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Quantum random walks - an introductory overview
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This article aims to provide an introductory survey on quantum random walks. Starting from a physical effect to illustrate the main ideas we will introduce quantum random walks, review some of their properties and outline their striking differences to classical walks. We will touch upon both physical effects and computer science applications, introducing some of the main concepts and language of present day quantum information science in this context. We will mention recent developments in this new area and outline some open questions.
Forward citations
Cited by 3 Pith papers
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Bottleneck Effects and Harmonic-Type Velocity Bounds for Periodic Quantum Walks
Proves explicit velocity upper bounds for periodic quantum walks including linear bottleneck effects for small transmission parameters and harmonic-mean bounds, plus a general lower bound.
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Haar-random coin quantum walks on d-regular graphs yield a non-ergodic averaged channel that depolarizes the coin while preserving forever-measurable initial-state information in the vertex subspace for Cayley graphs ...
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Emergence of Krylov complexity through quantum walks: An exploration of the quantum origins of complexity
Reducing a graph walk to distance-layers reproduces Krylov/spread complexity, yielding analytic finite-q SYK Lanczos coefficients and hypercube complexity D sin²(t/D), with faster saturation than classical-walk circuits.
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