Symmetries and noise in quantum walk

C. M. Chandrashekar, R. Srikanth, and Subhashish Banerjee
Phys. Rev. A 76, 022316 – Published 16 August 2007

Abstract

We study some discrete symmetries of unbiased (Hadamard) and biased quantum walk on a line, which are shown to hold even when the quantum walker is subjected to environmental effects. The noise models considered in order to account for these effects are the phase flip, bit flip, and generalized amplitude damping channels. The numerical solutions are obtained by evolving the density matrix, but the persistence of the symmetries in the presence of noise is proved using the quantum trajectories approach. We also briefly extend these studies to quantum walk on a cycle. These investigations can be relevant to the implementation of quantum walks in various known physical systems. We discuss the implementation in the case of NMR quantum information processor and ultracold atoms.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
7 More
  • Received 11 February 2007

DOI:https://doi.org/10.1103/PhysRevA.76.022316

©2007 American Physical Society

Authors & Affiliations

C. M. Chandrashekar1,*, R. Srikanth2,3,†, and Subhashish Banerjee3,‡

  • 1Institute for Quantum Computing, University of Waterloo, Canada N2L3G1
  • 2Poornaprajna Institute of Scientific Research, Devanahalli, Bangalore 562 110, India
  • 3Raman Research Institute, Sadashiv Nagar, Bangalore 560080, India

  • *cmadaiah@iqc.ca
  • srik@rri.res.in
  • subhashishb@rri.res.in

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 76, Iss. 2 — August 2007

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review A

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×