Exceptional quantum walk search on the cycle

Thomas Wong, Raqueline A.M. Santos

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Quantum walks are standard tools for searching graphs for marked vertices, and they often yield quadratic speedups over a classical random walk’s hitting time. In some exceptional cases, however, the system only evolves by sign flips, staying in a uniform probability distribution for all time. We prove that the one-dimensional periodic lattice or cycle with any arrangement of marked vertices is such an exceptional configuration. Using this discovery, we construct a search problem where the quantum walk’s random sampling yields an arbitrary speedup in query complexity over the classical random walk’s hitting time. In this context, however, the mixing time to prepare the initial uniform state is a more suitable comparison than the hitting time, and then, the speedup is roughly quadratic.

Original languageEnglish (US)
Article number154
JournalQuantum Information Processing
Volume16
Issue number6
DOIs
StatePublished - Jun 1 2017
Externally publishedYes

Fingerprint

Quantum Walk
Hitting Time
Probability distributions
Sampling
Cycle
cycles
Random walk
Speedup
Graph Searching
Query Complexity
Mixing Time
random walk
Random Sampling
Search Problems
Flip
Uniform distribution
apexes
Arrangement
random sampling
Probability Distribution

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Theoretical Computer Science
  • Electronic, Optical and Magnetic Materials
  • Signal Processing
  • Modeling and Simulation
  • Electrical and Electronic Engineering

Cite this

Exceptional quantum walk search on the cycle. / Wong, Thomas; Santos, Raqueline A.M.

In: Quantum Information Processing, Vol. 16, No. 6, 154, 01.06.2017.

Research output: Contribution to journalArticle

Wong, Thomas ; Santos, Raqueline A.M. / Exceptional quantum walk search on the cycle. In: Quantum Information Processing. 2017 ; Vol. 16, No. 6.
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