Quantum walks on cycles

Abstract

We consider asymptotic behaviour of a Hadamard walk on a cycle. For a walk which starts with a state in which all the probability is concentrated on one node, we find the explicit formula for the limiting distribution and discuss its asymptotic behaviour when the length of the cycle tends to infinity. We also demonstrate that for a carefully chosen initial state, the limiting distribution of a quantum walk on cycle can lie further away from the uniform distribution than its initial state.

References in corpus (4)

• Quantum random walks - an introductory overview
• A Quantum Random Walk Search Algorithm
• Controlling discrete quantum walks: coins and intitial states
• Quantum random walks in optical lattices

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• Phase-space approach to the study of decoherence in quantum walks
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• Asymptotic entanglement in a two-dimensional quantum walk
• One-Dimensional Coinless Quantum Walks
• Photonic quantum walks with four-dimensional coins
• Quantum random walks on the $N$-cycle subject to decoherence on the coin degree of freedom
• Asymptotic evolution of quantum walks on the $N$-cycle subject to decoherence on both the coin and position degrees of freedom
• Quantum walk transport properties on graphene structures
• Quantum walks with memory on cycles
• Discrete-time quantum walks on one-dimensional lattices
• Non-stationary quantum walks on the cycle
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• Transient temperature and mixing times of quantum walks on cycles
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• The switching effect of the side chain on quantum walks on triple graphs
• Periodicity for the Hadamard walk on cycles
• Interference-induced localization in quantum random walk on clean cyclic graph
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• Temporal Fluctuations of Continuous-Time Quantum Random Walks on Circles
• Improving quantum walk metrology with split-step quantum walk
• Exact solutions and symmetry analysis for the limiting probability distribution of quantum walks
• Fluctuations of Quantum Random Walks on Circles
• Asymptotic reduced density matrix of discrete-time quantum walks
• A group structure arising from Grover walks on complete graphs with self-loops and its application