Hamiltonian.

[0169] Specifically, the construction of the multi-bit quantum logic gate U includes:

[0170] A control pulse is generated based on the pulse parameters, the control pulse is adjusted iteratively through the pulse parameters, and the multi-bit quantum logic gate U is determined based on the adjusted control pulse.

[0171] See Figure 7 , Figure 7 This is a schematic diagram of a device for determining the energy of a target system based on Hamiltonian, provided in an embodiment of the present invention. Figure 3 Corresponding to the process shown, the apparatus includes:

[0172] The first acquisition module 701 is used to acquire target system information, the target system information including electronic information and electron spin orbital information;

[0173] The second acquisition module 702 is used to obtain the Hartree Fock state of the fermion form of the target system based on the electronic information and the electron spin orbital information;

[0174] The encoding module 703 is used to encode the Hartree Fock state in fermion form onto a quantum bit through a pre-set encoding method to obtain a quantum state in Pauli operator form;

[0175] The calculation module 704 is used to calculate the energy of the target system using the second Hamiltonian as described in the preceding claims, the quantum state in the form of the Pauli operator, and the evolution wave function.

[0176] Specifically, after the second obtaining module, the device further includes:

[0177] The third acquisition module is used to obtain the experimental state of the target system based on the Hartree Fock state in the fermionic form of the target system.

[0178] Specifically, the third obtaining module includes:

[0179] An evolution unit is used to evolve the Hartree Fock state according to a pre-selected scheme, and obtain the evolved quantum state as the test state of the target system.

[0180] Specifically, the evolutionary unit includes:

[0181] The computational subunit is used to calculate the cluster operator in the fermion form of the target system according to the pre-selected scheme and the Hartree Fock state;

[0182] The transformation subunit is used to select the mapping method and transform the cluster operator in the form of fermions of the target system into a cluster operator in the form of Pauli operators;

[0183] The decomposition subunit is used to decompose the cluster operator in the form of the Pauli operator into the corresponding unitary operator form and evolve it to obtain the evolved quantum state as the test state of the target system to be solved.

[0184] Compared with existing technologies, this invention first constructs a multi-qubit quantum logic gate and generates a second Hamiltonian based on the first Hamiltonian of the target system. Then, based on the electronic information and electron spin orbital information of the target system, it obtains the Hartree Fock state in fermion form. Through a pre-set encoding method, the Hartree Fock state in fermion form is encoded onto the qubits to obtain the quantum state in Pauli operator form. Finally, the energy of the target system is calculated using the second Hamiltonian, the quantum state in Pauli operator form, and the evolution wave function. It can characterize the Hamiltonian of the target system to be simulated using a smaller number of qubits, providing support for calculating the energy of the target system through quantum chemical simulation, improving the calculation speed and accuracy, and promoting the further development of quantum chemical simulation applications.

[0185] This invention also provides a storage medium storing a computer program, wherein the computer program is configured to execute the steps in any of the above method embodiments when running.

[0186] Specifically, in this embodiment, the storage medium can be configured to store a computer program for performing the following steps:

[0187] S201: Determine the first Hamiltonian H of the target system;

[0188] S202: Construct a multi-qubit quantum logic gate U, and generate a second Hamiltonian H′ based on the first Hamiltonian H, wherein the second Hamiltonian H′ satisfies The multi-bit quantum logic gate U satisfies Where j represents the number of the qubit, X q(j)Let τ represent the operation operator performed on the j-th qubit. j This represents the Hamiltonian reduction during the transition from the first Hamiltonian to the second Hamiltonian.

[0189] Specifically, in this embodiment, the storage medium may include, but is not limited to, USB flash drives, read-only memory (ROM), random access memory (RAM), portable hard drives, magnetic disks, or optical disks, and other media capable of storing computer programs.

[0190] This invention also provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor is configured to run the computer program to perform the steps in any of the above method embodiments.

[0191] Specifically, the aforementioned electronic device may further include a transmission device and an input / output device, wherein the transmission device is connected to the aforementioned processor, and the input / output device is connected to the aforementioned processor.

[0192] Specifically, in this embodiment, the processor can be configured to perform the following steps via a computer program:

[0193] S201: Determine the first Hamiltonian H of the target system;

[0194] S202: Construct a multi-qubit quantum logic gate U, and generate a second Hamiltonian H′ based on the first Hamiltonian H, wherein the second Hamiltonian H′ satisfies The multi-bit quantum logic gate U satisfies Where j represents the number of the qubit, X q(j) Let τ represent the operation operator performed on the j-th qubit. j This represents the Hamiltonian reduction during the transition from the first Hamiltonian to the second Hamiltonian.

[0195] The present invention can also provide a quantum computer operating system, which realizes the determination of the Hamiltonian of the target system and the determination of the energy of the target system based on the Hamiltonian according to any of the above-described method embodiments provided in the present invention.

[0196] Embodiments of this application may also provide a quantum computer, which includes the aforementioned quantum computer operating system.

[0197] The above description, based on the embodiments shown in the figures, details the structure, features, and effects of the present invention. The above description is only a preferred embodiment of the present invention, but the present invention is not limited to the scope of implementation shown in the figures. Any changes made in accordance with the concept of the present invention, or equivalent embodiments modified to have equivalent changes, that do not exceed the spirit covered by the specification and figures, should be within the protection scope of the present invention.

Claims

1. A method of determining a Hamiltonian of a target system, characterized by, The method comprises: determining a first hamiltonian of a target system ; Control pulses are generated based on pulse parameters, and the control pulses are adjusted iteratively through the pulse parameters. Multi-bit quantum logic gates are then determined based on the adjusted control pulses. And according to the first Hamiltonian Generate the second Hamiltonian The second Hamiltonian satisfy The multi-bit quantum logic gate satisfy ,in, The number representing the qubit. Indicates the first Operators operating on each qubit This represents the Hamiltonian reduction during the transition from the first Hamiltonian to the second Hamiltonian.

2. A method for determining the energy of a target system based on a Hamiltonian, characterized in that, The method comprises: Obtaining target system information, wherein the target system information comprises electronic information and electronic spin-orbit information; obtaining the fermion form of the target system based on the electronic information and the electronic spin-orbital information state; By using a pre-set encoding method, the fermion form The state is encoded onto the qubit to obtain a quantum state in the form of a Pauli operator; Using the second Hamiltonian, the quantum state in the form of the Pauli operator and the evolution wave function according to claim 1 to calculate the energy of the target system.

3. The method of claim 2, wherein, If the number of spin-orbitals of the target system is , the dimension of the second Hamiltonian matrix is , and the number of qubits used for encoding is .

4. The method of claim 3, wherein, said obtaining the fermionic form of the target system after said obtaining the fermionic form of the target system According to the fermionic form of the target system Obtain a trial state of the target system according to the fermionic form of the target system 5. The method of claim 4, wherein, the target system fermion form obtaining a trial state of the target system, comprising: According to the pre-selected assumed mode, the quantum state is evolved to obtain an evolved quantum state as a trial state of the target system. state is evolved to obtain an evolved quantum state as a trial state of the target system.

6. The method of claim 5, wherein, The method of setting up according to the pre-selected scheme is used to... The state evolves to obtain the evolved quantum state as the test state of the target system, including: According to the pre-selected way of setting, the In the state, the cluster operator of the fermion form of the target system is calculated; Selecting a mapping mode and transforming the cluster operator in the form of the fermion of the target system into a cluster operator in the form of the Pauli operator; Decomposing the cluster operator in the form of the Pauli operator into a corresponding unit operator form and performing evolution to obtain an evolved quantum state as a trial state of the target system to be solved.

7. A device for determining the Hamiltonian of a target system, characterized in that, The device comprises: determining module configured to determine a first Hamiltonian of the target system ; generating a control pulse based on pulse parameters, adjusting the control pulse by iteration of the pulse parameters, and determining a multi-bit quantum logic gate from the adjusted control pulse and generating a second Hamiltonian from the first Hamiltonian satisfying satisfying the multi-bit quantum logic gate satisfying wherein denotes the number of qubits, denotes an operation operator acting on the qubit, denotes a Hamiltonian reduced in the course of the conversion from the first Hamiltonian to the second Hamiltonian.

8. An apparatus for determining an energy of a target system based on a Hamiltonian, the apparatus comprising: a computer system configured to: receive a Hamiltonian; and determine an energy of a target system based on the Hamiltonian. The device comprises: A first obtaining module is configured to obtain target system information, wherein the target system information comprises electronic information and electronic spin-orbit information; a second obtaining module, configured to obtain the fermion form of the target system based on the electronic information and the electronic spin-orbit information state; The encoding module is used to encode the fermions in the form of pre-set encoding methods. The state is encoded onto the qubit to obtain a quantum state in the form of a Pauli operator; A calculating module is configured to use the second Hamiltonian, the quantum state in the form of the Pauli operator and the evolution wave function according to claim 1 to calculate the energy of the target system.

9. A storage medium, characterized by The storage medium stores a computer program, wherein the computer program is configured to execute the method according to claim 1 or any one of claims 2 to 6 when running. 10.An electronic device comprising a memory and a processor, the electronic device characterized by, The memory stores a computer program, and the processor is configured to execute the computer program to execute the method according to claim 1 or any one of claims 2 to 6.

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