Discrete-time quantum walk with feed-forward quantum coin

Abstract

Constructing a discrete model like a cellular automaton is a powerful method for understanding various dynamical systems. However, the relationship between the discrete model and its continuous analogue is, in general, nontrivial. As a quantum-mechanical cellular automaton, a discrete-time quantum walk is defined to include various quantum dynamical behavior. Here we generalize a discrete-time quantum walk on a line into the feed-forward quantum coin model, which depends on the coin state of the previous step. We show that our proposed model has an anomalous slow diffusion characterized by the porous-medium equation, while the conventional discrete-time quantum walk model shows ballistic transport.

18 pages, 5 figures, movie file is available from http://www.nature.com/srep/2014/140321/srep04427/extref/srep04427-s1.gif

References in corpus (20)

• Quantum walks of correlated particles
• Quantum walks: a comprehensive review
• Quantum Walk in Position Space with Single Optically Trapped Atoms
• Observation of topologically protected bound states in a one dimensional photonic system
• Two-particle bosonic-fermionic quantum walk via 3D integrated photonics
• Realization of quantum walks with negligible decoherence in waveguide lattices
• Anderson localization of entangled photons in an integrated quantum walk
• Microscopic observation of magnon bound states and their dynamics
• Universal computation by multi-particle quantum walk
• A 2D Quantum Walk Simulation of Two-Particle Dynamics
• Relationship Between Quantum Walk and Relativistic Quantum Mechanics
• Experimental realisation of a delayed-choice quantum walk
• Nonlinear optical Galton board
• Discrete-time quantum walks: continuous limit and symmetries
• Observation of quasiperiodic dynamics in a one-dimensional quantum walk of single photons in space
• From Discrete Time Quantum Walk to Continuous Time Quantum Walk in Limit Distribution
• q-Gaussians in the porous-medium equation: stability and time evolution
• Quantum walks with memory - goldfish, elephants and wise old men
• Tailoring discrete quantum walk dynamics via extended initial conditions: Towards homogeneous probability distributions
• Localization and Fractality in Inhomogeneous Quantum Walks with Self-Duality

Cited by in corpus (21)

• Entangling Power of Disordered Quantum Walks
• Quantum Walks with Dynamical Control: Graph Engineering, Initial State Preparation and State Transfer
• Quantum walk as a simulator of nonlinear dynamics: Nonlinear Dirac equation and solitons
• Fractional Fokker-Planck equation from non-singular kernel operators
• Attractor-repeller pair of topological zero-modes in a nonlinear quantum walk
• Self-trapped quantum walks
• Quantum and random walks as universal generators of probability distributions
• Classical-like behavior in quantum walks with inhomogeneous, time-dependent coin operators
• Bloch-like super-oscillations and unidirectional motion of phase driven quantum walkers
• Massless Dirac Equation from Fibonacci Discrete-Time Quantum Walk
• Stability of topologically protected edge states in nonlinear quantum walks: Additional bifurcations unique to Floquet systems
• Parrondo's effect in continuous-time quantum walks
• Negative correlations can play a positive role in disordered quantum walks
• Probing coherence and noise tolerance in discrete-time quantum walks: unveiling self-focusing and breathing dynamics
• Nonlinear flip-flop quantum walks through potential barriers
• Driven Gaussian quantum walks
• Dynamical Triangulation Induced by Quantum Walk
• Nonlinear three-state quantum walks
• Asymptotic stability of small bound state of nonlinear quantum walks
• Quantum spatial search with electric potential : long-time dynamics and robustness to noise
• Theoretical Studies on Quantum Walks with a Time-varying Coin