Quantum search by partial adiabatic evolution

TL;DR

This paper introduces a quantum search algorithm utilizing partial adiabatic evolution, significantly improving the time complexity over previous local adiabatic methods by reducing it from O(√N/M) to O(√N)/M.

Contribution

The paper presents a new quantum search algorithm based on partial adiabatic evolution with improved time complexity analysis.

Findings

The algorithm achieves a time complexity of O(√N)/M.

It improves upon the local adiabatic search algorithm.

The Hamiltonian is studied in a two-dimensional Hilbert space.

Abstract

A quantum search algorithm based on the partial adiabatic evolution\cite{Tulsi2009} is provided. We calculate its time complexity by studying the Hamiltonian in a two-dimensional Hilbert space. It is found that the algorithm improves the time complexity, which is $O(\sqrt{N/M})$, of the local adiabatic search algorithm\cite{Roland2002}, to $O(\sqrt{N}/M)$.