CN114511090A - Method, device and medium for preparing system test state based on spin symmetry - Google Patents
Method, device and medium for preparing system test state based on spin symmetry Download PDFInfo
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Abstract
The application provides a method, a device and a medium for preparing a system test state based on spin symmetry, wherein the method for preparing the system test state based on spin symmetry comprises the following steps: determining a system and the number of orbits and electrons of the system; determining the number of excitation terms included by a fermi-form cluster operator of the system according to the number of orbitals and the number of electrons of the system based on spin symmetry; calculating a fermi form cluster operator of the system according to the number of the excitation terms; solving the trial state of the system based on the fermi form of the system's cluster operator. The method belongs to the field of quantum computing, solves the technical problem that complex molecules are difficult to simulate in the prior art, saves computing resources, and improves the simulation efficiency of the complex molecules.
Description
Technical Field
The application belongs to the field of quantum computing, and particularly relates to a method, a device and a medium for preparing a system test state based on spin symmetry.
Background
Quantum computers are physical devices that perform high-speed mathematical and logical operations, store and process quantum information in compliance with the laws of quantum mechanics. When a device processes and calculates quantum information and runs quantum algorithms, the device is a quantum computer. Quantum computers have the ability to handle mathematical problems more efficiently than ordinary computers. It will be appreciated that the key properties of a chemical or material depend on the electronic properties of the chemical or material, so it is critical to accurately mimic the electronic properties of the chemical or material.
Theoretical explanations of the energy and properties of molecules and materials at the atomic level have long been considered as one of the most direct applications of quantum computing, which has received much attention as a new computational paradigm. In recent years, an algorithm for acquiring molecular energy by using a quantum computer has been the focus of attention, but due to the limits of quantum bit number and coherence time, the simulation of a complex molecular system still has difficulty.
Disclosure of Invention
The application aims to provide a method, a device and a medium for preparing a system test state based on spin symmetry, so as to solve the technical problem that complex molecules are difficult to simulate in the prior art, save computing resources and improve the simulation efficiency of the complex molecules.
In a first aspect, the present application provides a method for preparing a system test state based on spin symmetry, comprising:
determining a system and the number of orbits and electrons of the system;
determining the number of excitation terms included by a fermi-form cluster operator of the system according to the number of orbitals and the number of electrons of the system based on spin symmetry;
calculating a fermi form cluster operator of the system according to the number of the excitation terms;
solving the trial state of the system based on the fermi form of the system's cluster operator.
Optionally, the determining, based on the spin symmetry, the number of excitation terms included in the fermi-form cluster operator of the system according to the number of orbitals and the number of electrons of the system includes:
acquiring a Hartree-Fock state of the system according to the number of the tracks and the number of the electrons of the system;
and determining the number of excitation terms included by the fermi-form cluster operator of the system based on the spin symmetry and the Hartree-Fock state of the system according to a pre-selected proposed mode.
Optionally, the determining, according to a pre-selected proposed mode, the number of excitation terms included in the fermi-form cluster operator of the system based on the spin symmetry and the Hartree-focus state of the system includes:
when the proposed mode is a single excitation coupling cluster, determining that the Fermi form cluster operator of the system only comprises a single excitation item number;
and determining the number of the single excitation terms as excitation terms corresponding to the excitation of each electron in the system from the original spin direction orbit to other orbits with consistent spin directions based on the spin symmetry and the Hartree-Fock state.
Optionally, the determining, according to a pre-selected proposed mode, the number of excitation terms included in the fermi-form cluster operator of the system based on the spin symmetry and the Hartree-focus state of the system includes:
when the preselected simulation mode is a single-double excitation coupling cluster, determining that the Fermi-form cluster operator of the system only comprises a single excitation number and a double excitation number;
determining the number of the single excitation terms as excitation terms corresponding to other orbits with the same spin direction from the orbit of the original spin direction to the excitation terms corresponding to the orbits with the same spin direction of each electron in the system based on spin symmetry and Hartree-Fock state; and determining the number of the double excitation terms as the excitation terms of two electrons in the system which are excited from the original spin direction orbit to the other two orbits with the corresponding spin directions consistent.
Optionally, the solving the experimental state of the system based on the fermi form cluster operator of the system includes:
transforming the Fermi operator form cluster operator of the system into a Paglie operator form cluster operator according to a preselected mapping mode;
decomposing the cluster operator in the Pauli operator form into a corresponding unitary operator form and carrying out evolution so as to obtain an evolved quantum state; wherein the evolved quantum state is a test state of the system.
Optionally, decomposing the cluster operator in the form of the bubble operator into a corresponding unitary operator and performing evolution to obtain an evolved quantum state includes:
constructing a quantum simulation line based on the unitary operator corresponding to the decomposed cluster operator in the form of the Pally operator;
and carrying out analog evolution according to the quantum analog circuit to obtain an evolved quantum state.
Optionally, the mapping manner is one of Jordan-Wigner transformation, Parity transformation, Bravyi-Kitaev transformation, and SegmentParity transformation.
In a second aspect, the present application further provides an apparatus for preparing a test state of a system based on spin symmetry, comprising:
the system comprises a first determining module, a second determining module and a control module, wherein the first determining module is used for determining a system and the track number and the electron number of the system;
the second determination module is used for determining the number of excitation terms included by the fermi form cluster operator of the system according to the orbit number and the electron number of the system based on the spin symmetry;
the calculation module is used for calculating the fermi form cluster operator of the system according to the number of the excitation terms;
and the solving module is used for determining the cluster operator based on the Fermi form of the system and solving the experimental state of the system.
Optionally, the second determining module includes:
the acquisition unit is used for acquiring the Hartree-Fock state of the system according to the number of the tracks and the number of the electrons of the system;
and the determining unit is used for determining the number of excitation terms included by the fermi-form cluster operator of the system based on the spin symmetry and the Hartree-Fock state of the system according to a pre-selected proposed mode.
Optionally, the determining unit is further configured to: when the proposed mode is a single excitation coupling cluster, determining that the Fermi form cluster operator of the system only comprises a single excitation item number; and determining the number of the single excitation terms as excitation terms corresponding to the excitation of each electron in the system from the original spin direction orbit to other orbits with consistent spin directions based on the spin symmetry and the Hartree-Fock state.
Optionally, the determining unit is further configured to: when the preselected simulation mode is a single-double excitation coupling cluster, determining that the Fermi-form cluster operator of the system only comprises a single excitation number and a double excitation number; determining the number of the single excitation terms as the excitation terms corresponding to the excitation of each electron in the system from the original spin direction orbit to other orbits with the consistent spin direction based on the spin symmetry and the Hartree-Fock state; and determining the number of the double excitation terms as the excitation terms of two electrons in the system which are excited from the original spin direction orbit to the other two orbits with the corresponding spin directions consistent.
Optionally, the second determining module further includes:
a transformation unit for transforming the Fermi operator form of the system into a Paglie operator form of cluster operators according to a preselected mapping manner;
the evolution unit is used for decomposing the cluster operator in the form of the Pagli operator into a corresponding unitary operator form and carrying out evolution so as to obtain an evolved quantum state; wherein the evolved quantum state is a test state of the system.
Optionally, the evolution unit is further configured to: constructing a quantum simulation line based on the unitary operator corresponding to the decomposed cluster operator in the form of the Pally operator; and carrying out analog evolution according to the quantum analog circuit to obtain an evolved quantum state.
Optionally, the mapping manner is one of Jordan-Wigner transformation, Parity transformation, Bravyi-Kitaev transformation, and SegmentParity transformation.
In a third aspect, the present application further provides an electronic device, including:
a processor;
a memory for storing processor-executable instructions;
wherein the processor implements the method of any of the first aspect above by executing the executable instructions.
In a fourth aspect, the present application further provides a computer storage medium having stored thereon computer instructions, which when executed by a processor, implement the steps of the method according to any one of the first aspect.
In the process of preparing the system test state, when the Fermi form cluster operator of the system is calculated, due to the fact that the spin symmetry is considered, the number of excitation terms needing to be calculated in the Fermi form cluster operator is smaller than that when the spin symmetry is not considered in the prior art, the complexity of the system is reduced, further when the test state of the system is solved, the calculation amount is reduced, the technical problem that complex molecules are difficult to simulate in the prior art is solved, calculation resources are saved, calculation of subsequent system energy is facilitated, and the simulation efficiency of the complex molecules is improved.
Drawings
FIG. 1 is a block diagram of a hardware configuration of a computer terminal of a method for preparing a trial state of a system based on spin symmetry according to an exemplary embodiment of the present disclosure;
FIG. 2 is a schematic flow chart of a method for preparing a test state of a system based on spin symmetry as provided in an exemplary embodiment of the present application;
fig. 3 is a schematic diagram of a quantum wire structure corresponding to an exemplary embodiment of the present application;
FIG. 4 is a schematic illustration of a hydrogen molecular orbital provided by an exemplary embodiment of the present application;
FIG. 5 is a drawing illustrating an exemplary embodiment of the present application providing H1Corresponding quantum wire schematic;
FIG. 6 is a drawing illustrating an exemplary embodiment of the present application providing H1And H2Corresponding quantum wire schematic;
FIG. 7 is a drawing illustrating an exemplary embodiment of the present application providing H1、H2And H3Corresponding quantum wire schematic;
FIG. 8 is a drawing illustrating an exemplary embodiment of the present application providing H1、H2、H3And H4Corresponding quantum wire schematic;
FIG. 9 is a drawing illustrating an exemplary embodiment of the present application providing H1、H2、H3、H4And H5Corresponding quantum wire schematic;
FIG. 10 is a schematic structural diagram of an apparatus for preparing a test state of a system based on spin symmetry according to an exemplary embodiment of the present disclosure.
Detailed Description
This will be described in detail below by way of example as it would run on a computer terminal. Fig. 1 is a block diagram of a hardware structure of a computer terminal of a method for preparing a trial state of a system based on spin symmetry according to an exemplary embodiment of the present disclosure. As shown in fig. 1, the computer terminal may include one or more (only one shown in fig. 1) processors 102 (the processor 102 may include, but is not limited to, a processing device such as a microprocessor MCU or a programmable logic device FPGA) and a memory 104 for storing data, and optionally, a transmission device 106 for communication functions and an input-output device 108. It will be understood by those skilled in the art that the structure shown in fig. 1 is only an illustration and is not intended to limit the structure of the computer terminal. For example, the computer terminal may also include more or fewer components than shown in FIG. 1, or have a different configuration than shown in FIG. 1.
The memory 104 may be used to store software programs and modules of application software, such as program instructions/modules corresponding to the experimental state of the preparation system based on spin symmetry in the embodiment of the present application, and the processor 102 executes various functional applications and data processing by executing the software programs and modules stored in the memory 104, so as to implement the method described above. The memory 104 may include high speed random access memory, and may also include non-volatile memory, such as one or more magnetic storage devices, flash memory, or other non-volatile solid-state memory. In some examples, the memory 104 may further include memory located remotely from the processor 102, which may be connected to a computer terminal over a network. Examples of such networks include, but are not limited to, the internet, intranets, local area networks, mobile communication networks, and combinations thereof.
The transmission device 106 is used for receiving or transmitting data via a network. Specific examples of the network described above may include a wireless network provided by a communication provider of the computer terminal. In one example, the transmission device 106 includes a Network adapter (NIC) that can be connected to other Network devices through a base station to communicate with the internet. In one example, the transmission device 106 can be a Radio Frequency (RF) module, which is used to communicate with the internet in a wireless manner.
It should be noted that a true quantum computer is a hybrid structure, which includes two major components: one part is a classic computer which is responsible for executing classic calculation and control; the other part is quantum equipment which is responsible for running a quantum program to further realize quantum computation. The quantum program is a string of instruction sequences which can run on a quantum computer and are written by a quantum language such as a Qrun language, so that the support of the operation of the quantum logic gate is realized, and the quantum computation is finally realized. In particular, a quantum program is a sequence of instructions that operate quantum logic gates in a time sequence.
In practical applications, due to the limited development of quantum device hardware, quantum computation simulation is usually required to verify quantum algorithms, quantum applications, and the like. The quantum computing simulation is a process of realizing the simulation operation of a quantum program corresponding to a specific problem by means of a virtual architecture (namely a quantum virtual machine) built by resources of a common computer. In general, it is necessary to build quantum programs for a particular problem. The quantum program referred to in the embodiments of the present application is a program written in a classical language for characterizing a qubit and its evolution, where the qubit, a quantum logic gate, and the like related to quantum computation are all represented by corresponding classical codes.
A quantum circuit, which is an embodiment of a quantum program and also a weighing sub-logic circuit, is the most common general quantum computation model, and represents a circuit that operates on a quantum bit under an abstract concept, and the circuit includes the quantum bit, a circuit (timeline), and various quantum logic gates, and finally, a result is often read through a quantum measurement operation.
Unlike conventional circuits that are connected by metal lines to pass either voltage or current signals, in quantum circuits, the lines can be viewed as being connected by time, i.e., the state of a qubit evolves naturally over time, in the process being operated on as indicated by the hamiltonian until a logic gate is encountered.
A quantum program corresponds to an overall quantum circuit as a whole, and the quantum program refers to the overall quantum circuit, wherein the total number of quantum bits in the overall quantum circuit is the same as the total number of quantum bits of the quantum program. It can be understood that: a quantum program may consist of quantum wires, measurement operations for quantum bits in the quantum wires, registers to hold measurement results, and control flow nodes (jump instructions), and a quantum wire may contain tens to hundreds or even thousands of quantum logic gate operations. The execution process of the quantum program is a process executed for all the quantum logic gates according to a certain time sequence. It should be noted that timing is the time sequence in which the single quantum logic gate is executed.
It should be noted that in the classical calculation, the most basic unit is a bit, and the most basic control mode is a logic gate, and the purpose of the control circuit can be achieved through the combination of the logic gates. Similarly, the way qubits are handled is quantum logic gates. The quantum state can be evolved using quantum logic gates, which are the basis for forming quantum circuits, including single-bit quantum logic gates, such as Hadamard gates (H-gates, Hadamard-gates), pauli-X gates (X-gates), pauli-Y gates (Y-gates), pauli-Z gates (Z-gates), RX-gates, RY-gates, RZ-gates, and so on; two-bit or multi-bit quantum logic gates such as CNOT gates, CR gates, CZ gates, iSWAP gates, Toffoli gates, and the like. Quantum logic gates are typically represented using unitary matrices, which are not only matrix-form but also an operation and transformation. The function of a general quantum logic gate on a quantum state is calculated by multiplying a unitary matrix by a matrix corresponding to a quantum state right vector.
Referring to fig. 2, fig. 2 is a schematic flow chart of a method for preparing a test state of a system based on spin symmetry according to an embodiment of the present application, which may include the following steps:
and S21, determining a system and the orbit number and the electron number of the system.
Wherein, the system is a chemical molecular model needing simulation. The chemical molecular model may be considered as a model of the molecular structure that the user wants to calculate the ground state energy, including, for example, the types of atoms, the number of atoms, the coordinates of the atoms, the charge and spin multiplicities, etc. that make up the chemical molecule.
The system can be determined by, but is not limited to, the user can input information of the chemical molecular model to be simulated on a computer terminal. For example, a user opens a quantum chemical simulation application software of a computer, and chemical molecular model options to be simulated, such as a hydrogen molecular model, an oxygen molecular model and the like, can be displayed on the quantum chemical simulation application interface. And (4) clicking the chemical molecular model option to be simulated by a user, and determining the chemical molecular model by quantum chemical simulation application. After the chemical molecular model is determined, the number of electrons and the number of electron orbits of the chemical molecular model can be determined.
After the system is determined, the number of orbits and the number of electrons of the system can be determined, and at this time, step S22 is executed.
And S22, determining the number of excitation terms included by the Fermi-form cluster operator of the system according to the orbit number and the electron number of the system based on the spin symmetry.
Specifically, based on spin symmetry, determining the number of excitation terms included in the fermi-form cluster operator of the system according to the number of orbitals and the number of electrons of the system may include the following steps:
s221, acquiring the Hartree-Fock state of the system according to the number of the tracks and the number of the electrons of the system.
For example, the Hartree-Fock state for a hydrogen molecule containing two electrons in four one-electron spin molecular orbitals is represented by quantum state |0011>, i.e., one qubit represents one spin molecular orbit, 0 represents an empty orbit, and 1 represents an occupied orbit. By applying a NOT gate to the corresponding bit, respectively, |0000> can be initialized to |0011> in the quantum wire. For any N-electron system containing M spin molecular orbitals, the corresponding Hartree-Fock states can be expressed in the same way.
S222, determining the number of excitation terms included by the fermi-form cluster operator of the system based on the spin symmetry and the Hartree-Fock state of the system according to a pre-selected proposed mode.
Exemplary, the proposed method includes: UCC (Unitary Coupled Cluster operator) and the like, and the UCC can be specifically divided into a single-excitation Coupled Cluster UCCs and a single-double-excitation Coupled Cluster UCCSD.
Correspondingly, for UCCS and UCCSD, the quantum wires are supposed to be the same, for example, as shown in fig. 3. Fig. 3 is a schematic diagram of a quantum circuit structure corresponding to a pseudo-setup method provided in an embodiment of the present application, where the quantum circuit shown in fig. 3 is a quantum circuit with 4 qubits q0, q1, q2, and q3, and X is-π/2、Xπ/2X gate and Y gate with-pi/2 and-pi/2 parameters respectively, indicating CNOT gate by icon ^ and solid line, ZθA Z gate with a parameter theta is represented. The display simulation principle may include: the proposed formula may be, for example, a matrix operator U (θ) corresponding to a quantum line. For UCC, the corresponding approximate formula is as follows:
wherein,
i.e. the pseudo-device, PiFor generating a primitive, if the electron cluster operator T in UCC is T ═ T1This is called to be UCCS; if the cluster operator T in UCC is T ═ T1+T2This is called the intended UCCSD, where T1For single-particle excitation operators, T2Is a two-particle excitation operator. More specifically, in practical applications, T can be understood as a fermi-form of a cluster operator.
When the proposed mode is a single excitation coupling cluster, the Fermi form cluster operator of the system only comprises a single excitation item number, and on the basis, the single excitation item number is determined to be an excitation item corresponding to the excitation of each electron in the system from the original spin direction orbit to other orbitals with consistent spin directions based on the spin symmetry and the Hartree-Fock state.
When the preselected proposed mode is a single-double excitation coupling cluster, the Fermi-form cluster operator of the system only comprises a single excitation item number and a double excitation item number, and on the basis, the single excitation item number is determined to be an excitation item corresponding to the excitation of each electron in the system from the original spin direction orbit to other orbits with the same spin direction based on spin symmetry and Hartree-Fock state; and determining the number of the double excitation terms as the excitation terms of two electrons in the system which are excited from the original spin direction orbit to the other two orbits with the corresponding spin directions consistent.
The orbitals of the system include both spin-down and spin-up orbitals. That is, based on spin symmetry, if the electron is in the spin-up orbit, it is considered that the electron is excited to other spin-up orbitals. If the electron has the original spin-direction orbit that is the spin-down orbit, then only the electron is considered to be excited to the other spin-down orbit.
Taking hydrogen molecule as an example, |0011 for describing hydrogen molecule>Hartree-FockThe above-mentioned T is a cluster operator of Fermi form of hydrogen molecule. Referring to fig. 4, fig. 4 is a schematic diagram of a hydrogen molecular orbital according to an embodiment of the present disclosure. As shown in fig. 4, for hydrogen molecules, 1Sa orbit of hydrogen atom No. a in spin-down and spin-up is conveniently represented by q0 and q1 qubits, and 1Sb orbit of hydrogen atom No. b in spin-down and spin-up is represented by q2 and q3 qubits, respectively.
As shown in FIG. 4, assuming that two electrons of the hydrogen molecule are located above two orbitals q0 and q1, respectively, if one electron is located on the spin orbit represented by quantum state |1> and the spin orbit is empty represented by quantum state |0011>, then the Hartree-Fock state of the hydrogen molecule can be represented as |0011 >.
When an electron at q0 is excited onto q2, i.e., the electron is first "annihilated" from q0 and then "generated" at q2, it can be represented by the fermi operator:
wherein, t20As a function of the number of the coefficients,
to create an operator, a0Is the annihilation operator.
When an electron at q0 is excited onto q3, i.e., the electron is first "annihilated" from q0 and then "generated" at q3, it can be represented by the fermi operator:
wherein, t30As a function of the number of the coefficients,
to create an operator, a0Is the annihilation operator.
When an electron at q1 is excited onto q2, i.e., the electron is first "annihilated" from q1 and then "generated" at q2, it can be represented by the fermi operator:
wherein, t21As a function of the number of the coefficients,
to create an operator, a1Is the annihilation operator.
When an electron at q1 is excited onto q3, i.e., the electron is first "annihilated" from q1 and then "generated" at q3, it can be represented by the fermi operator:
wherein, t31As a function of the number of the coefficients,
to create an operator, a1Is the annihilation operator.
When electrons on q0 and q1 are excited simultaneously on q2 and q3, that is, electrons are first "annihilated" from q0 and q1 and then "generated" on q2 and q3, they can be expressed as fermi operators:
wherein, t3210As a function of the number of the coefficients,
to create an operator, a1、a0Is the annihilation operator.
[ 0011 ] for describing Hydrogen molecule>Hartree-FockThe state, T at this time, is the Fermi-form cluster operator H for the hydrogen moleculeu：
Wherein, T1Is a single particle excitation operator, T2Is a two-particle excitation operator.
When the proposed mode is single shot coupled cluster, the fermi-form cluster operator of the system includes the number of single shots. I.e. |0011 to describe hydrogen molecule>Hartree-FockState of the artWhen spin symmetry is considered:
the inventors of the present application combined spin symmetry, i.e. the transition rule, when the proposed approach is to excite a single coupled cluster, only two transition states, the electron excitation on q0 to q2 and the electron excitation on q1 to q3, need to be considered. Thus, in the present application, based on spin symmetry, when the proposed approach is to singly excite a coupled cluster:
that is, when the proposed mode is a single excitation coupled cluster, the fermi-form cluster operator for calculating hydrogen molecules of the present application includes only two excitation terms, while the fermi-form cluster operator for calculating hydrogen molecules of the prior art includes four excitation terms.
When the proposed mode is single-double excitation coupled cluster, the Fermi-form cluster operator of the system includes the number of single excitation terms and the number of double excitation terms, i.e. |0011 for describing hydrogen molecule>Hartree-FockStates, when spin symmetry is not considered:
the inventor only needs to consider three transition states that an electron on q0 is excited to q2 and an electron on q1 is excited to q3 and an electron on q0 and q1 is simultaneously excited to q2 and q3 when the proposed mode is a single-double excitation coupled cluster by combining spin symmetry, namely a transition rule. That is, when the proposed mode is single-double excitation coupled cluster, the fermi form cluster operator for calculating hydrogen molecules of the present application includes only three excitation terms, while the fermi form cluster operator for calculating hydrogen molecules of the prior art includes five excitation terms.
It should be emphasized that the above proposed design is only an example and does not constitute a limitation of the present invention, for example, the design may also include HE (Hardware Efficient), SP (Symmetry Preserved), and the like.
After the number of excitation terms included in the fermi-form cluster operator of the hierarchy is determined, step S23 is performed.
And S23, calculating the fermi form cluster operator of the system according to the number of the excitation terms.
In step S22, a fermi form cluster operator corresponding to the hydrogen molecule is given, and similarly, for other systems, after the number of excitation terms included in the fermi form cluster operator is determined, the fermi form cluster operator of the system can be calculated according to the corresponding algorithm of the system.
After the cluster operator in the fermi form of the hierarchy is calculated, step S24 is executed.
And S24, solving the experimental state of the system based on the Fermi form cluster operator of the system.
The test state of the system is an important intermediate parameter in calculating the ground state energy of the system. For any one trial state | ψ>(which is a gooey function) when the Hamiltonian H of a system is applied to the system, the average energy E of the system in this state can be obtained, and the average energy is larger than or equal to the ground state energy E of the system0The expression is as follows:
from this expression, it can be seen that by continuously adjusting the trial state, if the adjusted trial state | ψ>Is the ground state of the system | /)0>When the equal sign in the inequality is true, the ground state energy E of the system can be obtained0。
Alternatively, solving the trial state of the system based on the fermi form of the system's cluster operators may comprise the steps of:
s241, transforming the fermi operator form of the system into a pauli operator form of the cluster operator according to the pre-selected mapping method.
The mapping method may include: a Jordan-Wigner transform (J-W transform), a Parity transform, a Bravyi-Kitaev transform (B-K transform), an MSP (Multi layer Segmented Parity) transform, and so on.
As can be understood by those skilled in the art, the mapping principle corresponding to each mapping mode may include: the principle of state mapping and the principle of operator mapping.
For example, for a J-W transformation, the displayed state mapping is:
wherein,
represents the computational state of the qubit and,
a transformation matrix is represented that is,
representing the occupation state of the fermi system. The displayed operator map is:
wherein,
representing lifting operator, j representing qubit number, P representing parity set, ZP(j)A set of pauli Z matrices acting on the qubits belonging to the parity set P is represented, X representing the pauli X matrix and Y representing the pauli Y matrix.
Equally, the operator mapping can also be shown as:
wherein,
a representation generation operator, ajWhich represents the annihilation operator, is,
and ajCollectively called the lifting operator of the fermi system,
representing the generation operator/annihilation operator on the qubit,
representing an astronomical operator and n representing the number of quantum bits.
The state mapping and operator mapping display modes of other transformations are the same as those of J-W transformation.
Wherein the Fermi-form cluster operator is transformed into the Paglie operator-form cluster operator according to a preselected mapping manner. For example, for the design of UCCS
T is a fermi form of the cluster operator, which needs to be transformed into the pauli operator form in order to generate the unitary operator from the pauli operator, which is the basis for constructing the corresponding concrete quantum line.
After converting the fermi-form cluster operator into the pauli-form cluster operator, step S242 is executed.
S242, decomposing the cluster operator in the Pagli operator form into a corresponding unitary operator form and carrying out evolution to obtain an evolved quantum state; wherein the evolved quantum state is a test state of the system.
Optionally, decomposing the cluster operator in the form of the bubble operator into a corresponding unitary operator and evolving to obtain an evolved quantum state, may include the following steps:
and S2421, constructing a quantum simulation circuit based on the corresponding unitary operator after the cluster operator in the form of the Pally operator is decomposed.
And S2422, carrying out analog evolution according to the quantum analog circuit to obtain an evolved quantum state.
Next, please refer to fig. 5-9. Assuming that after J-W transformation of a Fermi sub-cluster operator containing five sub-terms, the Paglie operator form of the cluster operator T is as follows:
first, H is calculated1The corresponding unitary operator:
FIG. 5 is a drawing H provided in the examples of the present application1Corresponding quantum wire schematic. As shown in fig. 5, by H1As can be seen from the corresponding unitary operator, RZ (2 θ) is added to q01) Door, namely H can be obtained1Corresponding quantum wires.
Then, H is calculated2The corresponding unitary operator:
FIG. 6 is a drawing H provided in the examples of the present application1And H2Corresponding quantum wire schematic. As shown in fig. 6, by H2The corresponding unitary operator can know that q0 is used as a control bit, q1 is used as a target bit, and a CNOT gate is added; then, RZ (2 θ) is added to q12) A door; then, using q0 bit as controlThe system bit, q1 is the target bit, and CNOT gate is added to obtain H2Corresponding quantum wires.
Then, H is calculated3The corresponding unitary operator:
FIG. 7 is a drawing H provided in the examples of the present application1、H2And H3Corresponding quantum wire schematic. As shown in FIG. 7, by H3The corresponding unitary operator can know that two CNOT gates are required to be added in sequence by taking q0 as a control bit, q1 as a target bit, q1 as a control bit and q2 as a target bit; then, RZ (2,2 θ) is added to q23) A door; then, using q0 bit as control bit and q1 as target bit, adding CNOT gate to obtain H3Corresponding quantum wires.
Then, H is calculated4The corresponding unitary operator:
FIG. 8 is a drawing showing a schematic diagram of H according to an embodiment of the present application1、H2、H3And H4Corresponding quantum wire schematic. As shown in FIG. 8, by H4The corresponding unitary operator can know that a Hadamard gate is required to be added on q 0; adding a first CNOT gate by using q0 as a control bit and q1 as a target bit; then, RZ (2 θ) is added to q14) A door; then, add a second CNOT gate with q0 as the control bit and q1 as the target bit; finally, a Hadamard gate is added to q0 to obtain H4Corresponding quantum wires.
Then, H is calculated5The corresponding unitary operator:
FIG. 9 is a drawing showing a schematic diagram of H according to an embodiment of the present application1、H2、H3、H4And H5Corresponding quantum wire schematic. As shown in fig. 9, by H5The corresponding unitary operator can know that q0 needs to be added first
A door; adding a first CNOT gate by using q0 as a control bit and q1 as a target bit; then, RZ (2 θ) is added to q15) A door; then, add a second CNOT gate with q0 as the control bit and q1 as the target bit; finally, add to q1
Door, i.e. obtaining the simulation H5Corresponding quantum wires. That is to say that FIG. 9 includes H1、H2、H3、H4And H5The corresponding quantum wire schematic, i.e., H for H, is shown in fig. 9.
Fig. 5-9 illustrate how a fermi-form cluster operator containing five sub-entries constructs a quantum wire. [ 0011 ] for describing Hydrogen molecule>Hartree-FockAnd when the quasi-design mode is UCCSD, the mapping mode is J-W transformation, and the rotational symmetry mode is not considered, the Fermi-form cluster operator also comprises five subentries, namely, when constructing the quantum wire, the five subentries of the Fermi-form cluster operator need to be converted into the form of a Pachy operator and decomposed into the form of a corresponding unitary operator. Then, the quantum wires corresponding to the five sub-items are constructed in time series. Then, the quantum circuit corresponding to the five sub-items is combined to form the quantum analog circuit. And finally, carrying out analog evolution according to the quantum analog circuit to obtain an evolved quantum state.
Whereas the present application is for |0011 describing hydrogen molecules due to consideration of spin symmetry>Hartree-FockAnd in the state, under the conditions that the proposed mode is single-double excitation coupling cluster and the mapping mode is J-W conversion, the Fermi form cluster operator has only three sub-items. When constructing a quantum line, only three subentries need to be converted into a Pagli operator form and decomposed into a corresponding unitary operator form. Then theThe quantum wires corresponding to the three sub-items are constructed in time sequence. Then, the quantum circuit corresponding to the three sub-items is combined to form the quantum analog circuit. And finally, carrying out analog evolution according to the quantum analog circuit to obtain an evolved quantum state.
In the process of preparing the system test state, when the Fermi form cluster operator of the system is calculated, due to the fact that the spin symmetry is considered, the number of excitation terms needing to be calculated in the Fermi form cluster operator is smaller than that when the spin symmetry is not considered in the prior art, the complexity of the system is reduced, further when the test state of the system is solved, the calculation amount is reduced, the technical problem that complex molecules are difficult to simulate in the prior art is solved, calculation resources are saved, calculation of subsequent system energy is facilitated, and the simulation efficiency of the complex molecules is improved.
In practical application, for any one experimental state | ψ>(which is a product-wave function) which, when acted upon by the Hamilton of a system (e.g., a multi-electron system), yields the average energy E of the system in that state, which is greater than or equal to the energy E of the system0. Continuously adjusting the test state until the test state is | psi>Is the ground state of the system | /)0>Then correspondingly obtaining the energy E of the system0。
Therefore, further, after the system test state | ψ > is prepared by a method of calculating a system test state provided in the present application, the ground state energy of the system can be solved. For example, first, the average energy of the system in the trial state | ψ > is calculated; then, it is judged whether the average energy of the system in the test state | ψ > can be used as the ground state energy of the system. If so, obtaining the ground state energy of the system; otherwise, updating the test state and returning to the step of calculating the average energy of the system in the test state.
When the Fermi-form cluster operator of the system is calculated, due to the fact that the spin symmetry is considered, the number of excitation terms needing to be calculated in the Fermi-form cluster operator is smaller than that when the spin symmetry is not considered in the prior art, complexity of the system is reduced, further when energy of the system is solved, calculated amount is reduced, the technical problem that complex molecules are difficult to simulate in the prior art is solved, calculation resources are saved, and simulation efficiency of the complex molecules is improved.
Referring to fig. 10, fig. 10 is a schematic structural diagram of an apparatus for preparing a test state of a system based on spin symmetry according to an embodiment of the present invention, and the apparatus 110 for preparing a test state of a system based on spin symmetry includes, corresponding to the flow shown in fig. 2:
a first determining module 111, configured to determine a system and the number of tracks and the number of electrons of the system;
a second determining module 112, configured to determine, based on the spin symmetry, the number of excitation terms included in the fermi-form cluster operator of the system according to the number of orbitals and the number of electrons of the system;
a calculating module 113, configured to calculate a fermi form cluster operator of the system according to the number of the excitation terms;
and the solving module 114 is used for determining a cluster operator based on the Fermi form of the system and solving the experimental state of the system.
Optionally, the second determining module 112 includes:
the acquisition unit is used for acquiring the Hartree-Fock state of the system according to the number of the tracks and the number of the electrons of the system;
and the determining unit is used for determining the number of excitation terms included by the fermi-form cluster operator of the system based on the spin symmetry and the Hartree-Fock state of the system according to a pre-selected proposed mode.
Optionally, the determining unit is further configured to: when the proposed mode is single excitation coupling cluster, determining that the Fermi form cluster operator of the system only comprises single excitation item number; and determining the number of the single excitation terms as excitation terms corresponding to the excitation of each electron in the system from the original spin direction orbit to other orbits with consistent spin directions based on the spin symmetry and the Hartree-Fock state.
Optionally, the determining unit is further configured to: when the preselected simulation mode is a single-double excitation coupling cluster, determining that the Fermi-form cluster operator of the system only comprises a single excitation number and a double excitation number; determining the number of the single excitation terms as excitation terms corresponding to other orbits with the same spin direction from the orbit of the original spin direction to the excitation terms corresponding to the orbits with the same spin direction of each electron in the system based on spin symmetry and Hartree-Fock state; and determining the number of the double excitation terms as the excitation terms of two electrons in the system which are excited from the original spin direction orbit to the other two orbits with the corresponding spin directions consistent.
Optionally, the second determining module 112 further includes:
a transformation unit for transforming the Fermi operator form of the system into a Paglie operator form of the cluster operator according to a preselected mapping manner;
the evolution unit is used for decomposing the cluster operator in the form of the Pagli operator into a corresponding unitary operator form and carrying out evolution so as to obtain an evolved quantum state; wherein the evolved quantum state is a test state of the system.
Optionally, the evolution unit is further configured to: constructing a quantum simulation line based on the unitary operator corresponding to the decomposed cluster operator in the form of the Pally operator; and carrying out analog evolution according to the quantum analog circuit to obtain an evolved quantum state.
Optionally, the mapping manner is one of Jordan-Wigner transformation, Parity transformation, Bravyi-Kitaev transformation, and SegmentParity transformation.
In addition, the technical effect of the apparatus 110 for preparing the system experimental state based on spin symmetry can refer to the technical effect of the method for calculating the system experimental state shown in fig. 2, and will not be described herein again.
An embodiment of the present invention further provides a storage medium, in which a computer program is stored, where the computer program is configured to execute the steps in any of the above method embodiments when running.
Specifically, in the present embodiment, the storage medium may be configured to store a computer program for executing the steps of:
s1, determining a system and the orbit number and the electron number of the system;
s2, determining the number of excitation terms included by the Fermi-form cluster operator of the system according to the orbit number and the electron number of the system based on the spin symmetry;
s3, calculating a fermi form cluster operator of the system according to the number of the excitation terms;
and S4, solving the experimental state of the system based on the Fermi form cluster operator of the system.
Specifically, in this embodiment, the storage medium may include, but is not limited to: a U-disk, a Read-only Memory (ROM), a Random Access Memory (RAM), a removable hard disk, a magnetic disk, or an optical disk, which can store computer programs.
An embodiment of the present invention further provides an electronic apparatus, which includes a memory and a processor, where the memory stores a computer program, and the processor is configured to execute the computer program to perform the steps in any of the above method embodiments.
Specifically, the electronic apparatus may further include a transmission device and an input/output device, wherein the transmission device is connected to the processor, and the input/output device is connected to the processor.
Specifically, in this embodiment, the processor may be configured to execute the following steps by a computer program:
s1, determining a system and the orbit number and the electron number of the system;
s2, determining the number of excitation terms included by the Fermi form cluster operator of the system according to the orbit number and the electron number of the system based on the spin symmetry;
s3, calculating a fermi form cluster operator of the system according to the number of the excitation terms;
and S4, solving the experimental state of the system based on the Fermi form cluster operator of the system.
It should also be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
The foregoing description has been directed to specific embodiments of this disclosure. Other embodiments are within the scope of the following claims. In some cases, the actions or steps recited in the claims may be performed in a different order than in the embodiments and still achieve desirable results. In addition, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results. In some embodiments, multitasking and parallel processing may also be possible or may be advantageous.
The terminology used in the description of the one or more embodiments is for the purpose of describing the particular embodiments only and is not intended to be limiting of the description of the one or more embodiments. As used in one or more embodiments of the present specification and the appended claims, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It should also be understood that the term "and/or" as used herein refers to and encompasses any and all possible combinations of one or more of the associated listed items.
It should be understood that although the terms first, second, third, etc. may be used in one or more embodiments of the present description to describe various information, such information should not be limited to these terms. These terms are only used to distinguish one type of information from another. For example, first information may also be referred to as second information, and similarly, second information may also be referred to as first information, without departing from the scope of one or more embodiments herein. The word "if" as used herein may be interpreted as "at … …" or "when … …" or "in response to a determination", depending on the context. The above description is only for the purpose of illustrating the preferred embodiments of the one or more embodiments of the present disclosure, and is not intended to limit the scope of the one or more embodiments of the present disclosure, and any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the one or more embodiments of the present disclosure should be included in the scope of the one or more embodiments of the present disclosure.
The construction, features and functions of the present application are described in detail in the embodiments illustrated in the drawings, which are only preferred embodiments of the present application, but the present application is not limited by the drawings, and all changes that can be made and equivalents modified according to the idea of the present application are intended to be covered by the scope of the present application.
Claims (10)
1. A method for preparing a system test state based on spin symmetry is characterized by comprising the following steps:
determining a system and the number of orbits and electrons of the system;
determining the number of excitation terms included by a fermi-form cluster operator of the system according to the number of orbitals and the number of electrons of the system based on spin symmetry;
calculating a fermi form cluster operator of the system according to the number of the excitation terms;
solving the trial state of the system based on the fermi form of the system's cluster operator.
2. The method of claim 1, wherein determining the number of excitation terms included in the fermi-form cluster operator of the system based on the number of orbitals and the number of electrons of the system based on spin symmetry comprises:
acquiring a Hartree-Fock state of the system according to the number of the tracks and the number of the electrons of the system;
and determining the number of excitation terms included by the fermi-form cluster operator of the system based on the spin symmetry and the Hartree-Fock state of the system according to a pre-selected proposed mode.
3. The method of claim 2, wherein determining the number of excitation terms included by the fermi-form cluster operator for the regime based on spin symmetry and Hartree-focus states of the regime according to a preselected proposed approach comprises:
when the proposed mode is a single excitation coupling cluster, determining that the Fermi form cluster operator of the system only comprises a single excitation item number;
and determining the number of the single excitation terms as excitation terms corresponding to the excitation of each electron in the system from the original spin direction orbit to other orbits with consistent spin directions based on the spin symmetry and the Hartree-Fock state.
4. The method of claim 2, wherein determining the number of excitation terms included by the fermi-form cluster operator of the regime based on spin symmetry and the Hartree-focus state of the regime according to a preselected proposed approach comprises:
when the preselected simulation mode is a single-double excitation coupling cluster, determining that the Fermi-form cluster operator of the system only comprises a single excitation number and a double excitation number;
determining the number of the single excitation terms as excitation terms corresponding to other orbits with the same spin direction from the orbit of the original spin direction to the excitation terms corresponding to the orbits with the same spin direction of each electron in the system based on spin symmetry and Hartree-Fock state; and determining the number of the double excitation terms as the excitation terms of two electrons in the system which are excited from the original spin direction orbit to the other two orbits with the corresponding spin directions consistent.
5. The method of claim 2, wherein solving the trial state of the system based on the cluster operator of the fermi form of the system comprises:
transforming the Fermi operator form cluster operator of the system into a Paglie operator form cluster operator according to a preselected mapping mode;
decomposing the cluster operator in the form of the Pagli operator into a corresponding unitary operator form and carrying out evolution to obtain an evolved quantum state; wherein the evolved quantum state is a test state of the system.
6. The method of claim 5, wherein decomposing the Pally operator form of cluster operators into corresponding unitary operator forms and evolving to obtain evolved quantum states comprises:
constructing a quantum simulation line based on the unitary operator corresponding to the decomposed cluster operator in the form of the Pally operator;
and carrying out analog evolution according to the quantum analog circuit to obtain an evolved quantum state.
7. The method of claim 5 or 6, wherein the mapping is one of a Jordan-Wigner transform, a Party transform, a Bravyi-Kitaev transform, and a SegmentParty transform.
8. An apparatus for preparing a test state of a system based on spin symmetry, comprising:
the system comprises a first determining module, a second determining module and a control module, wherein the first determining module is used for determining a system and the track number and the electron number of the system;
the second determination module is used for determining the number of excitation terms included by the fermi form cluster operator of the system according to the orbit number and the electron number of the system based on the spin symmetry;
the calculation module is used for calculating the fermi form cluster operator of the system according to the number of the excitation terms;
and the solving module is used for determining the cluster operator based on the Fermi form of the system and solving the experimental state of the system.
9. An electronic device, comprising:
a processor;
a memory for storing processor-executable instructions;
wherein the processor implements the method of any one of claims 1-7 by executing the executable instructions.
10. A computer storage medium having stored thereon computer instructions which, when executed by a processor, carry out the steps of the method according to any one of claims 1 to 7.
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