Quantum walk search with time-reversal symmetry breaking

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We formulate Grover's unstructured search algorithm as a chiral quantum walk, where transitioning in one direction has a phase conjugate to transitioning in the opposite direction. For small phases, this breaking of time-reversal symmetry is too small to significantly affect the evolution: the system still approximately evolves in its ground and first excited states, rotating to the marked vertex in time π√N/2. Increasing the phase does not change the runtime, but rather changes the support for the 2D subspace, so the system evolves in its first and second excited states, or its second and third excited states, and so forth. Apart from the critical phases corresponding to these transitions in the support, which become more frequent as the phase grows, this reveals that our model of quantum search is robust against time-reversal symmetry breaking.

Original languageEnglish (US)
Article number405303
JournalJournal of Physics A: Mathematical and Theoretical
Volume48
Issue number40
DOIs
StatePublished - Sep 14 2015
Externally publishedYes

Fingerprint

Quantum Walk
Time Reversal
Excited states
Symmetry Breaking
broken symmetry
Excited States
excitation
apexes
Search Algorithm
symmetry
Rotating
Subspace
Symmetry
Vertex of a graph

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modeling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

Cite this

Quantum walk search with time-reversal symmetry breaking. / Wong, Thomas.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 48, No. 40, 405303, 14.09.2015.

Research output: Contribution to journalArticle

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