From Discrete Time Quantum Walk to Continuous Time Quantum Walk in Limit Distribution

Abstract

The discrete time quantum walk defined as a quantum-mechanical analogue of the discrete time random walk have recently been attracted from various and interdisciplinary fields. In this review, the weak limit theorem, that is, the asymptotic behavior, of the one-dimensional discrete time quantum walk is analytically shown. From the limit distribution of the discrete time quantum walk, the discrete time quantum walk can be taken as the quantum dynamical simulator of some physical systems.

This is the invited review paper on the special issue on Theoretical and Mathematical Aspects of Discrete Time Quantum Walk from Journal of Computational and Theoretical Nanoscience

References in corpus (3)

• Bound Molecules in an Interacting Quantum Walk
• Asymptotic entanglement in the discrete-time quantum walk
• Discrete time quantum walk model for single and entangled particles to retain entanglement in coin space

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• Detection of edge defects by embedded eigenvalues of quantum walks
• Discrete-time quantum walks as fermions of lattice gauge theory
• Localization and Recurrence of Quantum Walk in Periodic Potential on a Line
• From Disordered Quantum Walk to Physics of Off-diagonal Disorder
• Massless Dirac Equation from Fibonacci Discrete-Time Quantum Walk
• Moments of Coinless Quantum Walks on Lattices
• Quantum Encoding and Analysis on Continuous Time Stochastic Process with Financial Applications
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• Weak convergence of the Wojcik model
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• Repeated measurements and random scattering in quantum walks
• Two-dimensional quantum central limit theorem by quantum walks
• Response to glassy disorder in coin on spread of quantum walker