Unitary Equivalence of Quantum Walks

Abstract

A simple coined quantum walk in one dimension can be characterized by a $SU(2)$ operator with three parameters which represents the coin toss. However, different such coin toss operators lead to equivalent dynamics of the quantum walker. In this manuscript we present the unitary equivalence classes of quantum walks and show that all the nonequivalent quantum walks can be distinguished by a single parameter. Moreover, we argue that the electric quantum walks are equivalent to quantum walks with time dependent coin toss operator.

References in corpus (4)

• Environment-Assisted Quantum Walks in Photosynthetic Energy Transfer
• Spatial search by quantum walk
• Exploring Topological Phases With Quantum Walks
• Optimizing the discrete time quantum walk using a SU(2) coin

Cited by in corpus (9)

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• Controlling quantum random walk with a step-dependent coin
• Creating cat states in one-dimensional quantum walks using delocalized initial states
• Percolation assisted excitation transport in discrete-time quantum walks
• Unitary equivalence classes of split-step quantum walks
• Suitable bases for quantum walks with Wigner coins
• Unitary equivalent classes of one-dimensional quantum walks II
• Recurrence in discrete-time quantum stochastic walks
• Parameterization of quantum walks on cycles