In one dimension, ergodicity of homogeneous discrete-time quantum walks is equivalent to the absolutely continuous spectrum of the walk operator.
Quantum Walk on the Line
5 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
Motivated by the immense success of random walk and Markov chain methods in the design of classical algorithms, we consider_quantum_ walks on graphs. We analyse in detail the behaviour of unbiased quantum walk on the line, with the example of a typical walk, the ``Hadamard walk''. We show that after t time steps, the probability distribution on the line induced by the Hadamard walk is almost uniformly distributed over the interval [-t/sqrt(2),t/sqrt(2)]. This implies that the same walk defined on the circle mixes in_linear_ time. This is in direct contrast with the quadratic mixing time for the corresponding classical walk. We conclude by indicating how our techniques may be applied to more general graphs.
verdicts
UNVERDICTED 5representative citing papers
Source-target entanglement in quantum walks on arbitrary networks is upper-bounded by connectivity, with graph matchings controlling its generation and higher connectivity reducing the maximum in random graphs.
Nonlinear continuous-time quantum walks on paths and cycles can be trapped at the initial site to arbitrary fidelity by choosing the cubic nonlinearity coefficient, unlike spreading linear walks.
Quantum walks with randomly relocating detectors exhibit regime-dependent spreading, oscillatory probability ratios, and a crossover in saturation values at critical removal time t_R*, with the enhancement being a quantum effect.
Glassy disorder in the coin of a 1D discrete-time quantum walk inhibits ballistic spread while keeping it faster than classical diffusion, with slow or fast falloff and mid-strength inflection points depending on the disorder distribution.
citing papers explorer
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Ergodicity in discrete-time quantum walks
In one dimension, ergodicity of homogeneous discrete-time quantum walks is equivalent to the absolutely continuous spectrum of the walk operator.
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Entanglement capacity of complex networks from quantum walks
Source-target entanglement in quantum walks on arbitrary networks is upper-bounded by connectivity, with graph matchings controlling its generation and higher connectivity reducing the maximum in random graphs.
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One-Dimensional Nonlinear Quantum Walks
Nonlinear continuous-time quantum walks on paths and cycles can be trapped at the initial site to arbitrary fidelity by choosing the cubic nonlinearity coefficient, unlike spreading linear walks.
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Moving Detector Quantum Walk with Random Relocation
Quantum walks with randomly relocating detectors exhibit regime-dependent spreading, oscillatory probability ratios, and a crossover in saturation values at critical removal time t_R*, with the enhancement being a quantum effect.
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Response to glassy disorder in coin on spread of quantum walker
Glassy disorder in the coin of a 1D discrete-time quantum walk inhibits ballistic spread while keeping it faster than classical diffusion, with slow or fast falloff and mid-strength inflection points depending on the disorder distribution.