Binary integer coefficient polynomial unconstrained optimization method based on Grover search algorithm

Abstract

The invention provides a binary integer coefficient unconstrained optimization method based on a Grover search algorithm. The binary integer coefficient unconstrained optimization method comprises the following steps of converting an integer coefficient polynomial f (x) of n binary variables into a binary integer coefficient matrix polynomial; converting an unconstrained optimization problem of a binary integer coefficient matrix polynomial into a quantum quadratic unconstrained binary optimization problem; preparing an n-bit quantum input register to store an equivalent superposition state, and preparing an m-bit quantum output register to store a corresponding target state; an equivalent superposition state processed by Hadder gate transformation is used, and superposition of polynomials is completed; an initial threshold value y is determined, an operator is constructed, and phase deviation of a target state and coding of integer values are completed; an Oracle operator is constructed; constructing inverse transformation of G iteration and operators; and setting an iteration condition, and changing the probability of the target state by repeating G iteration until the probability of searching the target state is optimal.

Description

technical field [0001] The invention relates to a polynomial unconstrained optimization method, in particular, relates to a binary integer coefficient polynomial unconstrained optimization method based on a Grover search algorithm. Background technique [0002] Quantum computing uses qubits as the basic unit, and realizes data storage and computing through the controlled evolution of quantum states. It has huge information carrying and super parallel processing capabilities unmatched by classical computing, thereby bringing exponential information representation and computing capabilities. Quantum computing is based on the entanglement and superposition properties of quantum, and using the laws of quantum mechanics, quantum computers provide novel solutions to resource-intensive problems. Quantum computers have been theoretically shown to solve certain problems faster than classical devices, and can perform well on tasks such as factoring systems of linear equations, Monte C...

AI Technical Summary

Problems solved by technology

Unconstrained binary optimization and constrained polynomial binary optimization have been proven to be NP problems. Most of the traditional methods are based on linear weighting methods, which transform multi-objective problems into single-objective problems. Such methods can only obtain the optimal solution, and most of them are based on local search, and each search process selects the neighborhood with the largest gain. Usually, this method is easy to fall into the local optimal solution, which in turn has a large limit on the search space.

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