Engineering the Success of Quantum Walk Search Using Weighted Graphs

TL;DR

This paper demonstrates how adjusting edge weights in a graph can optimize quantum walk search success probability and runtime, overcoming trapping issues without increasing energy costs.

Contribution

It introduces a method to improve quantum walk search efficiency by tuning link weights in graphs, balancing success probability and runtime.

Findings

Weighted links can eliminate trapping in quantum walks.

Optimal weights maximize success probability without increasing energy scaling.

Increasing weights beyond a point slows down the search.

Abstract

Continuous-time quantum walks are natural tools for spatial search, where one searches for a marked vertex in a graph. Sometimes, the structure of the graph causes the walker to get trapped, such that the probability of finding the marked vertex is limited. We give an example with two linked cliques, proving that the captive probability can be liberated by increasing the weights of the links. This allows the search to succeed with probability 1 without increasing the energy scaling of the algorithm. Further increasing the weights, however, slows the runtime, so the optimal search requires weights that are neither too weak nor too strong.