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An example of the difference between quantum and classical random walks
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In this note, we discuss a general definition of quantum random walks on graphs and illustrate with a simple graph the possibility of very different behavior between a classical random walk and its quantum analogue. In this graph, propagation between a particular pair of nodes is exponentially faster in the quantum case.
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Cited by 2 Pith papers
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A Probabilistic Representation for Multi-State Discrete-time Quantum Walks
Three-state discrete-time quantum walks on Z admit an exact Monte Carlo representation via Poisson-driven classical processes that converges to multi-state Dirac PDEs.
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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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