Correcting for Potential Barriers in Quantum Walk Search

TL;DR

This paper addresses potential energy barriers in quantum walk search algorithms, proposing phase modifications to maintain optimal search times despite physical hindrances.

Contribution

It introduces a method to correct for potential barriers in quantum walk search by adjusting phases, preserving the optimal $\

Findings

Corrects for potential energy barriers in quantum walk search

Maintains $\

paper_type":"theoretical"}}

Abstract

A randomly walking quantum particle searches in Grover's $\Theta(\sqrt{N})$ iterations for a marked vertex on the complete graph of $N$ vertices by repeatedly querying an oracle that flips the amplitude at the marked vertex, scattering by a "coin" flip, and hopping. Physically, however, potential energy barriers can hinder the hop and cause the search to fail, even when the amplitude of not hopping decreases with $N$. We correct for these errors by interpreting the quantum walk search as an amplitude amplification algorithm and modifying the phases applied by the coin flip and oracle such that the amplification recovers the $\Theta(\sqrt{N})$ runtime.