CN117114119A - Method, device and medium for calculating target system energy - Google Patents
Method, device and medium for calculating target system energy Download PDFInfo
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Abstract
The application discloses a method, a device and a medium for calculating target system energy, wherein the method comprises the following steps: the method comprises the steps of firstly determining a ground state wave function of a target system to be solved, then executing evolution and measurement operation on the ground state wave function by utilizing a quantum phase estimation circuit to obtain a target quantum state, and finally calculating the ground state energy of the target system according to the ground state wave function and the target quantum state.
Description
Technical Field
The application belongs to the technical field of quantum computing, and particularly relates to a method, a device and a medium for computing target system energy.
Background
The quantum computer is a kind of physical device which performs high-speed mathematical and logical operation, stores and processes quantum information according to the law of quantum mechanics. When a device processes and calculates quantum information and operates on a quantum algorithm, the device is a quantum computer. Quantum computers are a key technology under investigation because of their ability to handle mathematical problems more efficiently than ordinary computers, for example, to accelerate the time to crack RSA keys from hundreds of years to hours.
The quantum computing simulation is a simulation computation which simulates and follows the law of quantum mechanics by means of numerical computation and computer science, and is taken as a simulation program, and the high-speed computing capability of a computer is utilized to characterize the space-time evolution of the quantum state according to the basic law of quantum bits of the quantum mechanics.
Along with the continuous perfection of quantum chemistry theory, computational chemistry has become an important tool for chemical workers to explain experimental phenomena, predict experimental results and guide experimental design, and has wide application in the aspects of drug synthesis, catalyst preparation and the like. However, in the face of huge calculation amount related to calculation chemistry, classical computers have limited capabilities in terms of calculation accuracy, calculation size and the like, which limits the development of calculation chemistry to a certain extent, thereby resulting in weak application of users to simulation calculation of chemical systems and affecting further development of quantum chemistry simulation application.
Disclosure of Invention
The application aims to provide a method, a device and a medium for calculating target system energy, which solve the defects in the prior art, and can provide support for realizing the quantum chemistry simulation calculation of the target system energy by utilizing a quantum phase estimation circuit, thereby improving the calculation speed and the calculation precision and promoting the further development of quantum chemistry simulation application.
One embodiment of the present application provides a method of calculating target system energy, the method comprising:
determining a ground state wave function of a target system to be solved;
performing evolution and measurement operations on the ground state wave function by using a quantum phase estimation circuit to obtain a target quantum state, wherein the quantum phase estimation circuit comprises a controlled second quantum logic gate, and the second quantum logic gate is determined by information of the target system;
and calculating the ground state energy of the target system according to the ground state wave function and the target quantum state.
Optionally, the target system information includes: the method for determining the ground state wave function of the target system to be solved comprises the following steps of:
based on the electronic information and the electronic spin orbit information, determining a Hartree Fock state of the Fermi form of the target system, and determining the Hartree Fock state as the ground state wave function.
Optionally, the target system information further includes: a hamiltonian amount of a target system, the quantum phase estimation circuit comprising:
a first quantum register for storing phase information and composed of n quantum bits;
the second quantum register is used for storing a ground state wave function of the target system, and the quantum bit number of the second quantum register is determined by the Hamiltonian amount of the target system;
the first quantum logic gate acts on n direct products of the first quantum register and the inverse quantum Fourier transform unit acts on the first quantum register, the controlled second quantum logic gate acts on the first quantum register and the second quantum register, the quantum bit of the first quantum register is a control bit, and the quantum bit of the second quantum register is a target bit.
Optionally, before the calculating the ground state energy of the target system according to the ground state wave function and the target quantum state, the method further includes:
performing the encoding operation of the ground state wave function by a preset encoding mode to obtain a quantum state in a form of a bubble operator;
and calculating Hartree Fock energy of the target system according to the Hamiltonian quantity of the target system and based on the quantum state of the form of the Bristle operator.
Optionally, the first quantum logic gate includes: hadamard gates; the unitary matrix of the second quantum logic gate satisfies:
U＝e -ibH
wherein U represents unitary matrix form of the second quantum logic gate, b represents scaling factor determined according to the Hartree Fock energy, and H represents Hamiltonian of the target system.
Optionally, the preset encoding mode includes:
party transformation, jordan-Wigner transformation, or Bravyi-Kitaev transformation.
Optionally, the calculating the ground state energy of the target system according to the ground state wave function and the target quantum state includes:
the ground state energy of the target system is calculated by the following equation:
wherein E represents the ground state energy of the target system, E HF The Hartree Fock energy representing the target system,representing the target quantum state.
Yet another embodiment of the present application provides an apparatus for calculating target system energy, the apparatus comprising:
the determining module is used for determining a ground state wave function of the target system to be solved;
the execution module is used for executing evolution and measurement operation on the ground state wave function by utilizing a quantum phase estimation circuit to obtain a target quantum state, and the quantum phase estimation circuit comprises a controlled second quantum logic gate, wherein the second quantum logic gate is determined by information of the target system;
and the calculation module is used for calculating the ground state energy of the target system according to the ground state wave function and the target quantum state.
Optionally, the determining module includes:
and the determining unit is used for determining the Hartree Fock state of the Fermi form of the target system based on the electronic information and the electronic spin orbit information, and determining the Hartree Fock state as the ground state wave function.
Optionally, the execution module includes:
a first quantum register unit for storing phase information and composed of n quantum bits;
a second quantum register unit for storing a ground state wave function of the target system, and the number of quantum bits of the second quantum register is determined by the Hamiltonian amount of the target system;
the function module unit is used for realizing a first quantum logic gate acting on n direct products of the first quantum register and an inverse quantum Fourier transform unit acting on the first quantum register, wherein the controlled second quantum logic gate acts on the first quantum register and the second quantum register, the quantum bit of the first quantum register is a control bit, and the quantum bit of the second quantum register is a target bit.
Optionally, the apparatus further includes:
the obtaining module is used for executing the encoding operation of the ground state wave function through a preset encoding mode to obtain a quantum state in a form of a Pauloside operator;
and the energy calculation module is used for calculating Hartree Fock energy of the target system according to the Hamiltonian quantity of the target system and based on the quantum state of the Brix operator form.
Optionally, the computing module includes:
a calculation unit for calculating the ground state energy of the target system by the following expression:
wherein E represents the ground state energy of the target system, E HF The Hartree Fock energy representing the target system,representing the target quantum state.
An embodiment of the application provides a storage medium having a computer program stored therein, wherein the computer program is arranged to perform the method of any of the above when run.
An embodiment of the application provides an electronic device comprising a memory having a computer program stored therein and a processor arranged to run the computer program to perform the method of any of the above.
Compared with the prior art, the method has the advantages that the ground state wave function of the target system to be solved is firstly determined, then the evolution and measurement operation of the ground state wave function are executed by utilizing the quantum phase estimation circuit, the target quantum state is obtained, and finally the ground state energy of the target system is calculated according to the ground state wave function and the target quantum state.
Drawings
FIG. 1 is a block diagram of a system network for calculating target system energy according to an embodiment of the present application;
FIG. 2 is a flow chart of a method for calculating energy of a target system according to an embodiment of the present application;
FIG. 3 is a schematic diagram of a quantum circuit for generating a ground state wave function according to an embodiment of the present application;
fig. 4 is a schematic structural diagram of a quantum phase estimation circuit according to an embodiment of the present application;
fig. 5 is a schematic structural diagram of an apparatus for calculating energy of a target system according to an embodiment of the present application.
Detailed Description
The embodiments described below by referring to the drawings are illustrative only and are not to be construed as limiting the application.
The embodiment of the application firstly provides a method for calculating the energy of a target system, which can be applied to electronic equipment such as a computer terminal, in particular to a common computer, a quantum computer and the like.
The following describes the operation of the computer terminal in detail by taking it as an example. FIG. 1 is a block diagram of a system network for calculating target system energy according to an embodiment of the present application. The system applied to calculate target architecture energy may include network 110, server 120, wireless device 130, client 140, storage unit 150, classical processing system 160, quantum processing system 170, and may also include additional memory, classical processors, quantum processors, and other devices not shown.
Network 110 is a medium that provides a communication link between various devices and computers connected together within a system network for use in a method of calculating target system energy, including but not limited to the internet, intranets, local area networks, mobile communication networks, and combinations thereof, and may be connected by wired, wireless communication links, or fiber optic cables, etc.
Server 120 and client 140 are conventional data processing systems that may contain data and have applications or software tools that perform conventional computing processes. The client 140 may be a personal computer or a network computer, so the data may also be provided by the server 120. The wireless device 130 may be a smart phone, tablet, notebook, smart wearable device, or the like. The memory unit 150 may include a database 151 that may be configured to store data of qubit parameters, quantum logic gate parameters, quantum circuits, quantum programs, and the like.
Classical processing system 160 (quantum processing system 170) may include a classical processor 161 (quantum processor 171) for processing classical data (quantum data), which may be boot files, operating system images, and applications 162 (application 173), and a memory 163 (memory 172) for storing classical data (quantum data), which may be quantum algorithms compiled for implementing the method of calculating target system energy provided in accordance with embodiments of the present application, applications 162 (application 173).
Any data or information stored or generated in classical processing system 160 (quantum processing system 170) may also be configured to be stored or generated in another classical (quantum) processing system in a similar manner, as may any application program executed thereby.
It should be noted that, the real quantum computer is a hybrid structure, and it includes at least two major parts in fig. 1: classical processing system 160, responsible for performing classical calculations and controls; the quantum processing system 170 is responsible for running quantum programs to implement quantum computing.
The classical processing system 160 and the quantum processing system 170 may be integrated in one device or may be distributed among two different devices. A first device, for example, comprising classical processing system 160 runs a classical computer operating system on which quantum application development tools and services are provided, and also provides storage and network services required by quantum applications. The user develops the quantum application through the quantum application development tool and service thereon, and sends the quantum application through the web service thereon to a second device comprising the quantum processing system 170. The second device runs the quantum computer operating system, analyzes the code of the quantum program through the quantum computer operating system, compiles the code into an instruction which can be identified and executed by the quantum computer measurement and control system, and the quantum processor 170 realizes a quantum algorithm corresponding to the quantum program according to the instruction.
In a classical processing system 160 based on silicon chips, the unit of classical processor 161 is a CMOS tube, and such a computational unit is not limited by time and coherence, i.e. it is not limited by time of use, and is ready to use. Furthermore, the number of such computational units is also sufficient in silicon chips, and the number of computational units in a classical processor is now thousands of. The number of computational cells is sufficient and the CMOS transistor selectable computational logic is fixed, e.g., and logic. When the CMOS tube is used for operation, a large number of CMOS tubes are combined with limited logic functions, so that the operation effect is realized.
Unlike such logic units in classical processing system 160, the basic computational unit of quantum processor 171 in quantum processing system 170 is a qubit, the input of which is limited by coherence and also by coherence time, i.e., the qubit is limited in terms of time of use and is not readily available. Full use of qubits within the usable lifetime of the qubits is a critical challenge for quantum computing. Furthermore, the number of qubits in a quantum computer is one of the representative indicators of the performance of the quantum computer, each qubit realizes a calculation function by a logic function configured as needed, whereas the logic function in the field of quantum calculation is diversified in view of the limited number of qubits, such as Hadamard gate (H gate), brix gate (X gate), brix-Y gate (Y gate) brix-Z gate (Z gate), X gate, RY gate, RZ gate, CNOT gate, CR gate, issnap gate, toffoli gate, and the like. In quantum computation, the operation effect is realized by combining limited quantum bits with various logic function combinations.
Based on these differences, the design of the logic function acting on the qubits (including the design of whether the qubits are used or not and the design of the use efficiency of each qubit) is a key to improving the operational performance of the quantum computer, and special designs are required. The above design for qubits is a technical problem that is not considered nor faced by common computing devices. Along with the continuous perfection of quantum chemistry theory, the computational chemistry has become an important tool for chemical workers to explain experimental phenomena, predict experimental results and guide experimental design, and has wide application in the aspects of medicine synthesis, catalyst preparation and the like. However, in the face of huge calculation amount related to calculation chemistry, classical computers have limited capabilities in terms of calculation accuracy, calculation size and the like, which limits the development of calculation chemistry to a certain extent, thereby resulting in weak application of users to simulation calculation of chemical systems and affecting further development of quantum chemistry simulation application. The application solves the defects in the prior art by providing the method, the device and the medium for calculating the target system energy, can provide support for realizing the quantum chemistry simulation calculation of the target system energy, improves the calculation speed and the calculation precision, and promotes the further development of quantum chemistry simulation application.
Referring to fig. 2, fig. 2 is a schematic flow chart of a method for calculating energy of a target system according to an embodiment of the present application.
The present embodiment provides an embodiment of a method for calculating a target system energy, where the method for calculating a target system energy may include:
s201: and determining a ground state wave function of the target system to be solved.
Specifically, a ground state wave function of a target system to be solved is determined, and first, target system information including hamiltonian, electronic information and electronic spin orbit information of the target system can be determined.
Specifically, the target system may be considered as a molecular structure modeling in which the user wants to perform ground state energy simulation, including, for example, the number of electrons constituting the molecule, the type of electrons, spin orbit information of the electrons, and the like.
The Hamiltonian (Hamiltonian) is a physical concept in classical mechanics, and in quantum mechanics, the physical quantity of classical mechanics becomes a corresponding operator, and the Hamiltonian corresponds to the Hamiltonian. Hamiltonian is understood to be the sum of the kinetic energy of all particles of the target system plus the potential energy of the particles associated with the target system. The hamiltonian is different for different situations or numbers of particles, because it includes the sum of the kinetic energies of the particles and the potential energy function corresponding to this situation, generally denoted by H.
In quantum mechanics, all measurable mechanical quantities can be described by a hermite matrix, which is defined as the transposed conjugate of the matrix, i.e. the matrix itself, i.e. there is:
such a matrix is commonly referred to as a measure operator, and non-zero operators will have at least one eigenvalue λ other than 0 and its corresponding eigenvalue |ψ >:
H|ψ>＝λ|ψ>
if the eigenvalue of the operator H corresponds to the energy level of a certain system, such an operator may also be referred to as hamiltonian.
Electrons are a basic particle, generally referring to the number of extra-nuclear electrons of the target system; the electron spin orbit information mathematically describes the probability of finding electrons in a specific space outside the atomic nucleus of a target system and indicates the possible positions of the electrons in three-dimensional space.
In an alternative embodiment, the Hartree Fock state of the fermi sub-form of the target system may be determined based on the electronic information and the electronic spin orbit information, and the Hartree Fock state may be determined as the ground state wave function.
Specifically, the ground state wave function of the target system can be obtained and represented in an analytic mode, such as a variational method and a virtual time evolution method. The basis of the ground state wave function obtained by using the variational method is that the ground state wave function is the lowest state where the energy of the target system can be; the main idea of the virtual time evolution method is to perform virtual time evolution and normalization on an arbitrary wave function, so that as long as the wave function has an overlapping part with the ground state wave function, the wave function finally converges to the ground state.
In quantum computing, a ground state wave function is required to be selected as a basis vector, for example, a Hartree Fock state vector is generally used as a ground state wave function in quantum chemistry to satisfy the following requirements:
ψ(θ)＝U(θ)|ψ> Hartree-Fock
wherein, psi (theta) represents the wave function corresponding to the set of parameters theta, U (theta) represents the matrix operator corresponding to the set of parameters theta, and the ground state wave function |psi> Hartree-Fock The electrons representing the molecules are all at the lowest orbit corresponding to the Hartree Fock ground state in chemistry.
In an alternative implementation, referring to fig. 3, fig. 3 is a schematic diagram of a quantum circuit for generating a ground state wave function according to an embodiment of the present application. For example, for a hydrogen molecular target system, it is only necessary to add a NOT gate to two qubits respectively, so that |0000> can be initialized to |0101> in the quantum circuit.
Taking the example that the target system is a hydrogen molecule, which contains four single electron spin molecular orbitals and two electrons, if one quantum bit is used to represent one electron spin orbit according to the electron number and electron spin orbit information of the hydrogen molecule, namely 0 represents an empty orbit, 1 represents an occupied orbit, so that the Hartree Fock (Hartrie-Fock) state of the target system of the hydrogen molecule can be represented by using the quantum state |0101>, and then determining the Hartree Fock state as the ground state wave function.
S202: and performing evolution and measurement operations on the ground state wave function by using a quantum phase estimation circuit to obtain a target quantum state, wherein the quantum phase estimation circuit comprises a controlled second quantum logic gate, and the second quantum logic gate is determined by information of the target system.
Specifically, the quantum phase estimation circuit may include:
the device comprises a first quantum register, a second quantum register and a plurality of quantum function modules; wherein,
the first quantum register is used for storing phase information and is composed of n quantum bits;
the second quantum register is used for storing a ground state wave function of the target system, and the quantum bit number of the second quantum register is determined by the Hamiltonian amount of the target system;
the quantum function module at least comprises n first quantum logic gates with direct products, n second quantum logic gates controlled by the first quantum logic gates, and an inverse quantum Fourier transform unit acting on the first quantum register.
For example, a first quantum logic gate acting on n direct products of the first quantum register and an inverse quantum fourier transform unit acting on the first quantum register, the controlled second quantum logic gate acting on the first quantum register and the second quantum register, and the qubit of the first quantum register being a control bit and the qubit of the second quantum register being a target bit.
Wherein the first quantum logic gate comprises: hadamard gates; the unitary matrix of the second quantum logic gate satisfies:
U＝e -ibH
wherein U represents unitary matrix form of the second quantum logic gate, b represents scaling factor determined according to the Hartree Fock energy, and H represents Hamiltonian of the target system.
S203: and calculating the ground state energy of the target system according to the ground state wave function and the target quantum state.
Specifically, before the calculating the ground state energy of the target system according to the ground state wave function and the target quantum state, the method may further include:
step 1: and executing the encoding operation of the ground state wave function by a preset encoding mode to obtain the quantum state in the form of the Paulownian.
Specifically, N preset qubits may be first determined, and the Hartree Fock state (ground state wave function) of the fermi sub-form may be converted into the hilbert space of the berkovich operator form by using a preset encoding manner, so that each fermi sub-state may be represented by one quantum state.
Wherein the electronic information of the target system can comprise alpha electrons and beta electrons, and the quantum state in the form of the berlite operator can be represented by the following forms:
p is the spin-orbit number of the alpha electron or the beta electron, M is the number of the spin orbitals of the alpha electron or the beta electron, and
in an alternative embodiment, the preset encoding mode may be one of a Party transform, a Jordan-Wigner transform, or a Bravyi-Kitaev transform. From Jordan-Wigner mapping to Party transformation or Bravyi-Kitaev mapping, since the electron number and spintronic number of the target system are conserved, this is true for any Slater determinant preserving the alpha electron number, so it is known that the ground state is simply a linear combination of Slater determinants, and since computing the ground state energy can be regarded essentially as a problem of electron distribution between orbitals, the above information can be used to make a simplified calculation. In particular, if the expected occupancy of a track is close to 0 or 1, it can be removed from the calculation. The computation is thus reduced to include only the most important trajectories, which is called performing the computation of target system energy in a reduced active space.
Illustratively, for the Jordan-Wigner transform, its Slater determinant may be expressed as:
step 2: and calculating Hartree Fock energy of the target system according to the Hamiltonian quantity of the target system and based on the quantum state of the form of the Bristle operator.
Specifically, according to the Hamiltonian of the target system, an expected value corresponding to the Hamiltonian can be measured. The Hamiltonian amount of the target system in the secondary quantization method can be mapped into a linear combination of local Brillouin operator products through an introduced preset transformation mode. The expected value of the secondary quantization operator must be equivalent to the expected value of the corresponding primary quantization operator. Since the primary quantization operator keeps the number of electrons unchanged, the secondary quantization operator must contain an equal number of generation and annihilation operators. The secondary quantized form of the electronic hamiltonian can be obtained by utilizing the requirements:
in an alternative embodiment, calculating the Hartree Fock energy of the target system according to the Hamiltonian amount of the target system and based on the quantum state of the form of the Brix operator may include:
step a: and acquiring the fermi Ha Midu quantity corresponding to the target system, and converting the fermi Ha Midu quantity corresponding to the target system into the Bridgman quantity of the target system.
Specifically, based on the mechanical analysis of the target system, the Hamiltonian amount of the system can be obtained, and the Hamiltonian amount corresponding to the target system is obtained by creating an operatorAnnihilation operator a q To achieve that they satisfy the inverse relationship.
Illustratively, for a hydrogen molecular system, the corresponding fermi Ha Midu amounts are:
in quantum computing, the hamiltonian in the fermi form cannot evolve directly on the circuit, so there is a need to have a process of solving and converting the desired value in the integral form into a quantum circuit readable, which is called mapping. It should be noted that the mapping is merely expressed by transforming hamiltonian into a form, and the system energy information represented by each type of hamiltonian is equivalent. In addition, for a quantum analog circuit or a real quantum chip, the British operator is easier to operate and generate, so that the Fermi Ha Midu quantity corresponding to the target system can be converted into the British Hamiltonian quantity of the target system, and the subsequent analog operation is convenient.
Following the above example, for a hydrogen molecular system, the corresponding fermi Ha Midu amount is transformed into the brihamiltonian amount, specifically:
step b: and constructing a quantum circuit corresponding to each sub-item of the Bridgman amount of the target system according to each sub-item of the Bridgman amount decomposition of the target system.
Specifically, the experimental state |ψ of the target system can be obtained first n >The experimental state |ψ is then calculated using a quantum expectation estimation algorithm n >Expectations in molecular hamiltonian. The quantum expectation estimation is that the hamiltonian H of a multi-electron system, a Heisenberg model (hessianberg model), a quantum Ising model (Yi Xin model) and the like can be expanded into the sum of a plurality of sub-items, namely:
where h is a real number, σ is a bubble operator, α, β and γ belong to (X, Y, Z, I), and I, j, k represent subspaces where Hamiltonian quantum terms act.
Since the observables are linear, the average energy of the system can be calculated using the formula:
E HF ＝<ψ * |H|ψ>
wherein, psi is * Being orthonormal to ψ, the right side of the equation can also be expanded into this form:
it follows that the average energy E of the system can be obtained by summing the expectations for each sub-term. It is noted that the measurement of each sub-item's expectations may be performed on a quantum processor, with a classical processor being responsible for summing the individual expectations.
By way of example, assuming that the hamiltonian of a certain system is H, it can eventually be expanded into this form:
in this formula, all the sub-term coefficients h are 1, and the acquired experimental state is assumed to be of the form:
|ψ n >＝a|00>+b|01>+c|10>+d|11>
wherein a is 2 、b 2 、c 2 、d 2 Respectively, collapse to |00 when the test state is measured>、|01>、|10>、|11>Probability P of (2) S Each subitem H of Hamiltonian quantity 1 、H 2 、H 3 Respectively acting on the test states to sequentially obtain the expected E 1 、E 2 、E 3 Specific:
E 1 ＝<ψ * |H 1 |ψ>
E 2 ＝<ψ * |H 2 |ψ>
E 3 ＝<ψ * |H 3 |ψ>
by E 1 、E 2 、E 3 For example, for desired E 1 The coefficient h is the desired, i.e. without constructing a circuit measurementFor the expected E 2 The Hamiltonian amount is->Since the measuring operation is at sigma Z Upper (with sigma) Z The eigenvectors of (a) are subspaces formed by basis vectors), it is only necessary to add measurement gates to the qubits, and then pass the measurement results to a classical processor for summation.
Step c: and measuring the Hartree Fock energy of the test state by utilizing a quantum circuit corresponding to each subitem of the Bridgman amount of the target system.
Specifically, expanding each subitem expected measurement circuit of the Bristout of the target system to obtain a measurement circuit of each subitem expected E (i), and then sequentially transmitting E (i) to a classical processor by a quantum processor to sum, so that Hartree Fock energy of the target system in the test state is obtained.
It should be noted that since the measurement operation is at σ Z The above is performed for the inclusion of sigma x 、σ y Is not directly measured at this time, and requires a measurement of sigma x Sum sigma y Performing the base-changing operation, i.e. letting the experimental state evolve once more, due to sigma x ＝H×σ Z ×H，I.e. for sigma x Sum sigma y Before measurement, it is necessary to add a Hadamard gate and +.>And (3) a gate, and then transmitting the measurement result to a classical processor for summation.
It should be emphasized that the proposed scheme, mapping scheme, optimization method, and the like are merely examples, and do not limit the present application, and the proposed scheme includes, for example, the schemes such as HE (Hardware Efficient, hardware efficiency), SP (Symmetry Preserved, symmetric hold), and the like.
In an alternative embodiment, the calculating the ground state energy of the target system according to the ground state wave function and the target quantum state may include:
the ground state energy of the target system is calculated by the following equation:
wherein E represents the ground state energy of the target system, E HF The Hartree Fock energy representing the target system,representing the target quantum state.
Illustratively, performing evolution and measurement operations on the ground state wave function using quantum phase estimation circuitry may be expressed as:
U|ψ>＝e (i*2πθ) |ψ>
namely:
e (-ibH) |ψ＝e (-ibE) |ψ>e (i*2πθ) |ψ>
it can be seen that:
wherein θ is the phase and θ ε [0, 1).
It is noted that due to e (i*2πθ) Is a periodic function, and a reasonable scaling factor b is required to be set at the moment in order to ensure that theta is within the range of [0,1 ]. For example, the scaling factor b may be determined according to the Hartree Fock energy of the target system, and the phase θ=0.5 is preset, so that it is obtained:
the ground state energy of the target system can be deduced at this time:
E＝2×E HF ×θ
referring to fig. 4, fig. 4 is a schematic structural diagram of a quantum phase estimation circuit according to an embodiment of the present application, in which a first quantum register includes n quantum bits, a second quantum register includes m quantum bits, and an approximate ground state wave function |ψ of a target system is constructed>For example, the Hartree-Fock state is selected as the ground-state wave function |ψ of the target system> Hartree-Fock And then stored onto a second quantum register. Quantum function module composed of controlled second quantum logic gate U in the figureWherein k is [0, n-1 ]]Applying an inverse quantum Fourier transform unit to the first quantum register, and performing measurement operation on the first quantum registerObtaining the target quantum state->According to quantum state of quantum target->The nature of (2) can be seen as follows: />Therefore the ground state energy of the target system +.>
Therefore, the application firstly determines the ground state wave function of the target system to be solved, then utilizes the quantum phase estimation circuit to execute evolution and measurement operation on the ground state wave function to obtain the target quantum state, and finally calculates the ground state energy of the target system according to the ground state wave function and the target quantum state.
Referring to fig. 5, fig. 5 is a schematic structural diagram of an apparatus for calculating energy of a target system according to an embodiment of the present application, corresponding to the flow shown in fig. 2, where the apparatus includes:
a determining module 501, configured to determine a ground state wave function of a target system to be solved;
an execution module 502, configured to perform evolution and measurement operations on the ground state wave function by using a quantum phase estimation circuit, to obtain a target quantum state, where the quantum phase estimation circuit includes a controlled second quantum logic gate, and the second quantum logic gate is determined by information of the target system;
a calculating module 503, configured to calculate ground state energy of the target system according to the ground state wave function and the target quantum state.
Specifically, the determining module includes:
and the determining unit is used for determining the Hartree Fock state of the Fermi form of the target system based on the electronic information and the electronic spin orbit information, and determining the Hartree Fock state as the ground state wave function.
Specifically, the execution module includes:
a first quantum register unit for storing phase information and composed of n quantum bits;
a second quantum register unit for storing a ground state wave function of the target system, and the number of quantum bits of the second quantum register is determined by the Hamiltonian amount of the target system;
the function module unit is used for realizing a first quantum logic gate acting on n direct products of the first quantum register and an inverse quantum Fourier transform unit acting on the first quantum register, wherein the controlled second quantum logic gate acts on the first quantum register and the second quantum register, the quantum bit of the first quantum register is a control bit, and the quantum bit of the second quantum register is a target bit.
Specifically, the device further comprises:
the obtaining module is used for executing the encoding operation of the ground state wave function through a preset encoding mode to obtain a quantum state in a form of a Pauloside operator;
and the energy calculation module is used for calculating Hartree Fock energy of the target system according to the Hamiltonian quantity of the target system and based on the quantum state of the Brix operator form.
Specifically, the computing module includes:
a calculation unit for calculating the ground state energy of the target system by the following expression:
wherein E represents the ground state energy of the target system, E HF Hartree Fock energy representing the target system，Representing the target quantum state.
Compared with the prior art, the method has the advantages that the ground state wave function of the target system to be solved is firstly determined, then the evolution and measurement operation of the ground state wave function are executed by utilizing the quantum phase estimation circuit, the target quantum state is obtained, and finally the ground state energy of the target system is calculated according to the ground state wave function and the target quantum state.
The embodiment of the application also provides a storage medium, in which a computer program is stored, wherein the computer program is configured to perform the steps of any of the method embodiments described above when run.
Specifically, in the present embodiment, the above-described storage medium may be configured to store a computer program for executing the steps of:
s201: determining a ground state wave function of a target system to be solved;
s202: performing evolution and measurement operations on the ground state wave function by using a quantum phase estimation circuit to obtain a target quantum state, wherein the quantum phase estimation circuit comprises a controlled second quantum logic gate, and the second quantum logic gate is determined by information of the target system;
s203: and calculating the ground state energy of the target system according to the ground state wave function and the target quantum state.
Specifically, in the present embodiment, the storage medium may include, but is not limited to: a usb disk, a Read-Only Memory (ROM), a random access Memory (Random Access Memory, RAM), a removable hard disk, a magnetic disk, or an optical disk, or other various media capable of storing a computer program.
An embodiment of the application also provides an electronic device comprising a memory and a processor, characterized in that the memory has stored therein a computer program, the processor being arranged to run the computer program to perform the steps of any of the method embodiments described above.
Specifically, the electronic apparatus may further include a transmission device and an input/output device, where the transmission device is connected to the processor, and the input/output device is connected to the processor.
Specifically, in the present embodiment, the above-described processor may be configured to execute the following steps by a computer program:
s201: determining a ground state wave function of a target system to be solved;
s202: performing evolution and measurement operations on the ground state wave function by using a quantum phase estimation circuit to obtain a target quantum state, wherein the quantum phase estimation circuit comprises a controlled second quantum logic gate, and the second quantum logic gate is determined by information of the target system;
s203: and calculating the ground state energy of the target system according to the ground state wave function and the target quantum state.
The embodiment of the application can also provide a quantum computer operating system which realizes the method for calculating the target system energy according to any one of the method embodiments provided in the embodiment of the application.
Embodiments of the present application may also provide a quantum computer comprising the quantum computer operating system.
While the foregoing is directed to embodiments of the present application, other and further embodiments of the application may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.
Claims (10)
1. A method of calculating target system energy, the method comprising:
determining a ground state wave function of a target system to be solved;
performing evolution and measurement operations on the ground state wave function by using a quantum phase estimation circuit to obtain a target quantum state, wherein the quantum phase estimation circuit comprises a controlled second quantum logic gate, and the second quantum logic gate is determined by information of the target system;
and calculating the ground state energy of the target system according to the ground state wave function and the target quantum state.
2. The method of claim 1, wherein the target system information comprises: the method for determining the ground state wave function of the target system to be solved comprises the following steps of:
based on the electronic information and the electronic spin orbit information, determining a Hartree Fock state of the Fermi form of the target system, and determining the Hartree Fock state as the ground state wave function.
3. The method of claim 2, wherein the target architecture information further comprises: a hamiltonian amount of a target system, the quantum phase estimation circuit comprising:
a first quantum register for storing phase information and composed of n quantum bits;
the second quantum register is used for storing a ground state wave function of the target system, and the quantum bit number of the second quantum register is determined by the Hamiltonian amount of the target system;
the first quantum logic gate acts on n direct products of the first quantum register and the inverse quantum Fourier transform unit acts on the first quantum register, the controlled second quantum logic gate acts on the first quantum register and the second quantum register, the quantum bit of the first quantum register is a control bit, and the quantum bit of the second quantum register is a target bit.
4. A method according to claim 3, wherein before said calculating the ground state energy of the target system from the ground state wave function and the target quantum state, the method further comprises:
performing the encoding operation of the ground state wave function by a preset encoding mode to obtain a quantum state in a form of a bubble operator;
and calculating Hartree Fock energy of the target system according to the Hamiltonian quantity of the target system and based on the quantum state of the form of the Bristle operator.
5. The method of claim 4, wherein the first quantum logic gate comprises: hadamard gates; the unitary matrix of the second quantum logic gate satisfies:
U＝e -ibH
wherein U represents unitary matrix form of the second quantum logic gate, b represents scaling factor determined according to the Hartree Fock energy, and H represents Hamiltonian of the target system.
6. The method of claim 5, wherein the preset encoding scheme comprises:
party transformation, jordan-Wigner transformation, or Bravyi-Kitaev transformation.
7. The method according to any one of claims 4 to 6, wherein said calculating the ground state energy of the target system from the ground state wave function and the target quantum state comprises:
the ground state energy of the target system is calculated by the following equation:
wherein E represents the ground state energy of the target system, E HF Hartree Foc representing the target systemThe energy of k is such that,representing the target quantum state.
8. An apparatus for calculating target system energy, the apparatus comprising:
the determining module is used for determining a ground state wave function of the target system to be solved;
the execution module is used for executing evolution and measurement operation on the ground state wave function by utilizing a quantum phase estimation circuit to obtain a target quantum state, and the quantum phase estimation circuit comprises a controlled second quantum logic gate, wherein the second quantum logic gate is determined by information of the target system;
and the calculation module is used for calculating the ground state energy of the target system according to the ground state wave function and the target quantum state.
9. A storage medium having a computer program stored therein, wherein the computer program is arranged to perform the method of any of claims 1 to 7 when run.
10. An electronic device comprising a memory and a processor, characterized in that the memory has stored therein a computer program, the processor being arranged to run the computer program to perform the method of any of the claims 1 to 7.
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