Symmetries and noise in quantum walk

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 ultra cold atoms.

19 pages, 24 figures : V3 - Revised version to appear in Phys. Rev. A. - new section on quantum walk in a cycle included

References in corpus (4)

• Spatial search by quantum walk
• Decoherence vs entanglement in coined quantum walks
• Implementing the one-dimensional quantum (Hadamard) walk using a Bose-Einstein Condensate
• Quantum random walks using quantum accelerator modes

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• Generic quantum walk using a coin-embedded shift operator