Quantum search by parallel eigenvalue adiabatic passage

TL;DR

This paper introduces a highly efficient adiabatic approach for quantum search that leverages parallel eigenvalues to exponentially reduce non-adiabatic losses, outperforming traditional methods.

Contribution

It presents a novel quantum search strategy using parallel eigenvalues in adiabatic passage, significantly improving efficiency and minimizing losses regardless of database size.

Findings

Non-adiabatic losses are exponentially small.

The method is effective regardless of database size.

It achieves efficient quantum search via parallel eigenvalues.

Abstract

We propose a strategy to achieve the Grover search algorithm by adiabatic passage in a very efficient way. An adiabatic process can be characterized by the instantaneous eigenvalues of the pertaining Hamiltonian, some of which form a gap. The key to the efficiency is based on the use of parallel eigenvalues. This allows us to obtain non-adiabatic losses which are exponentially small, independently of the number of items in the database in which the search is performed.