WO2023045078A1 - 量子体系的本征态获取方法、装置、设备及存储介质 - Google Patents

量子体系的本征态获取方法、装置、设备及存储介质 Download PDF

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WO2023045078A1
WO2023045078A1 PCT/CN2021/134932 CN2021134932W WO2023045078A1 WO 2023045078 A1 WO2023045078 A1 WO 2023045078A1 CN 2021134932 W CN2021134932 W CN 2021134932W WO 2023045078 A1 WO2023045078 A1 WO 2023045078A1
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eigenstate
direct product
cluster
hamiltonian
target
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PCT/CN2021/134932
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French (fr)
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吴建澜
尹艺
占泽
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深圳市腾讯计算机系统有限公司
浙江大学
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Priority to JP2022566475A priority Critical patent/JP7394413B2/ja
Priority to US18/078,234 priority patent/US20230124152A1/en
Publication of WO2023045078A1 publication Critical patent/WO2023045078A1/zh

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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N10/00—Quantum computing, i.e. information processing based on quantum-mechanical phenomena
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N10/00—Quantum computing, i.e. information processing based on quantum-mechanical phenomena
    • G06N10/60—Quantum algorithms, e.g. based on quantum optimisation, quantum Fourier or Hadamard transforms

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  • the embodiments of the present application relate to the field of quantum technology, and in particular to a method, device, equipment and storage medium for obtaining eigenstates of a quantum system.
  • quantum algorithms have important applications in many fields, among which, solving the eigenstates and eigenenergy of quantum systems is a very critical issue.
  • a quantum eigenstate solving algorithm based on a variational method is provided.
  • a trial wave function can be designed, and the minimum value of the corresponding energy can be found by continuously changing the trial wave function, which is the ground state energy and the ground state.
  • the first excited state of a quantum system is the state corresponding to the lowest energy in the wave function orthogonal to the ground state. After determining the ground state, it can be used to find the first excited state in the state space orthogonal to it.
  • the second excited state is the state corresponding to the lowest energy in the wave function orthogonal to the ground state and the first excited state, and so on. In theory, this method can be used to find all the eigenstates of the quantum system.
  • Embodiments of the present application provide a method, device, device, and storage medium for obtaining eigenstates of a quantum system. Described technical scheme is as follows:
  • a method for obtaining an eigenstate of a quantum system is provided, the method is executed by a computer device, and the method includes:
  • the eigenstate and eigenenergy of the equivalent Hamiltonian are obtained as the eigenstate and eigenenergy of the target quantum system.
  • an eigenstate acquisition device of a quantum system includes:
  • a division module configured to perform cluster division on a plurality of particles contained in the target quantum system to obtain a plurality of clusters, each of the plurality of clusters contains at least one particle;
  • the selection module is used to select a part of the direct product state as a set of basis vectors to represent a compressed Hilbert space from the plurality of direct product states, wherein the dimensionality of the compressed Hilbert space is, less than the number of dimensions of the original Hilbert space of the target quantum system;
  • the first acquisition module is used to acquire the Hamiltonian of the target quantum system, the equivalent Hamiltonian in the compressed Hilbert space;
  • the second acquisition module is configured to acquire the eigenstates and eigenenergy of the equivalent Hamiltonian as the eigenstates and eigenenergy of the target quantum system.
  • a computer device includes a processor and a memory, at least one instruction, at least one program, a code set or an instruction set are stored in the memory, and the at least one The instructions, the at least one segment of the program, the code set or the instruction set are loaded and executed by the processor to realize the method for obtaining the eigenstates of the quantum system described above.
  • a computer-readable storage medium stores at least one instruction, at least one section of program, code set or instruction set, the at least one instruction, the at least one section
  • the program, the code set or the instruction set is loaded and executed by the processor to realize the method for obtaining the eigenstates of the quantum system described above.
  • a computer program product or computer program includes computer instructions, and the computer instructions are stored in a computer-readable storage medium.
  • the processor of the computer device reads the computer instruction from the computer-readable storage medium, and the processor executes the computer instruction, so that the computer device executes the above method for obtaining eigenstates of the quantum system.
  • the eigenstates of multiple clusters are obtained, and then multiple direct product states are obtained.
  • some direct product states are selected to construct compressed Hill Bert space reduces the dimensionality of Hilbert space; the problem of solving the eigenstate of the Hamiltonian of a high-dimensional system with multi-bit interactions is split into multiple low-dimensional Hamiltonian eigenvalues state solving problem, and then construct a compressed Hilbert space, and obtain the eigenvalue of the equivalent Hamiltonian by calculating the equivalent Hamiltonian of the target quantum system in the compressed Hilbert space and eigenenergy, as the eigenvalue and eigenenergy of the target quantum system, since the dimension number of the compressed Hilbert space is smaller than the dimension number of the original Hilbert space of the target quantum system, it avoids the , the required quantum gate operations increase rapidly with the increase of the dimension of the system, and the number of gates to achieve multi-bit interaction increases rapidly with the increase of the interaction dimension, which reduces the requirement for eigen
  • Fig. 1 is the flow chart of the eigenstate acquisition method of the quantum system provided by one embodiment of the present application;
  • FIG. 2 is a flow chart of a method for obtaining an eigenstate of a quantum system provided in another embodiment of the present application;
  • Fig. 3 is a schematic diagram of a cluster division method provided by an embodiment of the present application.
  • Fig. 4 is a schematic diagram of a cluster division method provided by another embodiment of the present application.
  • Fig. 5 is a flow chart of a method for obtaining an eigenstate of a quantum system provided by another embodiment of the present application.
  • Fig. 6 is a schematic diagram of the ground state accuracy provided by an embodiment of the present application.
  • Fig. 7 is a schematic diagram of the intrinsic energy accuracy provided by an embodiment of the present application.
  • Fig. 8 is a block diagram of an eigenstate acquisition device of a quantum system provided by an embodiment of the present application.
  • Fig. 9 is a block diagram of an eigenstate acquisition device of a quantum system provided by an embodiment of the present application.
  • Fig. 10 is a structural block diagram of a computer device provided by an embodiment of the present application.
  • Quantum computing Based on quantum logic computing, the basic unit of data storage is the quantum bit (qubit).
  • Qubit The basic unit of quantum computing. Traditional computers use 0 and 1 as the basic units of binary. The difference is that quantum computing can process 0 and 1 at the same time, and the system can be in a linear superposition state of 0 and 1:
  • ⁇ > ⁇
  • 2 represent the probability of being 0 and 1, respectively.
  • Hamiltonian A Hermitian matrix that describes the total energy of a quantum system.
  • the Hamiltonian is a physical vocabulary and an operator that describes the total energy of a system, usually denoted by H.
  • Quantum state In quantum mechanics, a quantum state is a microscopic state determined by a set of quantum numbers.
  • Cluster It is a collection composed of multiple particles.
  • the particles in the embodiments of the present application may also be referred to as spins.
  • the qubit is the basic unit in quantum computing. We can use one qubit to simulate a particle/spin in a physical system, or use multiple qubits to simulate a particle/spin.
  • Eigenstate In quantum mechanics, the possible values of a mechanical quantity are all the eigenvalues of its operators. The state described by the eigenfunction is called the eigenstate of the operator. In its own eigenstate, this mechanical quantity takes on a definite value, that is, the eigenvalue to which this eigenstate belongs.
  • Direct product state In quantum mechanics, the state (state vector) of the system can be represented by a function, called "state function" (it can be understood as a function or as a vector, The two are not contradictory).
  • state function In quantum mechanics, the state function of a single-particle system is a one-variable function, and the state function of a multi-particle system is a multivariate function. If this multivariate function can separate variables, that is, it can be written as the direct product of multiple unary functions, we call it a "direct product state”.
  • the first excited state it is the excited state with the lowest energy among the excited states.
  • Second quantization The method of processing identical particle systems in the symmetric Hilbert space using generation operators and elimination operators, usually called the second quantization method.
  • Hilbert space refers to a complete inner product space.
  • Quantum gate In quantum computing, especially in the computing model of quantum circuits, a quantum gate (Quantum gate, or quantum logic gate) is a basic quantum circuit that operates a small number of qubits.
  • the ground state After determining the ground state, it can be used to find the first excited state in the state space orthogonal to it.
  • the second excited state is the state corresponding to the lowest energy in the wave function orthogonal to the ground state and the first excited state, and so on. In theory, this method can be used to find all the eigenstates of the system.
  • adiabatic approximation means that if a certain perturbation acts on a physical system slowly enough, the instantaneous eigenstate of the physical system can be regarded as constant. So if we can change the Hamiltonian of a physical system slowly enough, the physical system will always evolve along its instantaneous eigenstate. Therefore, by constructing a known eigenstate corresponding to a simple Hamiltonian on the quantum device, and then slowly evolving it to the Hamiltonian of the physical system we want to solve, the measured quantum device obtains The quantum state is the eigenstate corresponding to the Hamiltonian we want to solve.
  • adiabatic approximation requires the system to evolve slowly enough. On the basis of adiabatic approximation, the evolution of the system can be accelerated by introducing a fast adiabatic term, and it can evolve to the target state in a shorter time. symptoms.
  • Leapfrog quantum eigenstate solution algorithm realized by combining adiabatic approximation and adiabatic shortcut: For any target system, one or a group of reference points that are similar in form to the Hamiltonian of the target system but with relatively small coupling strength can be constructed , if we start from a known eigenstate corresponding to a simple Hamiltonian and try to evolve to a reference point with a relatively small coupling strength, its fast adiabatic term has a simpler form, and can be easily obtained through the fast adiabatic The quantum eigenstate solving algorithm solves the eigenstate of the reference point.
  • the Hamiltonian of the quantum system after the second quantization can be expressed as formula (1).
  • the Hamiltonian of this multi-electron quantum system can be rewritten as a multi-spin Hamiltonian, such as the formula ( 2) as shown.
  • the present application proposes an eigenstate acquisition method of a quantum system, which can realize an approximate but accurate diagonalization solution in a highly compressed space.
  • the eigenstate acquisition method of the quantum system provided by the embodiment of the present application can be implemented by a classical computer (such as a PC), for example, by performing a corresponding computer program on a classical computer to realize the method; it can also be implemented on a classical computer and a quantum computer Execution in a mixed device environment, for example, a classical computer and a quantum computer cooperate to realize the method.
  • a quantum computer is used to solve the eigenstates of multiple clusters and the eigenstates of the equivalent Hamiltonian in the embodiments of the present application, and a classical computer is used to realize the solutions except Additional steps beyond solving eigenstate problems.
  • the execution subject of each step is a computer device for introduction and description.
  • the computer device may be a classical computer, or may include a mixed execution environment of a classical computer and a quantum computer, which is not limited in this embodiment of the present application.
  • FIG. 1 shows a flowchart of a method for obtaining eigenstates of a quantum system provided by an embodiment of the present application.
  • the execution subject of each step of the method may be a computer device.
  • the method may include at least one of the following steps (110-150).
  • Step 110 performing cluster division on multiple particles contained in the target quantum system to obtain multiple clusters, each cluster containing at least one particle.
  • multiple particles included in the target quantum system are divided into clusters to obtain multiple clusters.
  • Each cluster contains one or more particles of the target quantum system, different clusters do not contain the same particles, and the sum of the number of particles contained in multiple clusters is equal to the number of particles contained in the target quantum system The total amount.
  • the target quantum system refers to the quantum system whose eigenstates are to be obtained.
  • there are multiple ways to divide the clusters. Exemplarily, suppose a quantum system with N particles can be divided into two clusters, each cluster contains N 1 and N 2 particles, N 1 +N 2 N, for a given N 1
  • the value of , the number of alternative ways of cluster division can be calculated by permutation and combination, the maximum value
  • the target quantum system contains 10 particles, the 10 particles contained in the target quantum system are divided into clusters to obtain multiple clusters, and each cluster contains at least one particle.
  • the 10 particles contained in the target quantum system are divided into two clusters, the first cluster and the second cluster, wherein the first cluster contains 5 particles, and the second cluster contains 5 particles.
  • divide the 10 particles contained in the target quantum system into two clusters, the first cluster and the second cluster, wherein the first cluster contains 4 particles, and the second cluster contains 6 particles .
  • Step 120 according to the eigenstates corresponding to the multiple clusters, multiple direct product states are obtained.
  • each cluster its corresponding eigenstate is solved, and then multiple direct product states are obtained according to the eigenstate corresponding to each of the multiple clusters.
  • step 120 may include the following several sub-steps (1-3):
  • the reduced Hamiltonian of the target cluster refers to the reduced representation of the real Hamiltonian of the target cluster.
  • the reduced Hamiltonian of the target cluster can be obtained .
  • the Hamiltonian of the target cluster under the environment is obtained to obtain the reduced Hamiltonian of the target cluster.
  • the target quantum system is divided into two clusters, cluster A and cluster B.
  • cluster A cluster B is used as the environment, and a partial trace of a specific quantum state is performed
  • the reduced Hamiltonian of cluster A can be obtained
  • ⁇ refers to the ⁇ th quantum state of cluster B
  • H refers to the Hamiltonian of the target quantum system
  • a specific quantum state refers to a specific quantum state of the environment
  • each quantum state of the environment corresponds to a cluster
  • the reduced Hamiltonian of cluster A Conversely, for cluster B, the same method applies.
  • the quantum state of the isolated cluster A As the quantum state of the environment, the reduced Hamiltonian of cluster B can then be obtained Among them, ⁇ refers to the ⁇ -th quantum state of cluster A, and H refers to the Hamiltonian of the target quantum system.
  • the ground state corresponding to the target cluster can be obtained according to the reduced Hamiltonian of the target cluster.
  • the excited state corresponding to the target cluster can also be obtained according to the reduced Hamiltonian of the target cluster.
  • a diagonalization algorithm is used to obtain at least one eigenstate corresponding to the target cluster.
  • the diagonalization algorithm includes but is not limited to at least one of the following: quantum eigenstate solving algorithm based on variational method, quantum eigenstate solving algorithm based on adiabatic approximation, quantum eigenstate solving algorithm based on adiabatic shortcut algorithm, a quantum eigenstate solution algorithm combining adiabatic approximation and adiabatic shortcut.
  • the target quantum system is divided into two clusters, cluster A and cluster B.
  • Reduced Hamiltonian for Cluster A Perform diagonalization to obtain at least one eigenstate and intrinsic energy where i refers to the ith eigenstate/eigenenergy, and ⁇ refers to the ⁇ th quantum state of cluster B.
  • the equivalent Hamiltonian for cluster B Diagonalize At least one eigenstate and eigenenergy are obtained, where j refers to the jth eigenstate/eigenenergy, and ⁇ refers to the ⁇ th quantum state of cluster A.
  • the target quantum system is divided into two clusters, the first cluster and the second cluster, wherein the first cluster corresponds to 2 eigenstates, and the second cluster corresponds to 2 eigenstates, for the above total
  • the direct product operation is performed on the 4 eigenstates to obtain four direct product states.
  • Step 130 select some direct product states from the plurality of direct product states as a set of basis vectors to represent a compressed Hilbert space.
  • the dimensionality of the compressed Hilbert space is smaller than the dimensionality of the original Hilbert space of the target quantum system.
  • the dimensionality of the original Hilbert space of the target quantum system is 2 10
  • the dimensionality of the compressed Hilbert space should be less than 2 10 .
  • the associated direct product states are chosen as a set of basis vectors to represent a compressed Hilbert space.
  • the associated direct product state refers to the direct product state with an orthogonal relationship, that is, the direct product state perpendicular to other states.
  • ⁇ x ⁇ represents a set
  • i refers to the i-th eigenstate/eigenenergy
  • ⁇ refers to the ⁇ -th quantum state of cluster B
  • j refers to the j-th eigenstate/eigenenergy
  • ⁇ is refers to the ⁇ th quantum state of cluster A, but the regular recursive iteration is divergent if multiple states are considered.
  • step 130 may include the following several sub-steps (1-2):
  • n direct product states with the smallest energy value as a set of basis vectors to represent the compressed Hilbert space
  • n is a positive integer.
  • n is a set number
  • the above n direct product states may also be referred to as a set number of direct product states.
  • the energy values of multiple direct product states are sorted in ascending order, and a set number of direct product states are selected as a set of basis vectors to represent the compressed Hilbert space.
  • the energy values of multiple direct product states are sorted in descending order, and a set number of direct product states among them are selected as a set of basis vectors to represent the compressed Hilbert space.
  • the set quantity refers to the set selection quantity for the direct product state
  • the former set quantity refers to selecting the first direct product state according to the set quantity when selecting the direct product state
  • the latter set quantity is It refers to selecting the next direct product state according to the set quantity when selecting the direct product state.
  • the set quantity is 2 then for the seven numbers 1, 2, 3, 4, 5, 6, and 7, the numbers selected according to the previous set quantity are 1 and 2, and according to the latter The numbers chosen for the set quantity are 6 and 7.
  • screening can also be performed according to the degree of entanglement of multiple direct product states, and some direct product states can be selected as a set of basis vectors to represent a compressed Hilbert space.
  • the application does not make a limitation on the selection method of the partial direct product state.
  • Step 140 obtaining the Hamiltonian of the target quantum system and the equivalent Hamiltonian in the compressed Hilbert space.
  • the equivalent Hamiltonian refers to the equivalent representation of the Hamiltonian of the target quantum system.
  • the eigenstate and eigenenergy of the equivalent Hamiltonian have the same eigenstate and eigenenergy as the original Hamiltonian of the target quantum system. Therefore, by solving the eigenstate and eigenenergy of the equivalent Hamiltonian, the eigenstate and eigenenergy of the target quantum system can be obtained.
  • the equivalent Hamiltonian is the equivalent representation of the Hamiltonian of the target quantum system in the compressed Hilbert space, its dimensionality is smaller than the dimensionality of the original Hamiltonian of the target quantum system, so the The technical solution can reduce the calculation amount required for obtaining the eigenstate.
  • Step 150 obtaining the eigenstate and eigenenergy of the equivalent Hamiltonian as the eigenstate and eigenenergy of the target quantum system.
  • the diagonalization algorithm is used to obtain the eigenstates and eigenenergy of the equivalent Hamiltonian; wherein the diagonalization algorithm includes at least one of the following: a quantum eigenstate solving algorithm based on the variational method, based on The quantum eigenstate solution algorithm of adiabatic approximation, the quantum eigenstate solution algorithm based on adiabatic shortcut, the quantum eigenstate solution algorithm combined with adiabatic approximation and adiabatic shortcut.
  • an appropriate diagonalization algorithm can be selected according to the actual situation to obtain the eigenstate and eigenenergy of the target quantum system, so that the eigenstate acquisition scheme of the quantum system provided in the embodiment of the present application can It is applicable to different situations and improves the reliability and accuracy of the eigenstate acquisition of the quantum system.
  • a diagonalization algorithm is used to obtain the ground state and the ground state energy of the equivalent Hamiltonian. Further, based on the ground state of the equivalent Hamiltonian, the eigenstates such as the first excited state and the second excited state of the equivalent Hamiltonian and the eigenenergy corresponding to each eigenstate can be solved.
  • the technical solution provided by this application obtains the eigenstates of multiple clusters by dividing the target quantum system into multiple clusters, and then obtains multiple direct product states.
  • Screening selecting partial direct product states to construct a compressed Hilbert space, reducing the dimensionality of the Hilbert space; solving the eigenstate problem of the Hamiltonian of a high-dimensional system with multi-bit interactions, splitting Solve the problem by forming multiple low-dimensional Hamiltonian eigenstates, and then construct a compressed Hilbert space, by calculating the equivalent Hamiltonian of the target quantum system in the compressed Hilbert space , to obtain the eigenvalue and eigenenergy of the equivalent Hamiltonian, as the eigenvalue and eigenenergy of the target quantum system, because the dimensionality of the compressed Hilbert space is smaller than the original Hilbert space of the target quantum system.
  • the number of dimensions of the special space avoids the rapid increase of the required quantum gate operation with the increase of the dimension of the system in the process of digitization, and the rapid increase of the number of gates
  • multiple direct product states whose energy values meet the conditions are selected as a set of basis vectors to represent the compressed Hilbert space.
  • some direct product states are selected to construct the compressed Hilbert space
  • the Hilbert space reduces the dimensionality of the Hilbert space.
  • different conditions are set according to the actual situation to construct a compressed Hilbert space that meets different requirements, so that the compressed Hilbert space Build more flexibility and freedom.
  • At least one eigenstate corresponding to the cluster is obtained through the reduced Hamiltonian of the cluster, and then a plurality of direct products are obtained through the direct product operation of the eigenstates Product state, that is to say, after dividing and obtaining multiple clusters, each cluster is obtained and processed separately to obtain multiple direct product states corresponding to each cluster, so that the subsequent selection of direct product states is more accurate. Accurate, improving the calculation accuracy of the eigenstate and eigenenergy of the target quantum system.
  • the Hamiltonian of the target cluster in the environment is obtained, and the reduced Hamiltonian of the target cluster is obtained, that is, after obtaining
  • the relationship between the target cluster and the remaining clusters is considered, so that the obtained reduced Hamiltonian of the target cluster is more accurate.
  • FIG. 2 shows a flowchart of a method for obtaining eigenstates of a quantum system provided by another embodiment of the present application.
  • the method may include at least one of the following steps (210-250).
  • Step 210 perform cluster division in multiple different ways on the multiple particles contained in the target quantum system to obtain multiple different cluster division results, wherein each cluster division result includes multiple clusters.
  • the target quantum system contains 10 particles, and the 10 particles contained in the target quantum system are divided into clusters in various ways to obtain various cluster division results.
  • the 10 particles contained in the target quantum system can be divided into two clusters, the first cluster and the second cluster, wherein the first cluster contains 4 particles, and the second cluster contains 6 particles;
  • the 10 particles contained in the target quantum system can also be divided into two clusters, the third cluster and the fourth cluster, wherein the third cluster contains 5 particles, and the fourth cluster contains Contains 5 particles.
  • multi-layer cluster division is performed on multiple particles contained in the target quantum system.
  • the multiple particles contained in the target quantum system are divided into clusters in the first layer to obtain two clusters, cluster A and cluster B, and then cluster A and cluster B Carry out the second layer of cluster division to obtain clusters a1, a2, a3, a4 and clusters b1, b2, b3, b4.
  • Step 220 for each cluster division result, according to the eigenstates corresponding to the multiple clusters included in the cluster division result, obtain a plurality of direct product states corresponding to the cluster division result.
  • each cluster division result solve the eigenstate corresponding to each cluster in the multiple clusters it contains, and then obtain the cluster division according to the eigenstate corresponding to each cluster in the multiple clusters
  • the results correspond to multiple direct product states.
  • Step 230 select a partial direct product state as a set of basis vectors from the direct product states corresponding to various cluster division results to represent the compressed Hilbert space.
  • the target quantum system contains 10 particles
  • the first division result is to divide the 10 particles contained in the target quantum system into two clusters, the first cluster and the second cluster, wherein in the first cluster contains 5 particles, and the second cluster contains 5 particles
  • the result of the second cluster division is that the 10 particles contained in the target quantum system are divided into two clusters, the third cluster and the fourth cluster, in which The three clusters contain 4 particles, and the fourth cluster contains 6 particles
  • the third division result is to divide the 10 particles contained in the target quantum system into two clusters, the fifth cluster and the sixth cluster, Among them, the fifth cluster contains 4 particles, and the sixth cluster contains 6 particles, wherein at least one of the particles contained in the fifth cluster is different from the particles contained in the third cluster, and the sixth cluster At least one of the particles contained in the cluster is different from the particles contained in the fourth cluster.
  • some direct product states are selected as a set of basis vectors to represent the compressed Hilbert space.
  • a set number of direct product states with the smallest energy value as a set of basis vectors to represent the compressed Hilbert space.
  • the energy values of multiple direct product states are sorted in ascending order, and a set number of direct product states are selected as a set of basis vectors to represent the compressed Hilbert space.
  • the energy values of multiple direct product states are sorted in descending order, and a set number of direct product states among them are selected as a set of basis vectors to represent the compressed Hilbert space.
  • the second division result and the third division result select a set number of direct product states with the smallest energy values as a set of basis vectors to represent the compressed Hill Burt space.
  • select a set number of direct product states with the smallest energy value to obtain the first group of direct product states select a set number of direct product states with the smallest energy value to obtain the first group of direct product states
  • select The set number of direct product states with the smallest energy value is used to obtain the second group of direct product states.
  • the set number of direct product states with the smallest energy value is selected to obtain the third group of direct product states.
  • Product states, the first group of direct product states, the second group of direct product states and the third group of direct product states are used as a set of basis vectors to represent the compressed Hilbert space.
  • the second partition result and the third partition result select a set number of direct product states with the smallest energy value as a set of basis vectors to characterize the compressed Hill Burt space.
  • all the direct product states corresponding to the first division result, the second division result and the third division result are sorted in ascending order, and the first set number of direct product states are selected as a set of basis vectors Represents a compressed Hilbert space.
  • screening can also be performed according to the degree of entanglement of multiple direct product states, and some direct product states can be selected as a set of basis vectors to represent a compressed Hilbert space.
  • the application does not make a limitation on the selection method of the partial direct product state.
  • Step 240 obtaining the Hamiltonian of the target quantum system and the equivalent Hamiltonian in the compressed Hilbert space.
  • Step 250 obtaining the eigenstate and eigenenergy of the equivalent Hamiltonian as the eigenstate and eigenenergy of the target quantum system.
  • Steps 240-250 in this method are the same as steps 140-150 shown in FIG. 1 in the method for obtaining eigenstates of the quantum system described above.
  • steps 140-150 shown in FIG. 1 in the method for obtaining eigenstates of the quantum system described above.
  • each cluster division result Including multiple clusters, multiple direct product states are obtained according to the eigenstates of multiple clusters. From the direct product states corresponding to the results of different cluster divisions, some direct product states are selected as a set of basis vectors to represent The compressed Hilbert space combines the direct product states obtained from the results of various cluster divisions to represent the compressed Hilbert space, which can reduce the error and improve the accuracy of the eigenstate acquisition of the quantum system.
  • the original Hamiltonian of the hydrogen chain quantum system can be expressed as shown in formula (3).
  • H represents the original Hamiltonian of the hydrogen chain quantum system
  • N represents the number of spins contained in the hydrogen chain quantum system
  • Z represents the Pauli Z operator
  • X represents the Pauli X operator
  • g 1 is a single spin self-acting force
  • g 2 is the interaction force between two spins.
  • FIG. 5 shows a flowchart of a method for obtaining eigenstates of a quantum system provided by another embodiment of the present application.
  • the method may include at least one of the following several steps (510-550).
  • Step 510 performing cluster division in multiple different ways on the multiple spins contained in the hydrogen chain quantum system to obtain multiple different cluster division results, wherein each cluster division result includes multiple clusters, Each cluster includes at least one spin.
  • Two cluster division methods are used to divide clusters, where s i refers to the i-th spin, and A, B, A’ and B’ correspond to a cluster respectively cluster. It should be noted that the present application does not make a limitation on the specific cluster division methods, and here only two cluster division methods are taken as examples for illustration.
  • Step 520 for each cluster division result, according to the eigenstates corresponding to the multiple clusters included in the cluster division result, obtain a plurality of direct product states corresponding to the cluster division result.
  • At least one eigenstate corresponding to the target cluster is obtained.
  • a diagonalization algorithm is used to obtain at least one eigenstate corresponding to the target cluster.
  • the diagonalization algorithm includes but is not limited to at least one of the following: quantum eigenstate solving algorithm based on variational method, quantum eigenstate solving algorithm based on adiabatic approximation, quantum eigenstate solving algorithm based on adiabatic shortcut algorithm, a quantum eigenstate solution algorithm combining adiabatic approximation and adiabatic shortcut.
  • a direct product operation is performed on the eigenstates respectively corresponding to multiple clusters to obtain multiple direct product states.
  • cluster A is first set as the target cluster, and cluster B is assumed The initial state of is Taking cluster B as the environment of cluster A, the reduced Hamiltonian of cluster A is obtained, and the reduced Hamiltonian can be expressed as formula (4).
  • Z represents the Pauli Z operator
  • X represents the Pauli X operator
  • g 1 is the self-action force of a single spin
  • g 2 is the interaction force between two spins
  • N represents the hydrogen chain quantum system contained in number of spins.
  • ⁇ ⁇ g,e ⁇
  • Z stands for Pauli Z operator
  • X stands for Pauli X operator
  • g 1 is the self-action force of a single spin
  • g 2 is the interaction force between two spins
  • N stands for The number of spins contained in the hydrogen chain quantum system.
  • the four eigenstates of cluster B As the state of the environment, eight eigenstates (ground state and first excited state) of cluster A are obtained
  • the eight eigenstates of the above cluster A and the four eigenstates of cluster B above Perform direct product operation to get eight direct product states.
  • the cluster can also be obtained according to the above method
  • the eight eigenstates of A' and the four eigenstates of cluster B' are subjected to direct product operation to obtain eight direct product states.
  • Step 530 from direct product states corresponding to various cluster division results, select partial direct product states as a set of basis vectors to represent the compressed Hilbert space.
  • Step 540 obtaining the Hamiltonian of the hydrogen chain quantum system and the equivalent Hamiltonian in the compressed Hilbert space.
  • the Hamiltonian of the hydrogen chain quantum system and the equivalent Hamiltonian in the eight-dimensional Hilbert space are obtained, and the equivalent Hamiltonian can be expressed as formula (6).
  • H represents the original Hamiltonian of the hydrogen chain quantum system
  • Step 550 obtain the eigenstate and eigenenergy of the equivalent Hamiltonian as the eigenstate and eigenenergy of the hydrogen chain quantum system.
  • the diagonalization algorithm is used to obtain the eigenstates and eigenenergy of the equivalent Hamiltonian; wherein the diagonalization algorithm includes at least one of the following: a quantum eigenstate solving algorithm based on the variational method, based on The quantum eigenstate solution algorithm of adiabatic approximation, the quantum eigenstate solution algorithm based on adiabatic shortcut, the quantum eigenstate solution algorithm combined with adiabatic approximation and adiabatic shortcut.
  • a quantum eigenstate solving algorithm combined with adiabatic approximation and adiabatic shortcut is used as a diagonalization algorithm as an example to obtain the eigenstates and eigenenergy of the equivalent Hamiltonian.
  • a quantum system will evolve along its instantaneous eigenstates.
  • an initial Hamiltonian H 0 is selected, and then a time-varying adiabatic Hamiltonian is designed, which can be expressed as formula (7).
  • an anti-adiabatic Hamiltonian needs to be introduced, and the anti-adiabatic Hamiltonian can be expressed as formula (8).
  • the parameters of initial Hamiltonian and reduced Hamiltonian can also be included: Therefore, the leapfrog process here has a total of 3 evolutionary processes.
  • the adiabatic Hamiltonian of each evolution can be designed as formula (10).
  • multi-layer cluster division can be used to limit the calculation space to the Hamiltonian of hydrogen chains with N′ ⁇ 4, for example, a hydrogen chain with 8 spins , can be decomposed into 50 2-spins, 5 3-spins, and 16 4-spins Hamiltonian for calculation. It should be noted that this application does not limit the size of the calculation space, and here only takes the Hamiltonian of hydrogen chains with N′ ⁇ 4 as an example for illustration.
  • an accuracy function is defined: in is the result of numerical calculation, is a strict result, and the strict result is obtained through the classical algorithm singular value decomposition on a classical computer.
  • the result obtained by the eigenstate acquisition method of the quantum system of the present application is very accurate, As shown in Figure 7, the ground state energy The accuracy is even higher (>99.9%).
  • the present application also implements the experimental realization of the eigenstate acquisition method of the quantum system of the present application in the superconducting qubit system. Taking the three-spin chain quantum system with three-spin interaction as an example, its Hamiltonian form is shown in formula (11).
  • the ground state accuracy Refers to the ground state accuracy obtained by numerically simulating the process on a classical computer; Refers to the process of diagonalizing the cluster and the equivalent Hamiltonian H eff on the qubit, and the final ground state accuracy is obtained.
  • the technical solution provided by this application is derived by taking the hydrogen chain quantum system with a hydrogen chain length of 3 ⁇ N ⁇ 8 as an example, and verified by experiments.
  • the accuracy of the eigenstate acquisition method is very high, and the hydrogen chain quantum system is used for verification, which proves that the method is universal.
  • FIG. 8 shows a block diagram of an eigenstate acquisition device of a quantum system provided by an embodiment of the present application.
  • the apparatus 800 may include the following modules: a dividing module 810 , an obtaining module 820 , a selecting module 830 , a first obtaining module 840 and a second obtaining module 850 .
  • the division module 810 is configured to perform cluster division on multiple particles contained in the target quantum system to obtain multiple clusters, each of which contains at least one particle.
  • the obtaining module 820 is configured to obtain multiple direct product states according to the eigenstates respectively corresponding to the multiple clusters.
  • the selection module 830 is used to select a partial direct product state from the plurality of direct product states as a set of basis vectors to represent a compressed Hilbert space, wherein the number of dimensions of the compressed Hilbert space , which is smaller than the dimensionality of the original Hilbert space of the target quantum system.
  • the selection module 830 is configured to select a partial direct product state from the direct product states corresponding to the various cluster division results as a set of basis vectors to characterize the compressed Hill Burt space.
  • the first acquiring module 840 is configured to acquire the Hamiltonian of the target quantum system and the equivalent Hamiltonian in the compressed Hilbert space.
  • the second acquisition module 850 is configured to acquire the eigenstates and eigenenergy of the equivalent Hamiltonian as the eigenstates and eigenenergy of the target quantum system.
  • the selection module 830 includes an acquisition unit 831 and a selection unit 832 .
  • the obtaining unit 831 is configured to obtain energy values respectively corresponding to the multiple direct product states.
  • the selection unit 832 is configured to select a plurality of direct product states whose energy values meet the conditions from the plurality of direct product states, and use them as a set of basis vectors to represent the compressed Hilbert space.
  • the selection unit 832 is configured to select the n direct product states with the smallest energy values from the plurality of direct product states as a set of basis vectors to characterize the compressed Hilber Te space, said n is a positive integer.
  • the obtaining module 820 is configured to obtain the reduced Hamiltonian of the target cluster for the target cluster among the plurality of clusters; according to the reduced Hamiltonian of the target cluster Obtaining at least one eigenstate corresponding to the target cluster; performing a direct product operation on the eigenstates respectively corresponding to the plurality of clusters to obtain the plurality of direct product states.
  • the first acquisition module 840 is configured to use clusters other than the target cluster in the plurality of clusters as the environment, and acquire the target cluster in the environment The Hamiltonian of the target cluster is obtained to obtain the reduced Hamiltonian of the target cluster.
  • the division module 810 is configured to divide the particles contained in the target quantum system in a variety of different ways to obtain a variety of cluster division results, wherein each The cluster division results include multiple clusters.
  • the second obtaining module 850 is configured to use a diagonalization algorithm to obtain the eigenstates and eigenenergy of the equivalent Hamiltonian; wherein the diagonalization algorithm includes at least one of the following Species: quantum eigenstate solution algorithm based on variational method, quantum eigenstate solution algorithm based on adiabatic approximation, quantum eigenstate solution algorithm based on adiabatic shortcut, quantum eigenstate solution algorithm combined with adiabatic approximation and adiabatic shortcut ; Determine the eigenstate and eigenenergy of the equivalent Hamiltonian as the eigenstate and eigenenergy of the target quantum system.
  • the diagonalization algorithm includes at least one of the following Species: quantum eigenstate solution algorithm based on variational method, quantum eigenstate solution algorithm based on adiabatic approximation, quantum eigenstate solution algorithm based on adiabatic shortcut, quantum eigenstate solution algorithm combined with adiabatic approximation and adiabatic shortcut ; Determine the
  • FIG. 10 shows a structural block diagram of a computer device 1000 provided by an embodiment of the present application.
  • the computer device 1000 may be a classic computer.
  • the computer equipment can be used to implement the method for obtaining the eigenstates of the quantum system provided in the above embodiments. Specifically:
  • the computer device 1000 includes a processing unit (such as CPU (Central Processing Unit, central processing unit), GPU (Graphics Processing Unit, graphics processing unit) and FPGA (Field Programmable Gate Array, Field Programmable Logic Gate Array) etc.) 1001, including RAM (Random-Access Memory, random access memory) 1002 and ROM (Read-Only Memory, read-only memory) 1003 system memory 1004, and system bus 1005 connecting system memory 1004 and central processing unit 1001.
  • the computer device 1000 also includes a basic input/output system (Input Output System, I/O system) 1006 that helps to transmit information between various devices in the server, and is used to store an operating system 1013, an application program 1014 and other program modules 1015 mass storage device 1007.
  • I/O system Input Output System
  • the basic input/output system 1006 includes a display 1008 for displaying information and input devices 1009 such as a mouse and a keyboard for users to input information.
  • input devices 1009 such as a mouse and a keyboard for users to input information.
  • both the display 1008 and the input device 1009 are connected to the central processing unit 1001 through the input and output controller 1010 connected to the system bus 1005 .
  • the basic input/output system 1006 may also include an input-output controller 1010 for receiving and processing input from a keyboard, a mouse, or an electronic stylus and other devices.
  • input output controller 1010 also provides output to a display screen, printer, or other type of output device.
  • the mass storage device 1007 is connected to the central processing unit 1001 through a mass storage controller (not shown) connected to the system bus 1005 .
  • the mass storage device 1007 and its associated computer-readable media provide non-volatile storage for the computer device 1000 . That is to say, the mass storage device 1007 may include a computer-readable medium (not shown) such as a hard disk or a CD-ROM (Compact Disc Read-Only Memory, CD-ROM) drive.
  • a computer-readable medium such as a hard disk or a CD-ROM (Compact Disc Read-Only Memory, CD-ROM) drive.
  • Computer readable media may comprise computer storage media and communication media.
  • Computer storage media includes volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules or other data.
  • Computer storage media include RAM, ROM, EPROM (Erasable Programmable Read-Only Memory, Erasable Programmable Read-Only Memory), EEPROM (Electrically Erasable Programmable Read-Only Memory, Electrically Erasable Programmable Read-Only Memory), flash memory or Other solid-state storage technologies, CD-ROM, DVD (Digital Video Disc, high-density digital video disc) or other optical storage, tape cartridges, tapes, magnetic disk storage or other magnetic storage devices.
  • the computer storage medium is not limited to the above-mentioned ones.
  • the above-mentioned system memory 1004 and mass storage device 1007 may be collectively referred to as memory.
  • the computer device 1000 can also run on a remote computer connected to the network through a network such as the Internet. That is, the computer device 1000 can be connected to the network 1012 through the network interface unit 1011 connected to the system bus 1005, or in other words, the network interface unit 1011 can also be used to connect to other types of networks or remote computer systems (not shown) .
  • the memory also includes at least one instruction, at least one program, a set of codes, or a set of instructions stored in the memory and configured to be executed by one or more processors , to realize the eigenstate acquisition method of the above quantum system.
  • FIG. 10 does not constitute a limitation to the computer device 1000, and may include more or less components than shown in the figure, or combine certain components, or adopt a different component arrangement.
  • a computer-readable storage medium is also provided. At least one instruction, at least one program, code set or instruction set are stored in the storage medium, and the at least one instruction, the at least one program , when the code set or the instruction set is executed by the processor, the method for obtaining the eigenstates of the above-mentioned quantum system can be realized.
  • the computer-readable storage medium may include: ROM (Read Only Memory, read-only memory), RAM (Random Access Memory, random access memory), SSD (Solid State Drives, solid state drive) or an optical disc, etc.
  • the random access memory may include ReRAM (Resistance Random Access Memory, resistive random access memory) and DRAM (Dynamic Random Access Memory, dynamic random access memory).
  • a computer program product or computer program comprising computer instructions stored in a computer readable storage medium.
  • the processor of the computer device reads the computer instruction from the computer-readable storage medium, and the processor executes the computer instruction, so that the computer device executes the above method for obtaining eigenstates of the quantum system.

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Abstract

一种量子体系的本征态获取方法、装置、设备及存储介质，涉及量子技术领域。所述方法包括：对目标量子体系中包含的多个粒子进行团簇划分，得到多个团簇，每个团簇中包含至少一个粒子(110)；根据多个团簇分别对应的本征态，得到多个直积态(120)；从多个直积态中，选择部分直积态作为一组基矢来表征一压缩的希尔伯特空间(130)；获取目标量子体系的哈密顿量，在压缩的希尔伯特空间中的等效哈密顿量(140)；获取等效哈密顿量的本征态和本征能量，作为目标量子体系的本征态和本征能量(150)。

Description

量子体系的本征态获取方法、装置、设备及存储介质
本申请要求于2021年9月26日提交的申请号为202111130173.1、发明名称为“量子体系的本征态获取方法、装置、设备及存储介质”的中国专利申请的优先权，其全部内容通过引用结合在本申请中。
技术领域
本申请实施例涉及量子技术领域，特别涉及一种量子体系的本征态获取方法、装置、设备及存储介质。
背景技术
随着量子计算的快速发展，量子算法在很多领域都有了重要的应用，其中，求解量子系统的本征态和本征能量是一个非常关键的问题。
在相关技术中，提供了一种基于变分法实现的量子本征态求解算法。对于一个任意的量子体系，可以设计一个试探波函数，通过不断改变试探波函数，来找到对应的能量的最小值，此时即为基态能量和基态。同样地，量子体系的第一激发态是与基态正交的波函数中对应能量最低的态。在确定基态以后，可以利用在与其正交的态空间中找到第一激发态。第二激发态则是与基态和第一激发态正交的波函数中对应能量最低的态，依次类推，理论上可以用这种方法找到量子体系的所有本征态。
为了在量子器件上实现态的含时演化，需要对态的含时演化方程进行数字化，将态的演化矩阵转换成量子器件上对应的量子门操作。在数字化过程中，所需要的量子门操作会随着量子比特数目的增加而快速增加。因而，计算所需要的资源会变大，量子算法的优势会减弱。
发明内容
本申请实施例提供了一种量子体系的本征态获取方法、装置、设备及存储介质。所述技术方案如下：
根据本申请实施例的一个方面，提供了一种量子体系的本征态获取方法，所述方法由计算机设备执行，所述方法包括：
对目标量子体系中包含的多个粒子进行团簇划分，得到多个团簇，所述多个团簇中的每个团簇中包含至少一个粒子；
根据所述多个团簇分别对应的本征态，得到多个直积态；
从所述多个直积态中，选择部分直积态作为一组基矢来表征一压缩的希尔伯特空间，其中，所述压缩的希尔伯特空间的维度数，小于所述目标量子体系的原始希尔伯特空间的维度数；
获取所述目标量子体系的哈密顿量，在所述压缩的希尔伯特空间中的等效哈密顿量；
获取所述等效哈密顿量的本征态和本征能量，作为所述目标量子体系的本征态和本征能量。
根据本申请实施例的一个方面，提供了一种量子体系的本征态获取装置，所述装置包括：
划分模块，用于对目标量子体系中包含的多个粒子进行团簇划分，得到多个团簇，所述多个团簇中的每个团簇中包含至少一个粒子；
得到模块，用于根据所述多个团簇分别对应的本征态，得到多个直积态；
选择模块，用于从所述多个直积态中，选择部分直积态作为一组基矢来表征一压缩的希尔伯特空间，其中，所述压缩的希尔伯特空间的维度数，小于所述目标量子体系的原始希尔伯特空间的维度数；
第一获取模块，用于获取所述目标量子体系的哈密顿量，在所述压缩的希尔伯特空间中 的等效哈密顿量；
第二获取模块，用于获取所述等效哈密顿量的本征态和本征能量，作为所述目标量子体系的本征态和本征能量。
根据本申请实施例的一个方面，提供了一种计算机设备，所述计算机设备包括处理器和存储器，所述存储器中存储有至少一条指令、至少一段程序、代码集或指令集，所述至少一条指令、所述至少一段程序、所述代码集或指令集由所述处理器加载并执行以实现上述量子体系的本征态获取方法。
根据本申请实施例的一个方面，提供了一种计算机可读存储介质，所述存储介质中存储有至少一条指令、至少一段程序、代码集或指令集，所述至少一条指令、所述至少一段程序、所述代码集或指令集由所述处理器加载并执行以实现上述量子体系的本征态获取方法。
根据本申请实施例的一个方面，提供了一种计算机程序产品或计算机程序，该计算机程序产品或计算机程序包括计算机指令，该计算机指令存储在计算机可读存储介质中。计算机设备的处理器从计算机可读存储介质读取该计算机指令，处理器执行该计算机指令，使得该计算机设备执行上述量子体系的本征态获取方法。
通过将目标量子体系划分为多个团簇，获取多个团簇的本征态，进而得到多个直积态，通过对多个直积态的筛选，选择部分直积态构建压缩的希尔伯特空间，降低了希尔伯特空间的维度数；将存在多比特相互作用的高维度系统的哈密顿量的本征态求解问题，拆分成多个低维度的哈密顿量的本征态求解问题，进而构建压缩的希尔伯特空间，通过计算目标量子体系的哈密顿量在压缩的希尔伯特空间中的等效哈密顿量，得到该等效哈密顿量的本征值和本征能量，作为目标量子体系的本征值和本征能量，由于压缩的希尔伯特空间的维度数小于目标量子体系原始的希尔伯特空间的维度数，避免了在数字化过程中，所需要的量子门操作随着系统的维度的增加而快速增加，以及实现多比特相互作用的门的数目随着相互作用的维度的增加而快速增加的情况，降低了本征态获取所需的计算量。
附图说明
图1是本申请一个实施例提供的量子体系的本征态获取方法的流程图；
图2是本申请另一个实施例提供的量子体系的本征态获取方法的流程图；
图3是本申请一个实施例提供的团簇划分方式的示意图；
图4是本申请另一个实施例提供的团簇划分方式的示意图；
图5是本申请另一个实施例提供的量子体系的本征态获取方法的流程图；
图6是本申请一个实施例提供的基态精度的示意图；
图7是本申请一个实施例提供的本征能量精度的示意图；
图8是本申请一个实施例提供的量子体系的本征态获取装置的框图；
图9是本申请一个实施例提供的量子体系的本征态获取装置的框图；
图10是本申请一个实施例提供的计算机设备的结构框图。
具体实施方式
在对本申请实施例进行介绍说明之前，首先对本申请中涉及的一些名词进行解释说明。
1.量子计算：基于量子逻辑的计算方式，存储数据的基本单元是量子比特(qubit)。
2.量子比特：量子计算的基本单元。传统计算机使用0和1作为二进制的基本单元。不同的是量子计算可以同时处理0和1，系统可以处于0和1的线性叠加态：|ψ>＝α|0>+β|1>，这边α，β代表系统在0和1上的复数概率幅。它们的模平方|α| 2，|β| 2分别代表处于0和1的概率。
3.哈密顿量：描述量子系统总能量的一个厄密共轭的矩阵。哈密顿量是一个物理词汇， 是一个描述系统总能量的算符，通常以H表示。
4.量子态：在量子力学中，量子态是由一组量子数所确定的微观状态。
5.本征态：对于一个哈密顿量矩阵H，满足方程：H(ψ)＝E(ψ)的解称之为H的本征态|ψ>，具有本征能量E。基态则对应了量子系统能量最低的本征态。
6.团簇(cluster)：是由多个粒子构成的集合。在物理领域中，本申请实施例中的粒子也可以用自旋(spin)来指代。另外，量子比特是量子计算中的基本单元，我们可以用一个量子比特模拟物理体系中的一个粒子/自旋，也可以用多个量子比特来模拟一个粒子/自旋。
7.本征态：在量子力学中，一个力学量所可能取的数值，就是它的算符的全部本征值。本征函数所描写的状态称为这个算符的本征态。在自己的本征态中，这个力学量取确定值，即这个本征态所属的本征值。
8.直积态：在量子力学中，体系的状态(态矢量)可以用一个函数来表示，称为“态函数”(既可以把它理解为一个函数，也可以把它理解为一个矢量，两者不矛盾)。单粒子体系的态函数是一元函数，多粒子体系的态函数是多元函数。如果这个多元函数可以分离变量，也就是可以写成多个一元函数直接的乘积，我们就把它称为“直积态”。
9.第一激发态：是激发态中能量最低的激发态。
10.对角化：对角矩阵是指只有主对角线上含有非零元素的矩阵，即，已知一个n×n矩阵M，如果对于i≠j，M ij＝0，则该矩阵为对角矩阵。如果存在一个矩阵A，使A -1MA的结果为对角矩阵，则称矩阵A将矩阵M对角化。
11.二次量子化(second quantization)：使用产生算符和消灭算符在对称化的希尔伯特空间处理全同粒子系统的方法，通常称为二次量子化方法。
12.希尔伯特空间：是指完备的内积空间。
13.自旋(spin)：是由粒子内禀角动量引起的内禀运动。在量子力学中，自旋是粒子所具有的内禀性质，其运算规则类似于经典力学的角动量，并因此产生一个磁场。
14.量子门：在量子计算，特别是量子线路的计算模型里面，一个量子门(Quantum gate，或量子逻辑门)是一个基本的，操作一个小数量量子比特的量子线路。
15.基于变分法实现的量子本征态求解算法：对于一个任意的物理体系，其哈密顿量H，设该物理体系包括H在内的一组力学量完全集的共同本征态为
Figure PCTCN2021134932-appb-000001
相对应的能量本征值为E 0<E 1<E 2<…，其中E 0为基态能量，
Figure PCTCN2021134932-appb-000002
为基态波函数。可以设计一个试探波函数
Figure PCTCN2021134932-appb-000003
它对应的能量为
Figure PCTCN2021134932-appb-000004
当且仅当
Figure PCTCN2021134932-appb-000005
时，等号可以取到。所以可以通过不断改变试探波函数，来找到对应的能量的最小值，此时即为基态能量和基态波函数。同样，体系的第一激发态是与基态
Figure PCTCN2021134932-appb-000006
正交的波函数中对应能量最低的态。在确定基态以后，可以利用在与其正交的态空间中找到第一激发态。第二激发态则是与基态和第一激发态正交的波函数中对应能量最低的态，依次类推，理论上可以用这种方法找到体系的所有本征态。
16.基于绝热近似的量子本征态求解算法：绝热近似是指如果某种微扰足够缓慢地作用于一个物理体系，则该物理体系的瞬时本征态可被看作是恒定不变的。所以我们如果能够足够缓慢地改变一个物理体系的哈密顿量，那么该物理体系会始终沿着它的瞬时本征态演化。所以可以通过在量子器件上构建一个简单哈密顿量所对应的已知本征态，然后将它足够缓慢地演化到我们想要求解的物理体系的哈密顿量上，此时测量量子器件得到的量子态即为我们想要求解的哈密顿量对应的本征态。
17.基于绝热捷径的量子本征态求解算法：绝热近似要求系统演化得足够缓慢，在绝热近似的基础上，可以通过引入快速绝热项，加速系统的演化，用更短的时间演化到目标本征态。
18.结合绝热近似和绝热捷径实现的蛙跳式量子本征态求解算法：对于任意的目标系统，可以构建一个或者一组形式与目标系统哈密顿量相似，但耦合强度相对较小的参考点，如果从一个简单哈密顿量所对应的已知本征态出发，试图演化到这种耦合强度相对较小的参考点，它的快速绝热项的形式较为简单，可以较容易地通过基于快速绝热的量子本征态求解算法求解出参考点的本征态。然后利用基于绝热近似的量子本征态求解算法从参考点的本征态出发，演化到下一个参考点或者目标系统的本征态上，因为参考点与目标系统的哈密顿量相对较为接近，可以在较少的时间(步数)内实现绝热近似。
在一个通常的多电子量子体系中，二次量子化后的量子体系的哈密顿量可以表示为公式(1)。
Figure PCTCN2021134932-appb-000007
其中，a i和
Figure PCTCN2021134932-appb-000008
是第i个电子基态上的产生算符和湮灭算符，a j、
Figure PCTCN2021134932-appb-000009
a k和a l可以同理解释，它们满足
Figure PCTCN2021134932-appb-000010
其中[x,y] +为反对易算符，δ {i，j}为一个跃变算符，当i＝j时，δ {i，j}＝1，当i≠j时，δ {i，j}＝0。而
Figure PCTCN2021134932-appb-000011
和
Figure PCTCN2021134932-appb-000012
是单电子和双电子积分系数，ε 0是该哈密顿量的基态能量。通过一种费米子和自旋之间的映射理论，比如Bravyi-Kitaev变换或者Jordan-Wigner变换，这个多电子量子体系的哈密顿量可以被重新写成多自旋形式的哈密顿量，如公式(2)所示。
Figure PCTCN2021134932-appb-000013
其中
Figure PCTCN2021134932-appb-000014
是第i个自旋上的泡利矩阵，
Figure PCTCN2021134932-appb-000015
与
Figure PCTCN2021134932-appb-000016
可以同理解释，{g (0)，g (1)，g (2)，...}是用来表示多自旋相互作用强度的系数，为了更好地体现出适用性，这个哈密顿量的表达式没有在4个自旋相互作用项截断(对应公式(1))，而是允许考虑到任意的N′(≤N)个自旋相互作用项。
为了求解公式(1)中的哈密顿量的本征态|Ψ n>和本征能量E n，一般情况下，我们需要一个2 N维希尔伯特空间中的对角化工具。而作为替代，本申请提出了一种量子体系的本征态获取方法，可以在一个高度压缩的空间里实现一个近似但是精确的对角化求解。
在介绍本申请方法实施例之前，先对本申请方法的执行环境进行介绍说明。
本申请实施例提供的量子体系的本征态获取方法，其可以由经典计算机(如PC)执行实现，例如通过经典计算机执行相应的计算机程序以实现该方法；也可以在经典计算机和量子计算机的混合设备环境下执行，例如由经典计算机和量子计算机配合来实现该方法。示例性地，量子计算机用于实现本申请实施例中对多个团簇的本征态的求解和对等效哈密顿量的本征态的求解，经典计算机用于实现本申请实施例中除本征态求解问题之外的其他步骤。
在下述方法实施例中，为了便于说明，仅以各步骤的执行主体为计算机设备进行介绍说明。应当理解的是，该计算机设备可以是经典计算机，也可以包括经典计算机和量子计算机的混合执行环境，本申请实施例对此不作限定。
请参考图1，其示出了本申请一个实施例提供的量子体系的本征态获取方法的流程图。该方法各步骤的执行主体可以是计算机设备。该方法可以包括如下几个步骤(110～150)中的至少一个步骤。
步骤110，对目标量子体系中包含的多个粒子进行团簇划分，得到多个团簇，每个团簇中包含至少一个粒子。
在本申请实施例中，对目标量子体系中包含的多个粒子进行团簇划分，得到多个团簇。 每个团簇中包含目标量子体系的一个或多个粒子，不同团簇之间不包含相同的粒子，得到的多个团簇中包含的粒子的数量之和等于目标量子体系中包含的粒子的总数量。
目标量子体系是指待获取其本征态的量子体系。可选地，团簇划分的方式有多种。示例性地，假设一个具有N个粒子的量子体系可以被分成两个团簇，每一个团簇中包含N 1和N 2个粒子，N 1+N 2＝N，对于一个给定的N 1的值，这种团簇划分可选择的方式的数量可通过排列组合计算，最大值
Figure PCTCN2021134932-appb-000017
示例性地，目标量子体系中包含10个粒子，对目标量子体系中包含的10个粒子进行团簇划分，得到多个团簇，每个团簇中包含至少一个粒子。例如，将目标量子体系中包含的10个粒子划分为第一团簇和第二团簇共2个团簇，其中第一团簇中包含5个粒子，第二团簇中包含5个粒子。又例如，将目标量子体系中包含的10个粒子划分为第一团簇和第二团簇共2个团簇，其中第一团簇中包含4个粒子，第二团簇中包含6个粒子。
步骤120，根据多个团簇分别对应的本征态，得到多个直积态。
本申请实施例中，对于每个团簇，求解其对应的本征态，然后根据多个团簇中每个团簇对应的本征态，得到多个直积态。
在示例性实施例中，步骤120可以包括如下几个子步骤(1～3)：
1、对于多个团簇中的目标团簇，获取目标团簇的约化哈密顿量。
目标团簇的约化哈密顿量是指目标团簇的真实哈密顿量的约化表示，通过求解目标团簇在当前环境中的哈密顿量，可以得到该目标团簇的约化哈密顿量。可选地，以多个团簇中除目标团簇之外的其他团簇作为环境，获取目标团簇在环境下的哈密顿量，得到目标团簇的约化哈密顿量。
示例性地，将目标量子体系划分为团簇A和团簇B两个团簇。对于团簇A，将团簇B作为环境，对特定量子态进行部分求迹
Figure PCTCN2021134932-appb-000018
即可得到团簇A的约化哈密顿量
Figure PCTCN2021134932-appb-000019
其中α是指团簇B的第α个量子态，H是指目标量子体系的哈密顿量，特定量子态是指环境的某一个特定的量子态，每一个环境的量子态，都对应一个团簇A的约化哈密顿量。反之，对于团簇B，同样的方法也适用。首先将孤立的团簇A的量子态
Figure PCTCN2021134932-appb-000020
作为环境的量子态，然后可以得到团簇B的约化哈密顿量
Figure PCTCN2021134932-appb-000021
其中，β是指团簇A的第β个量子态，H是指目标量子体系的哈密顿量。
2、根据目标团簇的约化哈密顿量，获取目标团簇对应的至少一个本征态。
可选地，可以根据目标团簇的约化哈密顿量，获取目标团簇对应的基态。可选地，还可以根据目标团簇的约化哈密顿量，获取目标团簇对应的激发态。
可选地，根据目标团簇的约化哈密顿量，采用对角化算法获取目标团簇对应的至少一个本征态。可选地，对角化算法包括但不限于以下至少一种：基于变分法实现的量子本征态求解算法、基于绝热近似的量子本征态求解算法、基于绝热捷径的量子本征态求解算法、结合绝热近似和绝热捷径的量子本征态求解算法。
示例性地，将目标量子体系划分为团簇A和团簇B两个团簇。对团簇A的约化哈密顿量
Figure PCTCN2021134932-appb-000022
进行对角化，得到至少一个本征态
Figure PCTCN2021134932-appb-000023
和本征能量
Figure PCTCN2021134932-appb-000024
其中i是指第i个本征态/本征能量，α是指团簇B的第α个量子态。同样地，对团簇B的等效哈密顿量
Figure PCTCN2021134932-appb-000025
进行对角化
Figure PCTCN2021134932-appb-000026
得到至少一个本征态和本征能量，其中j是指第j个本征态/本征能量，β是指团簇A的第β个量子态。
3、对多个团簇分别对应的本征态进行直积运算，得到多个直积态。
示例性地，将目标量子体系划分为第一团簇和第二团簇两个团簇，其中第一团簇对应2 个本征态，第二团簇对应2个本征态，对上述总共4个本征态进行直积运算，得到四个直积态。
步骤130，从多个直积态中，选择部分直积态作为一组基矢来表征一压缩的希尔伯特空间。
在本申请实施例中，压缩的希尔伯特空间的维度数，小于目标量子体系的原始希尔伯特空间的维度数。
示例性地，目标量子体系中包含10个粒子，则目标量子体系的原始希尔伯特空间的维度数为2 10，压缩的希尔伯特空间的维度数应小于2 10。
可选地，选择有关联的直积态作为一组基矢来表征一压缩的希尔伯特空间。有关联的直积态是指具有正交关系的直积态，即与其他态垂直的直积态。我们希望所有的直积态的确定都是自洽收敛的，例如
Figure PCTCN2021134932-appb-000027
和
Figure PCTCN2021134932-appb-000028
其中{x}表示集合，i是指第i个本征态/本征能量，α是指团簇B的第α个量子态，j是指第j个本征态/本征能量，β是指团簇A的第β个量子态，但是如果考虑多个状态，则正则递归迭代是发散的。
实验表明，通过递归迭代，有关联的直积态的数量通常是不变的，因此只需要采取数量有限的迭代步骤，选择有关联的直积态作为一组基矢来表征一压缩的希尔伯特空间。
在示例性实施例中，步骤130可以包括如下几个子步骤(1～2)：
1、获取多个直积态分别对应的能量值；
2、从多个直积态中，选择能量值符合条件的多个直积态，作为一组基矢来表征压缩的希尔伯特空间。
可选地，从多个直积态中，选择能量值最小的n个直积态，作为一组基矢来表征压缩的希尔伯特空间，n为正整数。在本申请实施例中，n为设定数量，上述n个直积态也可称为设定数量个直积态。示例性地，将多个直积态的能量值按照从小到大的顺序排序，选择其中的前设定数量个直积态，作为一组基矢来表征压缩的希尔伯特空间。示例性地，将多个直积态的能量值按照从大到小的顺序排序，选择其中的后设定数量个直积态，作为一组基矢来表征压缩的希尔伯特空间。其中，设定数量是指所设定的针对直积态的选择数量，前设定数量是指在选择直积态时，依据设定数量选择排序在前的直积态，后设定数量是指在选择直积态时，依据设定数量选择排序在后的直积态。示例性地，假设设定数量为2，则对于数字1、2、3、4、5、6、7这七个数字来说，依据前设定数量所选择的数字为1和2，依据后设定数量所选择的数字为6和7。
可选地，也可以根据多个直积态的纠缠度进行筛选，选择部分直积态作为一组基矢来表征一压缩的希尔伯特空间。对于部分直积态的选择方法，本申请不作限定。示例性地，从多个直积态中，选择纠缠度最小的设定数量个直积态，作为一组基矢来表征压缩的希尔伯特空间。
步骤140，获取目标量子体系的哈密顿量，在压缩的希尔伯特空间中的等效哈密顿量。
等效哈密顿量，是指目标量子体系的哈密顿量的等效表示。该等效哈密顿量的本征态和本征能量，具有和目标量子体系原始的哈密顿量相同的本征态和本征能量。因此，通过求解等效哈密顿量的本征态和本征能量，就可以得到目标量子体系的本征态和本征能量。但是，因为等效哈密顿量是目标量子体系在压缩的希尔伯特空间中的哈密顿量的等效表示，其维度数小于目标量子体系原始的哈密顿量的维度数，所以本申请的技术方案能够降低本征态获取所需的计算量。
步骤150，获取等效哈密顿量的本征态和本征能量，作为目标量子体系的本征态和本征能量。
可选地，采用对角化算法获取等效哈密顿量的本征态和本征能量；其中，对角化算法包括以下至少一种：基于变分法实现的量子本征态求解算法、基于绝热近似的量子本征态求解 算法、基于绝热捷径的量子本征态求解算法、结合绝热近似和绝热捷径的量子本征态求解算法。可见，在本申请实施例中，根据实际情况可以选择合适的对角化算法以获取目标量子体系的本征态和本征能量，使得本申请实施例提供的量子体系的本征态获取方案能够适用于不同的情况，提高量子体系的本征态获取的可靠性和准确性。
示例性地，采用对角化算法获取等效哈密顿量的基态和基态能量。进一步的，还可以基于等效哈密顿量的基态，求解等效哈密顿量的第一激发态、第二激发态等本征态以及各本征态对应的本征能量。
综上所述，本申请提供的技术方案，通过将目标量子体系划分为多个团簇，获取多个团簇的本征态，进而得到多个直积态，通过对多个直积态的筛选，选择部分直积态构建压缩的希尔伯特空间，降低了希尔伯特空间的维度数；将存在多比特相互作用的高维度系统的哈密顿量的本征态求解问题，拆分成多个低维度的哈密顿量的本征态求解问题，进而构建压缩的希尔伯特空间，通过计算目标量子体系的哈密顿量在压缩的希尔伯特空间中的等效哈密顿量，得到该等效哈密顿量的本征值和本征能量，作为目标量子体系的本征值和本征能量，由于压缩的希尔伯特空间的维度数小于目标量子体系原始的希尔伯特空间的维度数，避免了在数字化过程中，所需要的量子门操作随着系统的维度的增加而快速增加，以及实现多比特相互作用的门的数目随着相互作用的维度的增加而快速增加的情况，降低了本征态获取所需的计算量。
另外，通过多个直积态分别对应的能量值，选择能量值符合条件的多个直积态作为一组基矢来表征压缩的希尔伯特空间，一方面，选择部分直积态构建压缩的希尔伯特空间，降低了希尔伯特空间的维度数，另一方面，根据实际情况设置不同的条件以构建满足不同要求的压缩的希尔伯特空间，使得压缩的希尔伯特空间构建更加灵活自由。
另外，从多个直积态中，选择能量值最小的设定数量个直积态，作为一组基矢来表征压缩的希尔伯特空间，尽最大可能地降低压缩的希尔伯特空间的维度数，降低了本征态获取所需的计算量，提高本征态的计算效率。
另外，对于多个团簇中的每个团簇，通过团簇的约化哈密顿量，获取该团簇对应的至少一个本征态，进而通过对本征态的直积运算，得到多个直积态，也就是说，在划分得到多个团簇之后，获取每个团簇分别进行处理，以获取每个团簇分别对应的多个直积态，使得后续对直积态的选择结果更加准确，提高目标量子体系的本征态和本征能量的计算的准确性。
另外，以多个团簇中除目标团簇之外的其他团簇作为环境，获取目标团簇在环境下的哈密顿量，得到目标团簇的约化哈密顿量，也就是说，在获取目标团簇的约化哈密顿量时，考虑了该目标团簇与剩余团簇之间的关系，使得所获取的目标团簇的约化哈密顿量更加准确。
可选地，团簇划分的方式有多种，请参考图2，其示出了本申请另一个实施例提供的量子体系的本征态获取方法的流程图。该方法可以包括如下几个步骤(210～250)中的至少一个步骤。
步骤210，对目标量子体系中包含的多个粒子进行多种不同方式的团簇划分，得到多种不同的团簇划分结果，其中，每种团簇划分结果中包括多个团簇。
示例性地，目标量子体系中包含10个粒子，对目标量子体系中的包含的10个粒子进行多种不同方式的团簇划分，得到多种不同的团簇划分结果。例如，如图3所示，可以将目标量子体系中包含的10个粒子划分为第一团簇和第二团簇两个团簇，其中第一团簇中包含4个粒子，第二团簇中包含6个粒子；也可以将目标量子体系中包含的10个粒子划分为第三团簇和第四团簇两个团簇，其中第三团簇中包含5个粒子，第四团簇中包含5个粒子。
可选地，对目标量子体系中包含的多个粒子进行多层团簇划分。示例性地，如图4所示，将目标量子体系中包含的多个粒子进行第一层团簇划分，得到团簇A和团簇B两个团簇，再对团簇A和团簇B进行第二层团簇划分，得到团簇a1、a2、a3、a4和团簇b1、b2、b3、b4。
对目标量子体系中包含的多个粒子进行多种不同方式的团簇划分，得到多种不同的团簇划分结果，针对不同的团簇划分结果进行后续计算，能够考虑到不同粒子之间的相互作用，减小误差，提高量子体系的本征态获取的精度。
步骤220，对于每一种团簇划分结果，根据该团簇划分结果中包含的多个团簇分别对应的本征态，得到该团簇划分结果对应的多个直积态。
对于每一种团簇划分结果，求解其包含的多个团簇中每个团簇对应的本征态，然后根据多个团簇中每个团簇对应的本征态，得到该团簇划分结果对应的多个直积态。
步骤230，从多种不同的团簇划分结果分别对应的直积态中，选择部分直积态作为一组基矢来表征压缩的希尔伯特空间。
示例性地，目标量子体系中包含10个粒子，第一划分结果为将目标量子体系中包含的10个粒子划分为第一团簇和第二团簇两个团簇，其中第一团簇中包含5个粒子，第二团簇中包含5个粒子；第二团簇划分结果为将目标量子体系中包含的10个粒子划分为第三团簇和第四团簇两个团簇，其中第三团簇中包含4个粒子，第四团簇中包含6个粒子；第三划分结果为将目标量子体系中包含的10个粒子划分为第五团簇和第六团簇两个团簇，其中第五团簇中包含4个粒子，第六团簇中包含6个粒子，其中第五团簇中包含的粒子与第三团簇中包含的粒子至少有一个是不同的粒子，第六团簇中包含的粒子与第四团簇中包含的粒子至少有一个是不同的粒子。
从第一划分结果、第二划分结果和第三划分结果分别对应的直积态中，选择部分直积态作为一组基矢来表征压缩的希尔伯特空间。
可选地，从多个直积态中，选择能量值最小的设定数量个直积态，作为一组基矢来表征压缩的希尔伯特空间。示例性地，将多个直积态的能量值按照从小到大的顺序排序，选择其中的前设定数量个直积态，作为一组基矢来表征压缩的希尔伯特空间。示例性地，将多个直积态的能量值按照从大到小的顺序排序，选择其中的后设定数量个直积态，作为一组基矢来表征压缩的希尔伯特空间。
可选地，分别从第一划分结果、第二划分结果和第三划分结果对应的直积态中，选择能量值最小的设定数量个直积态，作为一组基矢来表征压缩的希尔伯特空间。示例性地，从第一划分结果对应的直积态中，选择能量值最小的设定数量个直积态，得到第一组直积态，从第二划分结果对应的直积态中，选择能量值最小的设定数量个直积态，得到第二组直积态，从第三划分结果对应的直积态中，选择能量值最小的设定数量个直积态，得到第三组直积态，将第一组直积态、第二组直积态和第三组直积态作为一组基矢来表征压缩的希尔伯特空间。
可选地，从第一划分结果、第二划分结果和第三划分结果对应的所有直积态中，选择能量值最小的设定数量个直积态，作为一组基矢来表征压缩的希尔伯特空间。示例性地，将第一划分结果、第二划分结果和第三划分结果对应的所有直积态按照从小到大的顺序排序，选择其中的前设定数量个直积态，作为一组基矢来表征压缩的希尔伯特空间。
可选地，也可以根据多个直积态的纠缠度进行筛选，选择部分直积态作为一组基矢来表征一压缩的希尔伯特空间。对于部分直积态的选择方法，本申请不作限定。示例性地，从多个直积态中，选择纠缠度最小的设定数量个直积态，作为一组基矢来表征压缩的希尔伯特空间。
步骤240，获取目标量子体系的哈密顿量，在压缩的希尔伯特空间中的等效哈密顿量。
步骤250，获取等效哈密顿量的本征态和本征能量，作为目标量子体系的本征态和本征能量。
该方法中步骤240～250与上述量子体系的本征态获取方法中图1所示的步骤140～150相同，具体可参见上文介绍说明，此处不再赘述。
综上所述，本申请提供的技术方案，通过对目标量子体系中包含的多个粒子进行多种不同方式的团簇划分，得到多种不同的团簇划分结果，每个团簇划分结果中包含多个团簇，根 据多个团簇的本征态得到多个直积态，从多种不同的团簇划分结果分别对应的直积态中，选择部分直积态作为一组基矢来表征压缩的希尔伯特空间，将多种团簇划分结果得到的直积态结合起来表征压缩的希尔伯特空间，能够减小误差，提高量子体系的本征态获取的精度。
下面以目标量子体系为氢链量子体系，且用一个量子比特来模拟一个自旋为例，对本申请技术方案进行介绍说明。氢链量子体系的原始哈密顿量可以表示为如公式(3)所示。
Figure PCTCN2021134932-appb-000029
其中，H代表氢链量子体系的原始哈密顿量，N代表该氢链量子体系中包含的自旋数目，Z代表泡利Z算符，X代表泡利X算符，g 1为单个自旋的自作用力，g 2为两个自旋之间的相互作用力。
请参考图5，其示出了本申请另一个实施例提供的量子体系的本征态获取方法的流程图。该方法可以包括如下几个步骤(510～550)中的至少一个步骤。
步骤510，对氢链量子体系中包含的多个自旋进行多种不同方式的团簇划分，得到多种不同的团簇划分结果，其中，每种团簇划分结果中包括多个团簇，每个团簇中包括至少一个自旋。
示例性地，氢链的长度N为3≤N≤8(N为正整数)，两个自旋(或量子比特)相互作用的相对大小固定在g 2/g 1＝2，其中g 2为两个自旋(或量子比特)之间的相互作用力，g 1为单个自旋(或量子比特)的自作用力。
示例性地，将目标量子体系按照{A＝{s 1,s 2},B＝{s 3,…,s N}}和{A＇＝{s 1,…，s N-2},B＇＝{s N-1,…,s N}}两种团簇划分方式，进行团簇划分，其中s i是指第i个自旋，A、B、A＇和B＇分别对应一个团簇。需要说明的是，对于具体的团簇划分方式，本申请不作限定，此处仅以两种团簇划分方式为例，进行示例性说明。
步骤520，对于每一种团簇划分结果，根据该团簇划分结果中包含的多个团簇分别对应的本征态，得到该团簇划分结果对应的多个直积态。
示例性地，根据上述四个团簇分别对应的本征态，得到四个直积态。
可选地，根据目标团簇的约化哈密顿量，获取目标团簇对应的至少一个本征态。
可选地，根据目标团簇的约化哈密顿量，采用对角化算法获取目标团簇对应的至少一个本征态。可选地，对角化算法包括但不限于以下至少一种：基于变分法实现的量子本征态求解算法、基于绝热近似的量子本征态求解算法、基于绝热捷径的量子本征态求解算法、结合绝热近似和绝热捷径的量子本征态求解算法。
可选地，对多个团簇分别对应的本征态进行直积运算，得到多个直积态。
示例性地，以{A＝{s 1,s 2},B＝{s 3,…,s N}}的团簇划分方式为例，首先将团簇A作为目标团簇，假设团簇B的初始状态为
Figure PCTCN2021134932-appb-000030
将团簇B作为团簇A的环境，得到团簇A的约化哈密顿量，该约化哈密顿量可以表示为公式(4)。
Figure PCTCN2021134932-appb-000031
其中，
Figure PCTCN2021134932-appb-000032
Z代表泡利Z算符，X代表泡利X算符，g 1为单个自旋的自作用力，g 2为两个自旋之间的相互作用力，N代表该氢链量子体系中包含的自旋数目。
示例性地，得到H A的两个本征态，基态和第一激发态，
Figure PCTCN2021134932-appb-000033
示例性地，根据团簇A的基态
Figure PCTCN2021134932-appb-000034
和第一激发态
Figure PCTCN2021134932-appb-000035
得到两个团簇B的约化哈密顿 量，该约化哈密顿量可以表示为公式(5)。
Figure PCTCN2021134932-appb-000036
其中，
Figure PCTCN2021134932-appb-000037
β＝{g，e}，Z代表泡利Z算符，X代表泡利X算符，g 1为单个自旋的自作用力，g 2为两个自旋之间的相互作用力，N代表该氢链量子体系中包含的自旋数目。
示例性地，得到两个H B的四个本征态(基态和第一激发态)
Figure PCTCN2021134932-appb-000038
其中，j＝{g，e}，β＝{g，e}。
示例性地，将团簇B的四个本征态
Figure PCTCN2021134932-appb-000039
作为环境的态，得到团簇A的八个本征态(基态和第一激发态)
Figure PCTCN2021134932-appb-000040
为了避免如此递归的进一步发散，我们仅迭代到第三步，对于迭代次数，本申请不作限定，此处仅以三次迭代为例进行示例性说明。
示例性地，将上述团簇A的八个本征态
Figure PCTCN2021134932-appb-000041
和上述团簇B的四个本征态
Figure PCTCN2021134932-appb-000042
进行直积运算，得到八个直积态。
示例性地，对于{A＇＝{s 1,…，s N-2},B＇＝{s N-1,…,s N}}的团簇划分方式，按照上述方法也可得到团簇A＇的八个本征态和团簇B＇的四个本征态，对其进行直积运算，得到八个直积态。
步骤530，从多种不同的团簇划分结果分别对应的直积态中，选择部分直积态作为一组基矢来表征压缩的希尔伯特空间。
示例性地，从上述团簇A和团簇B的八个直积态中，选择其中四个直积态
Figure PCTCN2021134932-appb-000043
{i＝g，α＝g g，g e}，{i＝e，α＝e g，e e}。同样的，从上述团簇A＇和团簇B＇的八个直积态中，选择其中四个直积态。将总共八个直积态{|ψ γ＝1，...，8>}，进行施密特正交化处理，得到一组基矢
Figure PCTCN2021134932-appb-000044
用以表征一个八维的希尔伯特空间。
步骤540，获取氢链量子体系的哈密顿量，在压缩的希尔伯特空间中的等效哈密顿量。
示例性地，获取氢链量子体系的哈密顿量，在八维希尔伯特空间中的等效哈密顿量，该等效哈密顿量可以表示为公式(6)。
Figure PCTCN2021134932-appb-000045
其中，
Figure PCTCN2021134932-appb-000046
H代表氢链量子体系的原始哈密顿量，
Figure PCTCN2021134932-appb-000047
是第一种团簇划分方式得到的基矢，
Figure PCTCN2021134932-appb-000048
是第二种团簇划分方式得到的基矢。
步骤550，获取等效哈密顿量的本征态和本征能量，作为氢链量子体系的本征态和本征能量。
可选地，采用对角化算法获取等效哈密顿量的本征态和本征能量；其中，对角化算法包括以下至少一种：基于变分法实现的量子本征态求解算法、基于绝热近似的量子本征态求解算法、基于绝热捷径的量子本征态求解算法、结合绝热近似和绝热捷径的量子本征态求解算法。
示例性地，以结合绝热近似和绝热捷径的量子本征态求解算法作为对角化算法为例，获取等效哈密顿量的本征态和本征能量。
示例性地，在基于绝热近似的量子本征态求解算法中，一个量子系统会沿着它的瞬时本征态进行演化。对于等效哈密顿量H eff，选择一个初始哈密顿量H 0，然后设计随时间变化的 绝热哈密顿量，该绝热哈密顿量可以表示为公式(7)。
H ad(t)＝H 0+λ(t)(H eff-H 0)    (7)
其中，λ(t)满足在初始时刻λ(t＝0)＝0，和在末尾时刻λ(t＝T)＝1。如果量子系统的初始状态被制备在本征态上，即
Figure PCTCN2021134932-appb-000049
在
Figure PCTCN2021134932-appb-000050
的情况下，这个量子系统会逐步演化到等效哈密顿量的对应本征态上，
Figure PCTCN2021134932-appb-000051
实际上，如果距离足够近，
Figure PCTCN2021134932-appb-000052
演化时间T也可以足够小。
示例性地，在基于绝热捷径的量子本征态求解算法中，需要引入一项反绝热哈密顿量，该反绝热哈密顿量可以表示为公式(8)。
Figure PCTCN2021134932-appb-000053
其中，
Figure PCTCN2021134932-appb-000054
是绝热哈密顿量H ad(t)在t时刻的瞬时本征态。因而，一个哈密顿量为H tot(t)＝H ad(t)+H cd(t)的量子系统，在
Figure PCTCN2021134932-appb-000055
和
Figure PCTCN2021134932-appb-000056
的情况下，在任意的操作时间，会严格在本征态上，
Figure PCTCN2021134932-appb-000057
实际上，反绝热哈密顿量可以通过单比特近似或者对易项展开等方法近似地估计。
绝热演化除非距离足够近，所需要的时间或者步骤会非常多，而绝热捷径法的快速绝热项比较复杂，因而我们将两者结合起来。以公式(3)的约化哈密顿量为例，选择初始哈密顿量
Figure PCTCN2021134932-appb-000058
以及设计两个中间参考点哈密顿量
Figure PCTCN2021134932-appb-000059
该中间参考点哈密顿量可以表示为公式(9)。
Figure PCTCN2021134932-appb-000060
其中，
Figure PCTCN2021134932-appb-000061
X代表泡利X算符。
示例性地，初始哈密顿量和约化哈密顿量的参数也可以囊括进来：
Figure PCTCN2021134932-appb-000062
Figure PCTCN2021134932-appb-000063
因而这里的蛙跳过程总共有3节演化过程。每一节演化的绝热哈密顿量可以设计为公式(10)。
Figure PCTCN2021134932-appb-000064
其中
Figure PCTCN2021134932-appb-000065
X代表泡利X算符。时间函数为η(0≤t i≤T i)＝sin 2(πt i/2T i)。其中T i是第i节的演化时间。初始状态制备在
Figure PCTCN2021134932-appb-000066
的基态上，则蛙跳过程的轨迹为：
Figure PCTCN2021134932-appb-000067
进而得到约化哈密顿量的本征态
Figure PCTCN2021134932-appb-000068
和本征能量
Figure PCTCN2021134932-appb-000069
将其作为氢链量子体系的本征态和本征能量。
示例性地，对于N>4的氢链，可以采用多层团簇划分的方式，将计算空间限制在N′≤4的氢链的哈密顿量上，例如一个具有8个自旋的氢链，可以分解为50个2自旋、5个3自旋、16个4自旋的哈密顿量进行计算。需要说明的一点是，对于计算空间的大小，本申请不作限定，此处仅以N′≤4的氢链的哈密顿量为例进行示例性说明。
对于上述氢链的长度N为3≤N≤8，两比特相互作用的相对大小固定在g 2/g 1＝2的氢链 量子体系的本征态获取，本申请进行了实验验证，其中，基态|Ψ g>的精度
Figure PCTCN2021134932-appb-000070
的结果图如图6所示，基态能量
Figure PCTCN2021134932-appb-000071
的结果图如图7所示。
为了衡量本申请量子体系的本征态获取方法的准确度，定义了一个精度函数：
Figure PCTCN2021134932-appb-000072
其中
Figure PCTCN2021134932-appb-000073
是数值计算得到的结果，
Figure PCTCN2021134932-appb-000074
是严格结果，严格结果是在经典计算机上，通过经典算法奇异值分解得到的。如图6所示，本申请量子体系的本征态获取方法得到的结果精度很高，
Figure PCTCN2021134932-appb-000075
如图7所示，基态能量
Figure PCTCN2021134932-appb-000076
的准确度甚至更高一些(>99.9％)。
另外，本申请还在超导量子比特系统中对本申请量子体系的本征态获取方法进行了实验实现。以有三自旋相互作用的三自旋链量子体系为例，它的哈密顿量形式如公式(11)所示。
H＝g 1(Z 1+Z 2+Z 3)+g 2(X 1X 2+X 2X 3)+g 3X 1X 2X 3     (11)
我们进行了两组实验，第一组实验固定三自旋相互作用的相对大小g 3/g 1＝0.1，改变两自旋相互作用的大小g 2/g 1从0～2.0，得到基态精度
Figure PCTCN2021134932-appb-000077
指全部过程在经典计算机上，通过数值模拟这一过程得到的基态精度；
Figure PCTCN2021134932-appb-000078
指对团簇和等效哈密顿量H eff对角化的过程在量子比特上实现，最后得到的基态精度。
第二组实验固定两自旋相互作用的相对大小g 2/g 1＝2.0，改变三自旋相互作用的大小g 3/g 1从0～2.0，得到基态精度
Figure PCTCN2021134932-appb-000079
指全部过程在经典计算机上，通过数值模拟这一过程得到的基态精度；
Figure PCTCN2021134932-appb-000080
指对团簇和等效哈密顿量H eff对角化的过程在量子比特上实现，最后得到的基态精度。
综上所述，本申请提供的技术方案，通过以氢链长度3≤N≤8的氢链量子体系为例，进行推导，并通过实验验证，通过实验数据，证实了本申请量子体系的本征态获取方法的精度很高，并且，采用氢链量子体系进行验证，证明了本方法具有普适性。
下述为本申请装置实施例，可以用于执行本申请方法实施例。对于本申请装置实施例中未披露的细节，请参照本申请方法实施例。
请参考图8，其示出了本申请一个实施例提供的量子体系的本征态获取装置的框图。该装置800可以包括如下几个模块：划分模块810、得到模块820、选择模块830、第一获取模块840和第二获取模块850。
划分模块810，用于对目标量子体系中包含的多个粒子进行团簇划分，得到多个团簇，所述多个团簇中的每个团簇中包含至少一个粒子。
得到模块820，用于根据所述多个团簇分别对应的本征态，得到多个直积态。
选择模块830，用于从所述多个直积态中，选择部分直积态作为一组基矢来表征一压缩的希尔伯特空间，其中，所述压缩的希尔伯特空间的维度数，小于所述目标量子体系的原始希尔伯特空间的维度数。
在一些实施例中，所述选择模块830，用于从所述多种不同的团簇划分结果分别对应的直积态中，选择部分直积态作为一组基矢来表征所述压缩的希尔伯特空间。
第一获取模块840，用于获取所述目标量子体系的哈密顿量，在所述压缩的希尔伯特空间中的等效哈密顿量。
第二获取模块850，用于获取所述等效哈密顿量的本征态和本征能量，作为所述目标量子体系的本征态和本征能量。
在一些实施例中，如图9所示，所述选择模块830包括获取单元831和选择单元832。
获取单元831，用于获取所述多个直积态分别对应的能量值。
选择单元832，用于从所述多个直积态中，选择所述能量值符合条件的多个直积态，作为一组基矢来表征所述压缩的希尔伯特空间。
在一些实施例中，所述选择单元832，用于从所述多个直积态中，选择所述能量值最小的n个直积态，作为一组基矢来表征所述压缩的希尔伯特空间，所述n为正整数。
在一些实施例中，所述得到模块820，用于对于所述多个团簇中的目标团簇，获取所述目标团簇的约化哈密顿量；根据所述目标团簇的约化哈密顿量，获取所述目标团簇对应的至少一个本征态；对所述多个团簇分别对应的本征态进行直积运算，得到所述多个直积态。
在一些实施例中，所述第一获取模块840，用于以所述多个团簇中除所述目标团簇之外的其他团簇作为环境，获取所述目标团簇在所述环境下的哈密顿量，得到所述目标团簇的约化哈密顿量。
在一些实施例中，所述划分模块810，用于对所述目标量子体系中包含的多个粒子进行多种不同方式的团簇划分，得到多种不同的团簇划分结果，其中，每种团簇划分结果中包括多个团簇。
在一些实施例中，所述第二获取模块850，用于采用对角化算法获取所述等效哈密顿量的本征态和本征能量；其中，所述对角化算法包括以下至少一种：基于变分法实现的量子本征态求解算法、基于绝热近似的量子本征态求解算法、基于绝热捷径的量子本征态求解算法、结合绝热近似和绝热捷径的量子本征态求解算法；将所述等效哈密顿量的本征态和本征能量，确定为所述目标量子体系的本征态和本征能量。
请参考图10，其示出了本申请一个实施例提供的计算机设备1000的结构框图。该计算机设备1000可以是经典计算机。该计算机设备可用于实施上述实施例中提供的量子体系的本征态获取方法。具体来讲：
该计算机设备1000包括处理单元(如CPU(Central Processing Unit，中央处理器)、GPU(Graphics Processing Unit，图形处理器)和FPGA(Field Programmable Gate Array，现场可编程逻辑门阵列)等)1001、包括RAM(Random-Access Memory，随机存储器)1002和ROM(Read-Only Memory，只读存储器)1003的系统存储器1004，以及连接系统存储器1004和中央处理单元1001的系统总线1005。该计算机设备1000还包括帮助服务器内的各个器件之间传输信息的基本输入/输出系统(Input Output System，I/O系统)1006，和用于存储操作系统1013、应用程序1014和其他程序模块1015的大容量存储设备1007。
可选地，该基本输入/输出系统1006包括有用于显示信息的显示器1008和用于用户输入信息的诸如鼠标、键盘之类的输入设备1009。其中，该显示器1008和输入设备1009都通过连接到系统总线1005的输入输出控制器1010连接到中央处理单元1001。该基本输入/输出系统1006还可以包括输入输出控制器1010以用于接收和处理来自键盘、鼠标、或电子触控笔等多个其他设备的输入。类似地，输入输出控制器1010还提供输出到显示屏、打印机或其他类型的输出设备。
可选地，该大容量存储设备1007通过连接到系统总线1005的大容量存储控制器(未示出)连接到中央处理单元1001。该大容量存储设备1007及其相关联的计算机可读介质为计算机设备1000提供非易失性存储。也就是说，该大容量存储设备1007可以包括诸如硬盘或者CD-ROM(Compact Disc Read-Only Memory，只读光盘)驱动器之类的计算机可读介质(未示出)。
不失一般性，该计算机可读介质可以包括计算机存储介质和通信介质。计算机存储介质包括以用于存储诸如计算机可读指令、数据结构、程序模块或其他数据等信息的任何方法或技术实现的易失性和非易失性、可移动和不可移动介质。计算机存储介质包括RAM、ROM、EPROM(Erasable Programmable Read-Only Memory，可擦写可编程只读存储器)、EEPROM (Electrically Erasable Programmable Read-Only Memory，电可擦写可编程只读存储器)、闪存或其他固态存储其技术，CD-ROM、DVD(Digital Video Disc，高密度数字视频光盘)或其他光学存储、磁带盒、磁带、磁盘存储或其他磁性存储设备。当然，本领域技术人员可知该计算机存储介质不局限于上述几种。上述的系统存储器1004和大容量存储设备1007可以统称为存储器。
根据本申请实施例，该计算机设备1000还可以通过诸如因特网等网络连接到网络上的远程计算机运行。也即计算机设备1000可以通过连接在该系统总线1005上的网络接口单元1011连接到网络1012，或者说，也可以使用网络接口单元1011来连接到其他类型的网络或远程计算机系统(未示出)。
所述存储器还包括至少一条指令、至少一段程序、代码集或指令集，该至少一条指令、至少一段程序、代码集或指令集存储于存储器中，且经配置以由一个或者一个以上处理器执行，以实现上述量子体系的本征态获取方法。
本领域技术人员可以理解，图10中示出的结构并不构成对计算机设备1000的限定，可以包括比图示更多或更少的组件，或者组合某些组件，或者采用不同的组件布置。
在示例性实施例中，还提供了一种计算机可读存储介质，所述存储介质中存储有至少一条指令、至少一段程序、代码集或指令集，所述至少一条指令、所述至少一段程序、所述代码集或所述指令集在被处理器执行时以实现上述量子体系的本征态获取方法。
可选地，该计算机可读存储介质可以包括：ROM(Read Only Memory，只读存储器)、RAM(Random Access Memory，随机存取记忆体)、SSD(Solid State Drives，固态硬盘)或光盘等。其中，随机存取记忆体可以包括ReRAM(Resistance Random Access Memory,电阻式随机存取记忆体)和DRAM(Dynamic Random Access Memory，动态随机存取存储器)。
在示例性实施例中，还提供了一种计算机程序产品或计算机程序，该计算机程序产品或计算机程序包括计算机指令，该计算机指令存储在计算机可读存储介质中。计算机设备的处理器从计算机可读存储介质读取该计算机指令，处理器执行该计算机指令，使得该计算机设备执行上述量子体系的本征态获取方法。

Claims (18)

  1. 一种量子体系的本征态获取方法，所述方法由计算机设备执行，所述方法包括：
    对目标量子体系中包含的多个粒子进行团簇划分，得到多个团簇，所述多个团簇中的每个团簇中包含至少一个粒子；
    根据所述多个团簇分别对应的本征态，得到多个直积态；
    从所述多个直积态中，选择部分直积态作为一组基矢来表征一压缩的希尔伯特空间，其中，所述压缩的希尔伯特空间的维度数，小于所述目标量子体系的原始希尔伯特空间的维度数；
    获取所述目标量子体系的哈密顿量，在所述压缩的希尔伯特空间中的等效哈密顿量；
    获取所述等效哈密顿量的本征态和本征能量，作为所述目标量子体系的本征态和本征能量。
  2. 根据权利要求1所述的方法，其中，所述从所述多个直积态中，选择部分直积态作为一组基矢来表征一压缩的希尔伯特空间，包括：
    获取所述多个直积态分别对应的能量值；
    从所述多个直积态中，选择所述能量值符合条件的多个直积态，作为一组基矢来表征所述压缩的希尔伯特空间。
  3. 根据权利要求2所述的方法，其中，所述从所述多个直积态中，选择所述能量值符合条件的多个直积态，作为一组基矢来表征所述压缩的希尔伯特空间，包括：
    从所述多个直积态中，选择所述能量值最小的n个直积态，作为一组基矢来表征所述压缩的希尔伯特空间，所述n为正整数。
  4. 根据权利要求1所述的方法，其中，所述根据所述多个团簇分别对应的本征态，得到多个直积态，包括：
    对于所述多个团簇中的目标团簇，获取所述目标团簇的约化哈密顿量；
    根据所述目标团簇的约化哈密顿量，获取所述目标团簇对应的至少一个本征态；
    对所述多个团簇分别对应的本征态进行直积运算，得到所述多个直积态。
  5. 根据权利要求4所述的方法，其中，所述获取所述目标团簇的约化哈密顿量，包括：
    以所述多个团簇中除所述目标团簇之外的其他团簇作为环境，获取所述目标团簇在所述环境下的哈密顿量，得到所述目标团簇的约化哈密顿量。
  6. 根据权利要求1所述的方法，其中，所述对目标量子体系中包含的多个粒子进行团簇划分，得到多个团簇，包括：
    对所述目标量子体系中包含的多个粒子进行多种不同方式的团簇划分，得到多种不同的团簇划分结果，其中，每种团簇划分结果中包括多个团簇；
    所述从所述多个直积态中，选择部分直积态作为一组基矢来表征一压缩的希尔伯特空间，包括：
    从所述多种不同的团簇划分结果分别对应的直积态中，选择部分直积态作为一组基矢来表征所述压缩的希尔伯特空间。
  7. 根据权利要求1至6任一项所述的方法，其中，所述获取所述等效哈密顿量的本征态和本征能量，作为所述目标量子体系的本征态和本征能量，包括：
    采用对角化算法获取所述等效哈密顿量的本征态和本征能量；其中，所述对角化算法包括以下至少一种：基于变分法实现的量子本征态求解算法、基于绝热近似的量子本征态求解算法、基于绝热捷径的量子本征态求解算法、结合绝热近似和绝热捷径的量子本征态求解算法；
    将所述等效哈密顿量的本征态和本征能量，确定为所述目标量子体系的本征态和本征能量。
  8. 一种量子体系的本征态获取装置，所述装置包括：
    划分模块，用于对目标量子体系中包含的多个粒子进行团簇划分，得到多个团簇，所述多个团簇中的每个团簇中包含至少一个粒子；
    得到模块，用于根据所述多个团簇分别对应的本征态，得到多个直积态；
    选择模块，用于从所述多个直积态中，选择部分直积态作为一组基矢来表征一压缩的希尔伯特空间，其中，所述压缩的希尔伯特空间的维度数，小于所述目标量子体系的原始希尔伯特空间的维度数；
    第一获取模块，用于获取所述目标量子体系的哈密顿量，在所述压缩的希尔伯特空间中的等效哈密顿量；
    第二获取模块，用于获取所述等效哈密顿量的本征态和本征能量，作为所述目标量子体系的本征态和本征能量。
  9. 根据权利要求8所述的装置，其中，所述选择模块，包括：
    获取单元，用于获取所述多个直积态分别对应的能量值；
    选择单元，用于从所述多个直积态中，选择所述能量值符合条件的多个直积态，作为一组基矢来表征所述压缩的希尔伯特空间。
  10. 根据权利要求9所述的装置，其中，所述选择单元，用于从所述多个直积态中，选择所述能量值最小的n个直积态，作为一组基矢来表征所述压缩的希尔伯特空间，所述n为正整数。
  11. 根据权利要求8所述的装置，其中，所述得到模块，用于：
    对于所述多个团簇中的目标团簇，获取所述目标团簇的约化哈密顿量；
    根据所述目标团簇的约化哈密顿量，获取所述目标团簇对应的至少一个本征态；
    对所述多个团簇分别对应的本征态进行直积运算，得到所述多个直积态。
  12. 根据权利要求11所述的装置，其中，所述第一获取模块，用于以所述多个团簇中除所述目标团簇之外的其他团簇作为环境，获取所述目标团簇在所述环境下的哈密顿量，得到所述目标团簇的约化哈密顿量。
  13. 根据权利要求8所述的装置，其中，
    所述划分模块，用于对所述目标量子体系中包含的多个粒子进行多种不同方式的团簇划分，得到多种不同的团簇划分结果，其中，每种团簇划分结果中包括多个团簇；
    所述选择模块，用于从所述多种不同的团簇划分结果分别对应的直积态中，选择部分直积态作为一组基矢来表征所述压缩的希尔伯特空间。
  14. 根据权利要求8至13任一项所述的装置，其中，所述第二获取模块，用于：
    采用对角化算法获取所述等效哈密顿量的本征态和本征能量；其中，所述对角化算法包括以下至少一种：基于变分法实现的量子本征态求解算法、基于绝热近似的量子本征态求解 算法、基于绝热捷径的量子本征态求解算法、结合绝热近似和绝热捷径的量子本征态求解算法；
    将所述等效哈密顿量的本征态和本征能量，确定为所述目标量子体系的本征态和本征能量。
  15. 一种计算机设备，所述计算机设备包括处理器和存储器，所述存储器中存储有至少一条指令、至少一段程序、代码集或指令集，所述至少一条指令、所述至少一段程序、所述代码集或指令集由所述处理器加载并执行以实现如权利要求1至7任一项所述的量子体系的本征态获取方法。
  16. 一种计算机可读存储介质，所述存储介质中存储有至少一条指令、至少一段程序、代码集或指令集，所述至少一条指令、所述至少一段程序、所述代码集或指令集由处理器加载并执行以实现如权利要求1至7任一项所述的量子体系的本征态获取方法。
  17. 一种计算机程序产品或计算机程序，所述计算机程序产品或计算机程序包括计算机指令，所述计算机指令存储在计算机可读存储介质中，处理器从所述计算机可读存储介质读取并执行所述计算机指令，以实现如权利要求1至7任一项所述的量子体系的本征态获取方法。
  18. 一种计算机程序产品或计算机程序，所述计算机程序产品或所述计算机程序包括计算机指令，所述计算机指令存储在计算机可读存储介质中，计算机设备的处理器从所述计算机可读存储介质读取所述计算机指令，处理器执行所述计算机指令，以实现如权利要求1至7任一项所述的量子体系的本征态获取方法。
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