Search

CN-122021953-A - Quick approximate block coding quantum circuit construction method, linear equation system solving method and device

CN122021953ACN 122021953 ACN122021953 ACN 122021953ACN-122021953-A

Abstract

The invention discloses a quick approximate block coding quantum circuit construction method, a linear equation set solving method and a device, wherein the solving method comprises the following steps of obtaining a linear equation set Ax=b, constructing a time-containing Hamiltonian amount H (f (s)) of adiabatic evolution, wherein an eigenstate of an initial Hamiltonian amount H (0) is represented as |b >, an eigenstate of a target Hamiltonian amount H (1) is represented as |A ‑1 b >, constructing a discrete adiabatic evolution quantum circuit, wherein the discrete adiabatic evolution quantum circuit is provided with an evolution operator U H(f(s)) corresponding to the time-containing Hamiltonian amount H (f (s)), the evolution operator U H(f(s)) continuously acts on the discrete adiabatic evolution quantum circuit, the initial quantum state corresponds to the eigenstate |b > of an adiabatic initial Hamiltonian amount H (0), and the final quantum state corresponds to the eigenstate |A ‑1 b > of an adiabatic evolution target Hamiltonian amount H (1). The invention provides a specific quantum circuit implementation method of sparse Hamiltonian quick approximate block coding, and an adiabatic quantum computing linear algorithm is implemented based on the quick approximate block coding, so that the solution of a linear equation set is completed.

Inventors

  • Dou Menghan

Assignees

  • 本源量子计算科技（合肥）股份有限公司

Dates

Publication Date
20260512
Application Date
20241030

Claims (10)

  1. 1. The construction method of the quick approximate block coding quantum circuit is characterized by comprising the following steps of: Acquiring a matrix query unitary operation logic gate O A acting on a plurality of quantum bits, wherein the matrix query unitary operation logic gate O A is provided with a plurality of quantum rotation gates and CNOT gates, the quantum rotation gates and the CNOT gates are alternately arranged, and target quantum bits of the CNOT gates are quantum bits acted by the quantum rotation gates; setting a preset critical value, and removing the quantum rotating gate from the compressed block coding quantum circuit when the parameter value of the rotating parameter of one quantum rotating gate is smaller than the preset critical value.
  2. 2. The method of claim 1, wherein after removing a portion of said quantum rotation gates, only one of said CNOT gates is retained on said qubit when control qubits of at least two of said CNOT gates are the same qubit among a plurality of consecutive said CNOT gates, and the remaining CNOT gates are removed from said compressed block encoded quantum circuit.
  3. 3. The construction method according to claim 1, wherein: The plurality of qubits comprises an auxiliary qubit group and a target qubit group, wherein the auxiliary qubit group comprises a first qubit and n second qubits, and the target qubit group comprises n third qubits; The method comprises the steps of obtaining a unitary operator U acting on an auxiliary quantum bit group and a target quantum bit group, wherein the unitary operator U comprises a first H gate, a matrix query unitary operation logic gate O A , a SWAP gate and a second H gate which are distributed in sequence along an action time sequence, the first H gate and the second H gate act on second quantum bits, the matrix query unitary operation logic gate O A is provided with a plurality of quantum rotation gates and CNOT gates, the target quantum bits of the CNOT gates and the quantum bits acted by the quantum rotation gates are all the first quantum bits, the control quantum bits of the CNOT gates are the second quantum bits, and the SWAP gate acts on the second quantum bits and the third quantum bits.
  4. 4. The method of claim 1, wherein the quantum rotation gate comprises an R y gate, an R z gate, or an R β gate, and wherein β is a normalized linear combination of σ y and σ z .
  5. 5. A solving method of a linear equation set based on adiabatic quanta is characterized by comprising the following steps: obtaining a linear equation set ax=b, wherein A is a coefficient matrix and b is a vector; Constructing an adiabatically evolving time-containing hamiltonian H (f (s)) comprising an initial hamiltonian H (0) and a target hamiltonian H (1), the eigenstates of the initial hamiltonian H (0) being denoted as |b <, the eigenstates of the target hamiltonian H (1) being denoted as |a -1 b >; Constructing a discrete adiabatic evolution quantum circuit, wherein the discrete adiabatic evolution quantum circuit is constructed by the construction method of any one of claims 1-4, the discrete adiabatic evolution quantum circuit is provided with an evolution operator U H(f(s)) corresponding to the time-containing Hamiltonian amount H (f (s)), the evolution operator U H(f(s)) is used for realizing fast approximate block coding of the time-containing Hamiltonian amount H (f (s)), the evolution operator U H(f(s)) continuously acts on the discrete adiabatic evolution quantum circuit, an initial quantum state of the discrete adiabatic evolution quantum circuit corresponds to an intrinsic state |b > of the initial Hamiltonian amount H (0) of adiabatic evolution, and a final quantum state of the discrete adiabatic evolution quantum circuit corresponds to an intrinsic state |A -1 b > of the target Hamiltonian amount H (1) of adiabatic evolution.
  6. 6. The method of claim 5, wherein: The unitary matrix query operation logic gate O A is defined as: Wherein a ij is an element of coefficient matrix A, the alpha ij is less than or equal to 1, i > and j > are n qubits to calculate the ground state.
  7. 7. The method of claim 5, wherein: The time-containing hamiltonian H (f (s)) is defined as: H(f(s))=(1-f(s))H 0 +f(s)H 1 ,0≤s≤1; Wherein f(s) is a scheduling function, and f (0) =0, f (1) =1; The H 0 is defined as: the H 1 is defined as: Wherein Q b ＝I N - |b > < b|.
  8. 8. A solution device, the device comprising: The acquisition module is used for acquiring a linear equation set ax=b, wherein A is a coefficient matrix and b is a vector; The time-containing Hamiltonian amount constructing module is used for constructing a time-containing Hamiltonian amount H (f (s)) of adiabatic evolution, the time-containing Hamiltonian amount H (f (s)) comprises an initial Hamiltonian amount H (0) and a target Hamiltonian amount H (1), the eigenstate of the initial Hamiltonian amount H (0) is represented as |b >, and the eigenstate of the target Hamiltonian amount H (1) is represented as |A -1 b >; A discrete adiabatic evolution quantum circuit construction module, configured to construct a discrete adiabatic evolution quantum circuit, where the discrete adiabatic evolution quantum circuit is a discrete adiabatic evolution quantum circuit according to any one of claims 5-7, the discrete adiabatic evolution quantum circuit has an evolution operator U H(f(s)) corresponding to the time-containing hamiltonian H (f (s)), the evolution operator U H(f(s)) is configured to implement fast approximate block coding of the time-containing hamiltonian H (f (s)), the evolution operator U H(f(s)) continuously acts on the discrete adiabatic evolution quantum circuit, an initial quantum state of the discrete adiabatic evolution quantum circuit corresponds to an intrinsic state |b > of the initial hamiltonian H (0) of the adiabatic evolution, and a final quantum state of the discrete adiabatic evolution quantum circuit corresponds to an intrinsic state |a -1 b > of the target hamiltonian H (1) of the adiabatic evolution.
  9. 9. A storage medium having a computer program stored therein, wherein the computer program is arranged to perform the method of any of claims 5 to 7 when run.
  10. 10. An electronic device comprising a memory and a processor, characterized in that the memory has stored therein a computer program, the processor being arranged to run the computer program to perform the method of any of the claims 5 to 7.

Description

Quick approximate block coding quantum circuit construction method, linear equation system solving method and device Technical Field The invention relates to the technical field of quantum computation, in particular to a method for constructing a quick approximate block coding quantum circuit, a method and a device for solving a linear equation set. Background One of the core problems in the field of applied mathematical and scientific engineering computing is how to solve a large-scale sparse linear system of equations in a reasonable time. Quantum computers are used as a type of physical device for performing high-speed mathematical and logical operations, storing and processing quantum information according to the laws of quantum mechanics, and have the capability of being more efficient than a common computer when the quantum algorithm is operated to process certain mathematical problems, while the problem of solving a linear system is one such problem. Since quantum computers have exponential acceleration when solving linear systems using quantum linear solvers, quantum linear solvers hold promise to accelerate the solving process of many practical problems in the scientific and engineering fields. Sparse Hamiltonian block coding is an important method for realizing Hamiltonian quantity simulation, is also an important precondition for realizing equal sub-algorithms of a quantum linear algorithm, and an adiabatic quantum computing linear algorithm is the currently known quantum linear algorithm for solving a sparse linear equation set most efficiently, so that the construction of a discrete adiabatic quantum linear solver can be realized by a mode of quickly approximating sparse Hamiltonian block coding, and the solution of the linear equation set is completed. Disclosure of Invention The invention aims to provide a quick approximate block coding quantum circuit construction method, a linear equation set solving method and a device, so as to solve the technical problems in the prior art. In a first aspect, the present invention provides a method for constructing a fast approximate block encoded quantum circuit, comprising the steps of: acquiring a matrix query unitary operation logic gate O A acting on a plurality of quantum bits, wherein the matrix query unitary operation logic gate O A is provided with a plurality of quantum rotation gates and a CNOT gate, and the target quantum bit of the CNOT gate is the quantum bit acted by the quantum rotation gate; setting a preset critical value, and removing the quantum rotating gate from the compressed block coding quantum circuit when the parameter value of the rotating parameter of one quantum rotating gate is smaller than the preset critical value. In the method for constructing a fast approximate block coding quantum circuit as described above, it is preferable that, after removing a part of the quantum rotation gates, when control qubits of at least two of the CNOT gates are the same qubit among a plurality of consecutive CNOT gates, only one of the CNOT gates is retained on the qubit, and the remaining CNOT gates are removed from the compressed block coding quantum circuit. A method of constructing a fast approximate block coded quantum circuit as described above, wherein, preferably, The plurality of qubits comprises an auxiliary qubit group and a target qubit group, wherein the auxiliary qubit group comprises a first qubit and n second qubits, and the target qubit group comprises n third qubits; The method comprises the steps of obtaining a unitary operator U acting on an auxiliary quantum bit group and a target quantum bit group, wherein the unitary operator U comprises a first H gate, a matrix query unitary operation logic gate O A, a SWAP gate and a second H gate which are distributed in sequence along an action time sequence, the first H gate and the second H gate act on second quantum bits, the matrix query unitary operation logic gate O A is provided with a plurality of quantum rotation gates and CNOT gates, the target quantum bits of the CNOT gates and the quantum bits acted by the quantum rotation gates are all the first quantum bits, the control quantum bits of the CNOT gates are the second quantum bits, and the SWAP gate acts on the second quantum bits and the third quantum bits. A method of constructing a fast approximation block encoded quantum circuit as described above, wherein preferably the quantum rotation gate comprises an R y gate, an R z gate or an R β gate, wherein β is a normalized linear combination of σ y and σ z. In a second aspect, the present invention provides a method for solving a linear equation set based on adiabatic quanta, comprising the steps of: obtaining a linear equation set ax=b, wherein A is a coefficient matrix and b is a vector; constructing an adiabatically evolving time-containing hamiltonian H (f (s)) comprising an initial hamiltonian H (0) and a target hamiltonian H (1), the eigenstates of the initial hami