Symmetries and noise in quantum walk

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 ampl...

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Bibliographic Details
Published in:Physical review. A, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2007-08, Vol.76 (2), Article 022316
Main Authors: Chandrashekar, C. M., Srikanth, R., Banerjee, Subhashish
Format: Article
Language:English
Subjects:
ATOMS
BOSE-EINSTEIN CONDENSATION
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
DAMPING
DENSITY MATRIX
NOISE
NUCLEAR MAGNETIC RESONANCE
NUMERICAL SOLUTION
QUANTUM COMPUTERS
QUANTUM INFORMATION
QUANTUM MECHANICS
RANDOMNESS
SYMMETRY
TEMPERATURE RANGE 0000-0013 K
TRAJECTORIES
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Summary: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.
ISSN:1050-2947
1094-1622
DOI:10.1103/PhysRevA.76.022316