1. A method for obtaining a ground state of a quantum system, the method comprising:

preparing an initial state of a target quantum system;

carrying out n-step evolution and post-processing on the target quantum system; the k step of evolution comprises the step of evolving the input quantum state of the k step to obtain an evolution end state of the k step; the k step post-processing comprises the step of removing the influence of auxiliary quantum bits used in the k step evolution from the k step evolution final state to obtain a k step output quantum state; the kth input quantum state comprises a direct product of the kth-1 output quantum state obtained by the kth-1 post-processing and the initial state of the auxiliary quantum bit used by the kth evolution, and k is a positive integer less than or equal to n; in the case where k is equal to 1, the 1 st input quantum state comprises a direct product of the initial state of the target quantum system and the initial state of the auxiliary qubit used in the 1 st evolution;

and acquiring the nth output quantum state obtained through the n-step evolution and post-processing to obtain the ground state of the target quantum system.

2. The method of claim 1, wherein the n-step evolving and post-processing the target quantum system comprises:

for the k step evolution, adopting a k quantum circuit to evolve the k step input quantum state to obtain a k step evolution final state;

and for the kth step post-processing, performing classical data post-processing on the kth step evolution final state by adopting a kth measuring circuit, and projecting the auxiliary quantum bit used by the kth step evolution to a 0 state to obtain the kth step output quantum state.

3. The method of claim 2, wherein the n-th evolution end state | φ is obtained through n-step evolution_n>The process of (2) is as follows:

wherein U (t) represents the quantum circuit adopted for evolution, | ψ₀>Represents the initial state of the target quantum system, U (t) ═ e^-iHt，H_SRepresenting a Hamiltonian of the target quantum system,representing the pauli operator acting on the ancillary qubit, and t representing time.

4. The method of claim 3, wherein a final state | φ is evolved for the nth step_n>The process of performing classical data post-processing is as follows:

|φ′_n>＝PU(t)ⁿ|ψ₀>|00...0>＝cosⁿ(H_St)|ψ₀>|00...0>；

wherein, P is a projection operator, is shown asA pauli operator for the auxiliary qubit used in the k-th evolution.

5. The method of claim 1, wherein 1 ancillary qubit is used for each of the n-step evolutions, and wherein the ancillary qubits are recycled in the n-step evolutions.

6. The method of claim 1, further comprising:

after the k-th evolution final state is obtained, adopting a variational quantum circuit corresponding to the k-th evolution to carry out transformation processing on the k-th evolution final state to obtain a quantum state after the k-th transformation;

taking the minimum energy expected value of the quantum state after the k step of transformation as a target, and adjusting the parameters of the variational quantum circuit corresponding to the k step of evolution;

under the condition that the parameters of the variation quantum circuit corresponding to the k-th evolution meet the condition of stopping optimization, acquiring the quantum state after the k-th transformation;

and executing the kth post-processing on the quantum state transformed in the kth step to obtain the output quantum state in the kth step.

7. The method of claim 6, further comprising:

in the process of adjusting the parameters of the variational quantum circuit corresponding to the k-th evolution step, the parameters of the variational quantum circuit corresponding to other evolution steps are kept unchanged;

and after the parameter adjustment of the variation quantum circuit corresponding to the k-th evolution step is completed, adjusting the parameter of the variation quantum circuit corresponding to the k + 1-th evolution step.

8. The method of claim 1, wherein the n-step evolution and post-processing are alternatively implemented by:

constructing a tentative quantum state by using a target variational quantum circuit;

aiming at enabling the probing quantum state to approach a target quantum state, adjusting the parameters of the target variational quantum line;

determining the tentative quantum state constructed by the target variational quantum circuit as the ground state of the target quantum system under the condition that the parameters of the target variational quantum circuit meet the stop optimization condition; and determining the expected energy value of the Hamiltonian of the target quantum system in the tentative quantum state as the ground state energy of the target quantum system.

9. The method according to any one of claims 1 to 8, wherein after obtaining the n-th step output quantum state obtained by the n-step evolution and post-processing to obtain the ground state of the target quantum system, the method further comprises:

calculating the ground state energy E of the target quantum system according to the following formula:

wherein H_SRepresenting the Hamiltonian, | φ, of the target quantum system_n>Represents the n-th step evolution final state, | phi'_n>Representing the output quantum state of the nth step, P is a projection operator, representing the pauli operator acting on the ancillary qubits used in the k-th evolution.

10. A ground state acquisition apparatus of a quantum system, the apparatus comprising:

the initial state preparation module is used for preparing the initial state of the target quantum system;

the evolution processing module is used for carrying out n-step evolution and post-processing on the target quantum system; the k step of evolution comprises the step of evolving the input quantum state of the k step to obtain an evolution end state of the k step; the k step post-processing comprises the step of removing the influence of auxiliary quantum bits used in the k step evolution from the k step evolution final state to obtain a k step output quantum state; the kth input quantum state comprises a direct product of the kth-1 output quantum state obtained by the kth-1 post-processing and the initial state of the auxiliary quantum bit used by the kth evolution, and k is a positive integer less than or equal to n; in the case where k is equal to 1, the 1 st input quantum state comprises a direct product of the initial state of the target quantum system and the initial state of the auxiliary qubit used in the 1 st evolution;

and the ground state acquisition module is used for acquiring the nth step output quantum state obtained through the n-step evolution and post-processing to obtain the ground state of the target quantum system.

11. A computer device, characterized in that the computer device is adapted to perform the method of any of claims 1 to 9.

12. A computer readable storage medium having stored therein at least one instruction, at least one program, a set of codes, or a set of instructions, which is loaded and executed by a processor to implement the method of any of claims 1 to 9.

Background

The ground state of a quantum system refers to the eigenstate where the quantum system has the lowest energy. The acquisition of the ground state of a quantum system, which represents the acquisition of the most stable state of the quantum system, has important applications in many studies.

In the related art, a scheme for solving a quantum system ground state based on virtual time evolution is provided. The theory of solving the ground state is very clear, so that the process of approaching the ground state is theoretically guaranteed. But use of e^-HτThe scheme is non-unitary and cannot be directly decomposed into a single-bit gate or a double-bit gate which can be used for a quantum circuit, so that the scheme is difficult to realize in practice.

Disclosure of Invention

The embodiment of the application provides a quantum system ground state acquisition method, device, equipment and storage medium. The technical scheme is as follows:

according to an aspect of an embodiment of the present application, there is provided a method for obtaining a ground state of a quantum system, the method including:

preparing an initial state of a target quantum system;

carrying out n-step evolution and post-processing on the target quantum system; the k step of evolution comprises the step of evolving the input quantum state of the k step to obtain an evolution end state of the k step; the k step post-processing comprises the step of removing the influence of auxiliary quantum bits used in the k step evolution from the k step evolution final state to obtain a k step output quantum state; the kth input quantum state comprises a direct product of the kth-1 output quantum state obtained by the kth-1 post-processing and the initial state of the auxiliary quantum bit used by the kth evolution, and k is a positive integer less than or equal to n; in the case where k is equal to 1, the 1 st input quantum state comprises a direct product of the initial state of the target quantum system and the initial state of the auxiliary qubit used in the 1 st evolution;

and acquiring the nth output quantum state obtained through the n-step evolution and post-processing to obtain the ground state of the target quantum system.

According to an aspect of an embodiment of the present application, there is provided a ground state acquisition apparatus of a quantum system, the apparatus including:

the initial state preparation module is used for preparing the initial state of the target quantum system;

the evolution processing module is used for carrying out n-step evolution and post-processing on the target quantum system; the k step of evolution comprises the step of evolving the input quantum state of the k step to obtain an evolution end state of the k step; the k step post-processing comprises the step of removing the influence of auxiliary quantum bits used in the k step evolution from the k step evolution final state to obtain a k step output quantum state; the kth input quantum state comprises a direct product of the kth-1 output quantum state obtained by the kth-1 post-processing and the initial state of the auxiliary quantum bit used by the kth evolution, and k is a positive integer less than or equal to n; in the case where k is equal to 1, the 1 st input quantum state comprises a direct product of the initial state of the target quantum system and the initial state of the auxiliary qubit used in the 1 st evolution;

and the ground state acquisition module is used for acquiring the nth step output quantum state obtained through the n-step evolution and post-processing to obtain the ground state of the target quantum system.

According to an aspect of the embodiments of the present application, there is provided a computer apparatus for performing the above method.

According to an aspect of embodiments of the present application, there is provided a computer-readable storage medium having stored therein at least one instruction, at least one program, set of codes, or set of instructions that is loaded and executed by a processor to implement the above-mentioned method.

The technical scheme provided by the embodiment of the application can have the following beneficial effects:

the target quantum system is gradually evolved from an initial state to a ground state by carrying out multi-step evolution and post-processing on the target quantum system, so that the ground state of the target quantum system is obtained, auxiliary quantum bits are introduced in the evolution process to realize unitary evolution, a quantum simulation algorithm based on a non-Hermite process is provided to simulate the ground state of the target quantum system, the effect of imaginary and real evolution is realized by real-time unitary evolution related to the Hamilton quantity of the system, the simulation of the ground state of the target quantum system is clearly and definitely realized theoretically, the process can be realized by a quantum circuit directly, and the operability of the scheme is fully improved.

Drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present application, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.

Fig. 1 is a flow chart of a method for obtaining a ground state of a quantum system according to an embodiment of the present application;

FIG. 2 is a schematic diagram of a quantum circuit structure for implementing a non-Hermite quantum simulation algorithm according to an embodiment of the present application;

FIG. 3 is a schematic diagram of a quantum circuit structure for implementing a non-Hermite quantum simulation algorithm in conjunction with a variational quantum circuit according to an embodiment of the present application;

FIG. 4 is a schematic diagram of quantum state compression using a variational quantum circuit according to an embodiment of the present application;

fig. 5 to 7 exemplarily show diagrams of some experimental data;

fig. 8 is a block diagram of a ground state acquisition device of a quantum system according to an embodiment of the present application.

Detailed Description

To make the objects, technical solutions and advantages of the present application more clear, embodiments of the present application will be described in further detail below with reference to the accompanying drawings.

Explanation of some key terms referred to in this application.

1. Quantum computing: based on the quantum-logic computational approach, the basic unit of storage data is a quantum bit (qubit).

2. Quantum bit: basic unit of quantum computation. Conventional computers use 0 and 1 as the basic units of the binary system. Except that quantum computation can process 0 and 1 simultaneously, the system can be in a linear superposition state of 0 and 1: phi>＝α|0>+β|1>Here, α and β represent the complex probability amplitude of the system at 0 and 1. Their modulus squared | α²，|β|²Representing the probabilities at 0 and 1, respectively.

3. Quantum wires: also known as quantum circuits, a representation of a quantum general purpose computer, represents a hardware implementation of a corresponding quantum algorithm/program in a quantum gate model. If the Quantum wires include adjustable parameters for controlling the Quantum gate, they are called Parameterized Quantum wires (PQC) or Variational Quantum wires (VQC), and both are the same concept.

4. Hamilton amount: a matrix describing the hermitian conjugate of the total energy of the quantum system. The hamiltonian is a physical word, an operator describing the total energy of the system, usually denoted by H.

5. The eigenstate: for a Hamiltonian matrix H, the equation is satisfied: the solution of H | ψ > ═ E | ψ > is referred to as the eigenstate | ψ > of H, with the eigenenergy E. The ground state corresponds to the eigenstate where the quantum system has the lowest energy.

NISQ (Noisy Intermediate-Scale Quantum): recent medium-scale noisy quantum hardware is the current stage and focus of research in the development of quantum computing. This stage of quantum computation cannot be applied as an engine for general purpose computation for a while due to size and noise limitations, but results beyond the strongest classical computer have been achieved on part of the problem, which is often referred to as quantum dominance or quantum dominance.

7. Variational Quantum intrinsic solver (VQE for short): the estimation of the ground state energy of a specific quantity subsystem is realized through a variation line (namely PQC/VQC), is a typical quantum classical hybrid calculation paradigm, and has wide application in the field of quantum chemistry.

8. Non-unitary: so-called unitary matrix, i.e. satisfyAll matrices of (2) and all evolution processes directly allowed by quantum mechanics can be described by unitary matrices. Where U is a Unitary Matrix (Unitary Matrix), also referred to as Unitary Matrix, or the like,is the conjugate transpose of U. In addition, a matrix that does not satisfy this condition is non-unitary, which requires even exponentially many resources through auxiliary means to be realized experimentally, but a non-unitary matrix tends to have a stronger expression capability and a faster ground state projection effect. The resource with more indexes refers to that the required quantity of the resource increases exponentially with the increase of the number of the quantum bits, and the resource with more indexes may refer to that the total number of the quantum lines to be measured is multiple, that is, the calculation time with more indexes is correspondingly needed.

9. Pauli string (Pauli string): in terms of the direct product of multiple pauli at different lattice points, the general Hamiltonian can be decomposed into the sum of a set of pauli strings. The measurement of VQE is also typically measured item by item according to a pauli string decomposition.

10. Paglie operator: also known as the pauli matrix, is a set of three 2 x 2 unitary hermitian complex matrices (also known as unitary matrices), generally expressed in terms of the greek letters σ (sigma). Wherein the Pauli X operator isThe Paulii Y operator isThe Pauli Z operator is

The method for obtaining the ground state of the quantum system represents the most stable state of the quantum system, and has very important application in research of basic properties of quantum physical and quantum chemical systems, solution of combinatorial optimization problems, pharmaceutical research and the like. An important application scenario for quantum computers is to efficiently solve or express the quantum system ground state. At present, some research institutions and manufacturers are also continuously researching new quantum computers, and are dedicated to exploring the solution of the ground state.

The related art provides an introduction description of a scheme for obtaining a ground state of a quantum system.

Scheme 1: solving quantum system ground state through virtual time evolution

Virtual time evolution is a basic method for solving the ground state of a quantum system.

The time-dependent schrodinger equation is:

where H is the hamiltonian of the target quantum system, ψ (r, t) represents the quantum state of the target quantum system at time t, and i is an imaginary unit.

The stationary schrodinger equation is:

Hφ_i(r)＝E_iφ_i(r)；

wherein phi_i(r) (r ═ 1,2,3 …) is an eigenstate corresponding to the eigenenergy E_i。E₀≤E₁≤E₂≤E₃…，E₀Is the ground state energy. Defining the virtual time tau to it, then the virtual time Schrodinger equation is:

to calculate the ground state of the target quantum system, an initial state ψ (r,0) is randomly given when τ is 0, and the superposition ψ (r,0) Σ of eigenstates can be written_ic_iφ_i(r) wherein c_iIs the expansion coefficient.

The wave function at time τ is:

due to E_i≥E₀As psi (r, tau) evolves, in contrast to phi₀The other states decay more rapidly, leaving only the ground state at the end.

Scheme 2: VQE (Variational Quantum eigenresolver)

VQE is a fault tolerant quantum algorithm that can be run on a NISQ quantum device, simulating the ground state of the target quantum system.

Given an initial quantum state | ψ₀>In general, all 0 states, homogeneous stack states, or Hartree-Fock states can be considered, and can be written as a linear combination of eigenstates. Providing a parameterized quantum wire U (theta) such that U (theta) | ψ₀>＝|ψ(θ)>Solving the target quantum system ground state E as long as the quantum state space that this parameterized quantum wire can express contains the target quantum system ground state₀The process of (2) can be converted into an optimization process of parameters in quantum wires:

an optimal group of theta can be found through a gradient descent method, and then the parameterized quantum circuit is updated to obtain an eigenstate phi corresponding to the ground state energy₀。

Scheme 3: solving quantum system ground state through variable division virtual time evolution

And (3) simulating the process of virtual time evolution by utilizing a classical and quantum combined variation method in the variation virtual time evolution so as to solve the basic state of the target quantum system.

Given an initial state | ψ (0) >, the virtual time evolution is defined as:

|ψ(τ)>＝A(τ)e^-Hτ|ψ(0)>；

whereinIs a normalization factor.

The Wick rotation Schrodinger equation is:

wherein E_τ＝<ψ(τ)|H|ψ(τ)>. Then, using heuristics with parametersWave function | phi (theta (tau))>To approximate | ψ (τ)>The following can be obtained:

|φ(θ)>＝V(θ)|ψ(0)>。

this simulation can be achieved by the McLachlan's variational principle:

the scheme 1 introduced above, namely the method for solving the quantum system ground state by the virtual time evolution, has a clear theory for solving the ground state, so that the process of approaching the ground state is theoretically guaranteed. But use of e^-HτIs non-unitary and cannot be directly decomposed into single-bit gates or double-bit gates that can be used for quantum wires.

Scheme 2 introduced above, VQE requires the assumption of a reasonably reliable parameterized quantum wire, such that its expressed quantum state space covers the target quantum state. And as quantum systems become more complex, heuristic quantum wires become deeper and deeper, parameter space is large, and the ground state cannot be obtained because the optimization space is complex and is easy to fall into a local optimal solution.

In the scheme 3 introduced above, the method for solving the ground state of the quantum system by variable division virtual time evolution uses a parameterized quantum circuit to simulate the process of virtual time evolution, and needs to slow the evolution process enough to gradually optimize the parameters of the quantum circuit so as to ensure that the accurate ground state is finally obtained.

The application provides a brand-new technical scheme, and effective ground state simulation is realized by a non-Hermite simulation thought. No matter for the recent NISQ stage, a ground state simulation method for reducing the operation and design difficulty of scientists is theoretically provided, and the ground state simulation method has good reference value for carrying out the ground state simulation on multi-bit high-quality quantum hardware which is possibly realized in the future.

In addition, the method for obtaining the ground state of the quantum system provided by the application can be implemented by being executed by a quantum computer, and can also be implemented in the environment of a mixed device of a classical computer and the quantum computer, for example, the method is implemented by being matched by the classical computer and the quantum computer. In the following method embodiments, for convenience of description, only the execution subject of each step is described as a computer device. It should be understood that the computer device may be a quantum computer, and may also include a hybrid execution environment of a classical computer and a quantum computer, which is not limited in this application.

Referring to fig. 1, a flowchart of a method for obtaining a ground state of a quantum system according to an embodiment of the present application is shown. The method comprises the following steps (110-130):

step 110, prepare the initial state of the target quantum system.

Step 120, carrying out n-step evolution and post-processing on the target quantum system; the k step of evolution comprises the step of evolving the input quantum state of the k step to obtain an evolution end state of the k step; the kth step of post-processing comprises the steps of removing the influence of auxiliary quantum bits used in the kth step of evolution from the kth step of evolution final state to obtain the kth step of output quantum state; the input quantum state in the k step comprises a direct product of the output quantum state in the k-1 step obtained by the post-processing in the k-1 step and the initial state of the auxiliary quantum bit used in the k evolution step, wherein k is a positive integer less than or equal to n; in the case where k equals 1, the 1 st input quantum state comprises the direct product of the initial state of the target quantum system and the initial state of the auxiliary qubit used in the 1 st evolution.

And step 130, obtaining the nth output quantum state obtained through the n-step evolution and post-processing to obtain the ground state of the target quantum system.

The application designs a non-Hermite quantum simulation algorithm to obtain the ground state of a target quantum system. The target quantum system refers to any quantum system which is required to acquire a ground state, and the target quantum system can be a quantum physical system or a quantum chemical system, which is not limited in the application.

The present application designs a quantum circuit structure as shown in fig. 2, on which a quantum process similar to virtual-real evolution is implemented to obtain a ground state of a target quantum system. In fig. 2, "S" refers to the qubit space corresponding to the investigated quantum system (i.e., the target quantum system), and "a" refers to the qubit space corresponding to the auxiliary qubit. And carrying out n-step evolution and post-processing on the target quantum system, wherein each step of evolution and post-processing comprises executing an evolution process first and then executing a post-processing process. That is, the step 1 evolution, the step 1 post-processing, the step 2 evolution, the step 2 post-processing, … …, the step nth evolution, the step nth post-processing are performed in sequence.

In the embodiment of the present application, the input quantum state of the k-th evolution is referred to as a k-th input quantum state, for example, the input quantum state of the 1-step evolution is referred to as a 1-step input quantum state. In each step of the evolution process, auxiliary qubits are used to help implement the unitary evolution process. Optionally, 1 auxiliary qubit is used in each of the n-step evolutions, and the auxiliary qubits are recycled in the n-step evolutions. And the k step evolution comprises evolving the k step input quantum state to obtain a k step evolution final state, wherein the k step input quantum state comprises a direct product of the k-1 step output quantum state obtained through the k-1 step post-processing and the initial state of the auxiliary qubit used in the k step evolution. For the 1 st evolution (i.e. the case that k is 1), the 1 st evolution includes evolving the 1 st input quantum state to obtain a 1 st evolution end state, where the 1 st input quantum state includes a direct product of an initial state of the target quantum system and an initial state of the auxiliary qubit used in the 1 st evolution.

Optionally, each step of the evolution process is implemented by a quantum circuit. And for the k step evolution, a k quantum circuit is adopted to evolve the k step input quantum state to obtain a k step evolution final state. Optionally, each step of post-processing is implemented by a measurement circuit. And for the kth step post-processing, performing classical data post-processing on the k step evolution final state by adopting a kth measuring circuit, and projecting the auxiliary quantum bit used by the k step evolution to a 0 state to obtain the kth step output quantum state.

As shown in fig. 2, the quantum circuit used in the evolution process is denoted by u (t), which is e^-iHt，WhereinRepresenting the direct product of two matrices, H_SRepresenting the hamiltonian of the target quantum system,representing a Palyre operator acting on the ancillary qubit, which may be a Palyre X operator Or the Paulii Y operatort represents time.

Optionally, preparing the target quantum system to | ψ₀>In the initial state, the auxiliary qubit is given by |0>Is an initial state, namely a 1 st step input quantum state | phi corresponding to the 1 st step evolution₀>＝|ψ₀>|0>. The 1 st step inputs the quantum state | phi₀>The unitary evolution is realized through a quantum circuit U (t) to obtain the 1 st evolution end state | phi₁>：

The last state | φ is then evolved for this 1 st step via a measurement circuit (not shown in FIG. 2)₁>Performing classical-processing (post-processing) to project the auxiliary qubits to |0>To obtain the output quantum state | phi of the step 1₁′>：

|φ′₁〉＝PU(t)|ψ₀>|0〉＝cos(H_St)|ψ₀>|0〉；

Wherein, P is a projection operator,the Palyre operator is a Palyre Z operator that acts on the ancillary qubit.

The same principle can be derived, and the n-th evolution final state | phi acquired after n-step evolution_n>Comprises the following steps:

adopting the nth measuring circuit to evolve the last state | phi for the nth step_n>Performing classical data post-processing to project the auxiliary qubits to |0>Obtaining the output quantum state | phi 'of the n-th step'_n>Comprises the following steps:

|φ′_n〉＝PU(t)ⁿ|ψ₀>|00...0>＝cosⁿ(H_St)|ψ₀>|00...0>；

wherein, P is a projection operator,represents the pauli operator, which is the pauli Z operator, acting on the ancillary qubits used in the k-th evolution.

Through the n-step evolution and post-treatment, the output quantum state phi of the n-step is finally obtained'_n>I.e. the ground state of the target quantum system.

Further, the nth step of output quantum state | phi 'is obtained'_n>Corresponding energy eigenvalue E_n(i.e., the ground state energy E of the target quantum system):

wherein P is used²P and [ P, H ═ P_S]0 (represents P and H)_SEasy to do). It can be found that, according to the nature of the cos function, for a single-step evolution time scale t of suitable length, the following is satisfied:

cos(E_gt)＞cos(E_k≠gt)＞0,0＜E_g＜E_k≠g；

wherein E is_gRepresenting the ground state energy, E_k≠gRepresenting the non-ground state energy. Notably, for intrinsicH with spectrum not positive_SCan be through H_S+λI_SThe eigenspectrum is shifted to positive, resulting in the lowest energy E'_gThen backward E_g＝E′_gλ, where λ is a translation parameter determined by prediction, I_SIs an identity matrix.

Through the above n-step evolution, cosⁿ(E_gt)＞＞cosⁿ(E_k≠gt) > 0, thereby obtaining an effective non-Hermite quantum simulation algorithm which has the effect similar to the virtual and real evolution, namely: with the gradual increase of the evolution steps, the proportion of the ground state of the target quantum system is increased more and more, the proportion of the excited state is decreased more and more, and the ground state of the target quantum system is finally obtained.

In the process, the technical scheme provided by the application naturally shows the following advantages: 1) the effect of virtual-real evolution is realized by real-time unitary evolution related to the system Hamiltonian, which can be realized by a quantum circuit directly; 2) the auxiliary qubits used in each evolution step can be recycled, that is, 1 auxiliary qubit is needed in total, thereby saving qubit resources; 3) the optimization process is clearer and more stable on a theoretical level without depending on a variational quantum circuit; 4) classical data post-processing (post-processing) is adopted, instead of traditional measurement result post-selection (post-selection), so that the complexity of quantum experiments is reduced at the cost of consuming classical computing resources.

In order to realize the effect that the quantum simulation algorithm provided by the application follows similar virtual and real quantum dynamics evolution in the operation process, the application adopts real-time quantum dynamics evolution under auxiliary quantum bit, and then obtains the quantum evolution of a target quantum system by a method of classical data post-processing (post-processing):

|ψ_T＝nt>＝cosⁿ(H_St)|ψ₀>；

wherein the energy eigenvalues need to be calculated when they are obtained<φ_n|PH_S|φ_n>And<φ_n|P|φ_n>and is andn is the number of steps of the kinetic evolution. It is easy to see that the combination term of the Pagli matrix in P is exponential (2) with the increase of the step number nⁿ) Increase, i.e. classical computational complexity of 2ⁿAn exponential increase. The present application therefore further proposes an alternative to this classical data post-processing.

Since the projection operator P satisfies P²P and [ P, H ═ P_S]As 0, we can prove that:

<ψ₁|Z₁|ψ₁>＝<ψ₂|Z₁I₂|ψ₂>＝<ψ₃|Z₁I₂I₃|ψ₃>＝…；

<ψ₁|H_SZ₁|ψ₁>＝<ψ₂|H_SZ₁I₂|ψ₂>＝<ψ₃|H_SZ₁I₂I₃|ψ₃>＝...；

because of the fact thatWe can demonstrate that:

<ψ_n|Z₁|ψ_n>＝<ψ_n|Z₂|ψ_n>＝<ψ_n|Z₃|ψ_n>＝…；

<ψ_n|Z₁Z₂|ψ_n>＝<ψ_n|Z₁Z₃|ψ_n>＝<ψ_n|Z₂Z₃|ψ_n>＝...；

……

<ψ_n|Z₁Z₂...Z_n|ψ_n>；

and because ofWe can demonstrate that:

<ψ_n|H_SZ₁|ψ_n>＝<ψ_n|H_SZ₂|ψ_n>＝<ψ_n|H_SZ₃|ψ_n>＝...；

<ψ_n|H_SZ₁Z₂|ψ_n>＝<ψ_n|H_SZ₁Z₃|ψ_n>＝<ψ_n|H_SZ₂Z₃|ψ_n>＝...；

……

<ψ_n|H_SZ₁Z₂...Z_n|ψ_n>；

therefore, the energy expectation value corresponding to the evolution step number n can be finally written as:

thus, for the result of step n, only two terms need to be calculated:<ψ_n|H_SZ₁Z₂...Z_n|ψ_n>and<ψ_n|Z₁Z₂...Z_n|ψ_n>thereby greatly reducing the amount of calculation. It can be concluded that the complexity of the energy eigenvalue calculation grows linearly with the number of evolution steps at 2 n.

In summary, according to the technical scheme provided by the embodiment of the application, the target quantum system is gradually evolved from the initial state to the ground state by performing multi-step evolution and post-processing on the target quantum system, so that the ground state of the target quantum system is obtained, the auxiliary quantum bit is introduced in the evolution process to realize unitary evolution, and therefore a quantum simulation algorithm based on a non-hermite process is provided to simulate the ground state of the target quantum system, the effect of imaginary and real evolution is realized by real-time unitary evolution related to the Hamiltonian quantity of the system, so that the simulation of the ground state of the target quantum system is theoretically clearly and definitely realized, the process can be directly realized by the quantum circuit, and the operability of the scheme is fully improved.

In addition, the auxiliary qubits used in each step of evolution can be recycled, that is, 1 auxiliary qubit is needed altogether, thereby saving quantum computing resources.

Since the larger the Hamiltonian scale of the target quantum system, the more complex the form, the longer the number of evolution steps to get its ground state may be, meaning deeper quantum circuits, which may put pressure on the near-term medium-scale noisy quantum chips. In order to further improve the ground state simulation efficiency and be better suitable for quantum hardware at the present stage, an exemplary embodiment of the application provides that a non-hermite evolution algorithm is ingeniously combined with a variational quantum circuit structure. Optionally, a variational quantum circuit is followed after the quantum circuit used in each step of the evolution. As shown in fig. 3, "S" refers to the qubit space corresponding to the quantum system under study (i.e., the target quantum system), "a" refers to the qubit space corresponding to the auxiliary qubit, u (t) represents the quantum circuit used in the evolution process, and u (t) ═ e^-iHt，WhereinRepresenting the direct product of two matrices, H_SRepresenting the hamiltonian of the target quantum system,representing a Palyre operator acting on the ancillary qubit, which may be a Palyre X operatorOr the Paulii Y operator t represents time. U (theta) is a variation quantum circuit introduced, so that each layer is further optimized after evolution operation is completed through U (t). Taking the first layer as an example,the optimization goal of U (theta) is to adjust the parameters of U (theta) so that

Taking the k-th step evolution and post-processing process as an example, after the k-th step evolution end state is obtained, adopting a variational quantum circuit corresponding to the k-th step evolution to carry out transformation processing on the k-th step evolution end state to obtain a k-th transformed quantum state; the energy expected value of the quantum state after the k-th step of transformation is minimized, and parameters of the variational quantum circuit corresponding to the k-th step of evolution are adjusted; under the condition that the parameters of the variation quantum circuit corresponding to the k-th evolution meet the condition of stopping optimization, acquiring the quantum state after the k-th transformation output at the moment; and then executing the kth post-processing on the quantum state transformed in the kth step to obtain the output quantum state in the kth step.

Thus, u (t) is on the one hand a powerful drive to evolve the quantum state to the ground state, which does not rely on parametric optimization of the variational structure, and on the other hand is also a reliable drive to jump out of the variational optimization resulting in a locally optimal solution. The auxiliary of U (theta) can more quickly guide the quantum state to lower energy by introducing a certain degree of variation, and is greatly beneficial to reducing the number of modules of U (t) originally required, namely reducing the depth of a quantum circuit.

Optionally, a parameter optimization strategy of updating the variational quantum circuit layer by layer is adopted, the parameter quantity for realizing variational each time is controlled in a space as small as possible, a simpler optimization curved surface is created, and the current global optimal solution can be obtained more favorably. For example, in the process of adjusting the parameters of the variational quantum circuit corresponding to the k-th evolution step, the parameters of the variational quantum circuit corresponding to other evolution steps are kept unchanged; and after the parameter adjustment of the variation quantum circuit corresponding to the k-th step of evolution is completed, adjusting the parameter of the variation quantum circuit corresponding to the k + 1-th step of evolution.

In the circuit structure shown in fig. 3, only one variational quantum circuit U (θ) is connected after each quantum circuit U (t), and in some other embodiments, U (θ) may be connected after only a part of U (t), and U (θ) is not connected after another part of U (t), which is not limited in this application.

In this embodiment, by combining a simple variational quantum circuit, the non-hermite evolution algorithm is combined with a variational quantum circuit structure, which is helpful for reducing the depth of the quantum circuit and can further effectively improve the hardware efficiency of the simulation.

In the above embodiment, the quantum circuit u (t) e used by the evolution^-iHtIn real circuit operation, Trotter (Trotter) decomposition is often used to approximate the expression with a series of operations of single-bit and double-bit quantum gates:

whereinExpressed as single-bit and double-bit quantum gate operations, the Hamiltonian of the target-quantum system can be decomposed into a sum of a series of Paglie character strings, K is the number of terms of the Paglie character strings decomposed by the Hamiltonian, H_iRefers to the Hamiltonian corresponding to one of the Pagli strings. It is easy to see that as the target quantum system H is more complex, the single-step evolution corresponds to deeper quantum circuits u (t). And multiple quantum evolution steps mean multiple u (t), i.e., deeper and deeper quantum circuits. For the current stage of development of quantum computing chips, the depth of the quantum circuit gate is still largely limited by hardware noise. In order to better embody the advantages of the algorithm of the present application in terms of complex problems, the present application provides another exemplary embodiment of a method for compressing quantum states by using a variable-component quantum circuit, thereby further improving the hardware utilization efficiency.

In an exemplary embodiment, the n-step evolution and post-processing introduced above is alternatively implemented using the following method:

1. constructing a tentative quantum state by using a target variational quantum circuit;

2. aiming at enabling the probing quantum state to approach the target quantum state, adjusting the parameters of the target variational quantum line;

3. determining a tentative quantum state constructed by the target variation quantum circuit as a ground state of the target quantum system under the condition that the parameters of the target variation quantum circuit meet the stop optimization condition; and determining the energy expectation value of the Hamiltonian of the target quantum system in the tentative quantum state as the ground state energy of the target quantum system.

The variational quantum circuit compresses the quantum state, namely a heuristic quantum state | ψ (ω) is constructed by a quantum circuit (namely the target variational quantum circuit) which has a proper number of parameters to be optimized and has the function of realizing the quantum circuit U (t) (and optionally the variational quantum circuit U (θ)) in a medium scale_t)>Then, the parameters are optimized to be as close as possible to the target quantum state | phi (t)>。ω_t∈R^pIs a p-dimensional vector of parameters. The evolution of quantum states from time t to the next time t + dt can be written as:

|φ(t+dt)>＝e^-iHdt|ψ(ω_t)>；

then by optimizing omega_t+dtSuch that:

this calculation can be obtained by the quantum circuit shown in fig. 4.

Finally, the implementation is carried out from the initial state | phi (t)₀)>At the beginning, through quantum evolution of a plurality of steps, a final state | phi (t) is obtained_T＝NT)>The corresponding circuit compression version quantum state | ψ (ω)_T)>。

In the following, some experiments performed by the technical solution of the present application are described.

The non-Hermite quantum simulation algorithm provided by the application is adopted to simulate the hydrogen molecule (H)₂) The ground state of (2). A quantum computing process as shown in figure 2 is employed. Hamiltonian H of hydrogen molecule in the form of a beryl_SComprises the following steps:

H_S＝g₀+g₁Z₁+g₂Z₂+g₃Z₁Z₂+g₄X₁X₂+g₅Y₁Y₂；

whereinAll are Paglie operators, i is 1 or 2. Setting g₀＝0.2252，g₁＝0.3435，g₂＝-0.4347，g₃＝0.5716，g₄＝0.0910，g₅0.0910. Preparing the ground state of the target quantum systemThe step dt of the kinetic evolution is 0.2. Quantum simulation was performed on top of the simulator for IBMQ, and the results are shown in FIG. 5.

The line 51 in fig. 5 shows that the expected energy value of the target quantum system gradually decreases with the evolution step, and reaches the ground state energy by 7 steps, so that the simulation of the ground state is successfully realized.

We further apply the non-Hermite quantum simulation algorithm provided by the present application to simulate the ground state of the one-dimensional transverse-field Eschen model. A quantum computation process as shown in fig. 2 and 3 is employed. Transverse field Esinon model Hamiltonian H with 4 grid points_SComprises the following steps:

whereinAll are Paulian operators, Z_iAnd Z_jAre pauli operators representing different grid points. Setting upPreparing the ground state of the target quantum systemThe step dt of the kinetic evolution is 0.2. Performing quantities on a simulator of an IBMQThe results obtained by the submodules are shown in FIG. 6.

Fig. 6 shows that the energy expectation of the target quantum system gradually decreases with the evolution step. Line 61 is the result of its exact ground state, line 62 is the result of using the quantum computation process shown in fig. 2, and line 63 is the result of using the quantum computation process shown in fig. 3. It can be seen that: 1) both algorithms of fig. 2 and 3 can achieve simulation of the target hamiltonian ground state; 2) the speed of realizing the ground state can be accelerated after the combination of the variational quantum circuit, and the evolution steps are greatly reduced to 3 steps.

Finally, we apply the non-Hermite quantum simulation algorithm provided by the present application to simulate the ground state of the one-dimensional transverse field Escion model of 8 lattice points. A quantum computation process as shown in fig. 2 and 3 is employed. Transverse field Esinon model Hamiltonian H with 8 grid points_SComprises the following steps:

whereinAll are Paulian operators, Z_iAnd Z_jAre pauli operators representing different grid points. Setting upPreparing the ground state of the target quantum systemThe step dt of the kinetic evolution is 0.2. Quantum simulation was performed on top of the simulator for IBMQ, and the results are shown in FIG. 7.

Fig. 7 shows that the energy expectation of the target quantum system gradually decreases with the evolution step. Line 71 is the result of its exact ground state, lines 72, 73 and 74 are the results obtained using the quantum computing process shown in fig. 2, and line 75 is the result obtained using the quantum computing process shown in fig. 3. It can be seen that: 1) both algorithms of fig. 2 and 3 can achieve simulation of the target hamiltonian ground state; 2) by using the algorithm of FIG. 2, the evolution step length is gradually increased, and the convergence speed can be accelerated; 3) the speed of realizing the ground state can be accelerated after the combination of the variational quantum circuit, and the evolution steps are greatly reduced to 3 steps.

The following are embodiments of the apparatus of the present application that may be used to perform embodiments of the method of the present application. For details which are not disclosed in the embodiments of the apparatus of the present application, reference is made to the embodiments of the method of the present application.

Referring to fig. 8, a block diagram of a ground state obtaining device of a quantum system according to an embodiment of the present application is shown. The device has the functions of realizing the method examples, and the functions can be realized by hardware or by hardware executing corresponding software. The apparatus may be the computer device described above, or may be provided in a computer device. As shown in fig. 8, the apparatus 800 may include: an initial state preparation module 810, an evolution processing module 820 and a ground state acquisition module 830.

And an initial state preparation module 810 for preparing an initial state of the target quantum system.

An evolution processing module 820, configured to perform n-step evolution and post-processing on the target quantum system; the k step of evolution comprises the step of evolving the input quantum state of the k step to obtain an evolution end state of the k step; the k step post-processing comprises the step of removing the influence of auxiliary quantum bits used in the k step evolution from the k step evolution final state to obtain a k step output quantum state; the kth input quantum state comprises a direct product of the kth-1 output quantum state obtained by the kth-1 post-processing and the initial state of the auxiliary quantum bit used by the kth evolution, and k is a positive integer less than or equal to n; in the case where k is equal to 1, the 1 st input quantum state comprises the direct product of the initial state of the target quantum system and the initial state of the auxiliary qubit used in the 1 st evolution.

And a ground state obtaining module 830, configured to obtain the nth-step output quantum state obtained through the n-step evolution and post-processing, so as to obtain a ground state of the target quantum system.

In an exemplary embodiment, the evolution processing module 820 is configured to:

for the k step evolution, adopting a k quantum circuit to evolve the k step input quantum state to obtain a k step evolution final state;

and for the kth step post-processing, performing classical data post-processing on the kth step evolution final state by adopting a kth measuring circuit, and projecting the auxiliary quantum bit used by the kth step evolution to a 0 state to obtain the kth step output quantum state.

In an exemplary embodiment, the n-th evolution end state | φ is obtained through n-step evolution_n>The process of (2) is as follows:

wherein U (t) represents the quantum circuit adopted for evolution, | ψ₀>Represents the initial state of the target quantum system, U (t) ═ e^-iHt，H_SRepresenting a Hamiltonian of the target quantum system,representing the pauli operator acting on the ancillary qubit, and t representing time.

In an exemplary embodiment, a last state | φ is evolved for the nth step_n>The process of performing classical data post-processing is as follows:

|φ′_n>＝PU(t)ⁿ|ψ₀>|00...0>＝cosⁿ(H_St)|ψ₀>|00...0>；

wherein, P is a projection operator,representing the pauli operator acting on the ancillary qubits used in the k-th evolution.

In an exemplary embodiment, 1 ancillary qubit is used for each of the n-step evolutions, and the ancillary qubits are recycled in the n-step evolutions.

In an exemplary embodiment, the evolution processing module 820 is further configured to:

after the k-th evolution final state is obtained, adopting a variational quantum circuit corresponding to the k-th evolution to carry out transformation processing on the k-th evolution final state to obtain a quantum state after the k-th transformation;

taking the minimum energy expected value of the quantum state after the k step of transformation as a target, and adjusting the parameters of the variational quantum circuit corresponding to the k step of evolution;

under the condition that the parameters of the variation quantum circuit corresponding to the k-th evolution meet the condition of stopping optimization, acquiring the quantum state after the k-th transformation;

and executing the kth post-processing on the quantum state transformed in the kth step to obtain the output quantum state in the kth step.

In an exemplary embodiment, the evolution processing module 820 is further configured to:

in the process of adjusting the parameters of the variational quantum circuit corresponding to the k-th evolution step, the parameters of the variational quantum circuit corresponding to other evolution steps are kept unchanged;

and after the parameter adjustment of the variation quantum circuit corresponding to the k-th evolution step is completed, adjusting the parameter of the variation quantum circuit corresponding to the k + 1-th evolution step.

In an exemplary embodiment, the n-step evolution and post-processing are alternatively implemented by the following method:

constructing a tentative quantum state by using a target variational quantum circuit;

aiming at enabling the probing quantum state to approach a target quantum state, adjusting the parameters of the target variational quantum line;

determining the tentative quantum state constructed by the target variational quantum circuit as the ground state of the target quantum system under the condition that the parameters of the target variational quantum circuit meet the stop optimization condition; and determining the expected energy value of the Hamiltonian of the target quantum system in the tentative quantum state as the ground state energy of the target quantum system.

In an exemplary embodiment, the apparatus 800 further includes an energy calculation module (not shown in FIG. 8) for calculating the ground state energy E of the target quantum system according to the following formula:

wherein H_SRepresenting the Hamiltonian, | φ, of the target quantum system_n>Represents the n-th step evolution final state, | phi'_n>Representing the output quantum state of the nth step, P is a projection operator, representing the pauli operator acting on the ancillary qubits used in the k-th evolution.

According to the method, the target quantum system is gradually evolved from the initial state to the ground state by carrying out multi-step evolution and post-processing on the target quantum system, so that the ground state of the target quantum system is obtained, the auxiliary quantum bit is introduced in the evolution process to realize unitary evolution, a quantum simulation algorithm based on a non-Hermite process is provided to simulate the ground state of the target quantum system, the effect of imaginary and real evolution is realized by real-time unitary evolution related to the Hamilton quantity of the system, the simulation of the ground state of the target quantum system is clearly and definitely realized theoretically, the process can be realized by a quantum circuit directly, and the operability of the scheme is fully improved.

It should be noted that, when the apparatus provided in the foregoing embodiment implements the functions thereof, only the division of the functional modules is illustrated, and in practical applications, the functions may be distributed by different functional modules according to needs, that is, the internal structure of the apparatus may be divided into different functional modules to implement all or part of the functions described above. In addition, the apparatus and method embodiments provided by the above embodiments belong to the same concept, and specific implementation processes thereof are described in the method embodiments for details, which are not described herein again.

An exemplary embodiment of the present application also provides a computer device for executing the above-described method for obtaining the ground state of the quantum system. Optionally, the computer device is a quantum computer, or the computer device is a hybrid execution environment comprising a quantum computer and a classical computer.

An exemplary embodiment of the present application further provides a computer-readable storage medium, in which at least one instruction, at least one program, a set of codes, or a set of instructions is stored, and the at least one instruction, the at least one program, the set of codes, or the set of instructions is loaded and executed by a processor to implement the above-mentioned method for obtaining the ground state of the quantum system.

Optionally, the computer-readable storage medium may include: ROM (Read-Only Memory), RAM (Random-Access Memory), SSD (Solid State drive), or optical disk. The Random Access Memory may include a ReRAM (resistive Random Access Memory) and a DRAM (Dynamic Random Access Memory).

In an exemplary embodiment, a computer program product or a computer program is also provided, which comprises computer instructions, which are stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer readable storage medium, and executes the computer instructions to cause the computer device to perform the method for ground state acquisition of a quantum system as described above.

It should be understood that reference to "a plurality" herein means two or more. "and/or" describes the association relationship of the associated objects, meaning that there may be three relationships, e.g., a and/or B, which may mean: a exists alone, A and B exist simultaneously, and B exists alone. The character "/" generally indicates that the former and latter associated objects are in an "or" relationship. In addition, the step numbers described herein only exemplarily show one possible execution sequence among the steps, and in some other embodiments, the steps may also be executed out of the numbering sequence, for example, two steps with different numbers are executed simultaneously, or two steps with different numbers are executed in a reverse order to the order shown in the figure, which is not limited by the embodiment of the present application.

The above description is only exemplary of the present application and should not be taken as limiting the present application, and any modifications, equivalents, improvements and the like that are made within the spirit and principle of the present application should be included in the protection scope of the present application.