Quantum walk search through potential barriers

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Abstract

An ideal quantum walk transitions from one vertex to another with perfect fidelity, but in physical systems, the particle may be hindered by potential energy barriers. Then the particle has some amplitude of tunneling through the barriers, and some amplitude of staying put. We investigate the algorithmic consequence of such barriers for the quantum walk formulation of Grover's algorithm. We prove that the failure amplitude must scale as for search to retain its quantum runtime; otherwise, it searches in classical O(N) time. Thus searching larger 'databases' requires increasingly reliable hop operations or error correction. This condition holds for both discrete- and continuous-time quantum walks.

Original languageEnglish (US)
Article number484002
JournalJournal of Physics A: Mathematical and Theoretical
Volume49
Issue number48
DOIs
StatePublished - Nov 9 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

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

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