Local adiabatic quantum search with different paths

TL;DR

This paper analyzes a generalized local adiabatic quantum search algorithm that uses alternative evolution paths, demonstrating that the search time can be made independent of database size through Hamiltonian modification.

Contribution

It introduces a new evolution path in the adiabatic quantum search, enabling size-independent search times by Hamiltonian modification.

Findings

Search time can be independent of database size

Alternative evolution paths improve quantum search efficiency

Hamiltonian modification is key to the new approach

Abstract

We report on a detailed analysis of generalization of the local adiabatic search algorithm. Instead of evolving directly from an initial ground state Hamiltonian to a solution Hamiltonian a different evolution path is introduced and is shown that the time required to find an item in a database of size $N$ can be made to be independent of the size of the database by modifying the Hamiltonian used to evolve the system.