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CN-122021952-A - Method and device for adiabatic quantum computing linear equation set based on block coding

CN122021952ACN 122021952 ACN122021952 ACN 122021952ACN-122021952-A

Abstract

The invention discloses a method and a device for calculating a linear equation set based on adiabatic quanta of block coding, wherein the method comprises the following steps of obtaining a linear equation set ax=b, constructing an adiabatic evolution time-containing Hamiltonian volume H (f (s)), wherein an eigenstate of an initial Hamiltonian volume H (0) is represented as |b >, an eigenstate of a target Hamiltonian volume H (1) is represented as |A ‑1 b >, constructing a discrete adiabatic evolution quanta line, the discrete adiabatic evolution quanta line is provided with an evolution operator U H(f(s)) corresponding to the time-containing Hamiltonian volume H (f (s)), the evolution operator U H(f(s)) continuously acts on the discrete adiabatic evolution quanta line, the initial quanta state corresponds to the eigenstate |b > of the adiabatic evolution initial Hamiltonian volume H (0), and the final quanta state corresponds to the eigenstate |A ‑1 b > of the adiabatic evolution target Hamiltonian volume H (1). Compared with the prior art, the invention provides a specific implementation method of the Hamiltonian block coding quantum circuit, and the discrete adiabatic quantum linear solver can be constructed based on the block coding to finish solving a linear equation set.

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. A method for calculating a linear equation set based on adiabatic quantum of block coding 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)), the time-containing hamiltonian H9f (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 >, and 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 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 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 eigenstate |b > of the adiabatic evolution initial Hamiltonian amount H (0), and a final quantum state of the discrete adiabatic evolution quantum circuit corresponds to an eigenstate |A -1 b > of the adiabatic evolution target Hamiltonian amount H (1).
  2. 2. The method of claim 1, wherein the discrete adiabatic evolution quantum circuit comprises an auxiliary quantum bit group and a target quantum bit group, the evolution operator U H(f(s)) acts on the auxiliary quantum bit group and the target quantum bit group, an initial quantum state of the auxiliary quantum bit group is a |0> state, an initial quantum state of the target quantum bit group is a |b > state, and after the evolution operator U H(f(s)) acts, when a quantum state measurement result of the auxiliary quantum bit group is the |0> state, a quantum state of the target quantum bit group is the |A -1 b > state.
  3. 3. The method of claim 2, wherein the family of auxiliary qubits comprises a first qubit and n second qubits, and wherein the family of target qubits comprises n third qubits; the evolution operator U H(f(s)) includes a first H gate, a matrix query unitary operation logic gate O A , a SWAP gate, and a second H gate distributed in sequence along an action timing sequence, where the first H gate and the second H gate act on the second qubit, the matrix query unitary operation logic gate O A is configured to encode the time-containing hamiltonian H (f (s)) to the second qubit, and the SWAP gate acts on the second qubit and the third qubit.
  4. 4. A method according to claim 3, characterized in that: the unitary matrix query operation logic gate O A is defined as: Wherein alpha ij is an element of the coefficient matrix A, alpha ij is less than or equal to 1, i > and j are n quantum bits to calculate a ground state.
  5. 5. The method of claim 4, wherein said matrix query unitary operation logic gate O A comprises 2 n multi-control quantum turngates, one for each element of said coefficient matrix A, said multi-control quantum turngate having a target qubit of said first qubit and a control qubit of said multi-control quantum turngate of said second qubit.
  6. 6. The method of claim 5, wherein the multi-controlled quantum rotating gate comprises an RX gate, a RY gate, or an RZ gate.
  7. 7. The method according to claim 1, characterized in that: 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 >; The discrete adiabatic evolution quantum circuit construction module is used for constructing a discrete adiabatic evolution quantum circuit, the discrete adiabatic evolution quantum circuit is provided with an evolution operator U H(f(s)) corresponding to the time-containing Hamiltonian quantity H (f (s)), the evolution operator U H(f(s)) is used for realizing block coding of the time-containing Hamiltonian quantity 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 eigenstate |b > of the adiabatic evolution initial Hamiltonian quantity H (0), and a final quantum state of the discrete adiabatic evolution quantum circuit corresponds to an eigenstate |A -1 b > of the adiabatic evolution target Hamiltonian quantity H (1).
  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 1 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 1 to 7.

Description

Method and device for adiabatic quantum computing linear equation set based on block coding Technical Field The invention relates to the technical field of quantum computation, in particular to a method and a device for computing a linear equation set by using adiabatic quantum. 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. The sparse Hamiltonian block coding is an important method for realizing Hamiltonian volume 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 through a sparse Hamiltonian block coding mode, and the solution of the linear equation set is completed. Disclosure of Invention The invention aims to provide a method and a device for calculating a linear equation set based on adiabatic quantum of block coding, which are used for solving the technical problems in the prior art. In a first aspect, the present invention provides a method of adiabatic quantum computing a system of linear equations based on block encoding, 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 hamiltonian H (0) being denoted as |b >, and 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 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 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 eigenstate |b > of the adiabatic evolution initial Hamiltonian amount H (0), and a final quantum state of the discrete adiabatic evolution quantum circuit corresponds to an eigenstate |A -1 b > of the adiabatic evolution target Hamiltonian amount H (1). In the method for calculating the linear equation set based on the adiabatic quantum of block coding, preferably, the discrete adiabatic evolution quantum circuit includes an auxiliary quantum bit group and a target quantum bit group, the evolution operator U H(f(s)) acts on the auxiliary quantum bit group and the target quantum bit group, an initial quantum state of the auxiliary quantum bit group is an |0> state, an initial quantum state of the target quantum bit group is an |b > state, and after the evolution operator U H(f(s)) acts, when a quantum state measurement result of the auxiliary quantum bit group is the |0> state, a quantum state of the target quantum bit group is the |a -1 b > state. A method of computing a system of linear equations based on block encoded adiabatic quantum as described above, wherein preferably the family of auxiliary qubits comprises a first qubit and n second qubits, and the family of target qubits comprises n third qubits; the evolution operator U H(f(s)) includes a first H gate, a matrix query unitary operation logic gate O A, a SWAP gate, and a second H gate distributed in sequence along an action timing sequence, where the first H gate and the second H gate act on the second qubit, the matrix query unitary operation logic gate O A is configured to encode the time-containing hamiltonian H (f (s)) to the second qubit, and the SWAP gate acts on the second qubit and the third qubit. A method of adiabatic quantum computing a system of linear equations based on block coding as described above, wherein preferably the matrix query unitary operation logic gate O A is defined as: wherein alpha ij is an element of the coefficient matrix A, al