Revivals in One-dimensional Quantum Walks with a Time and Spin-dependent Phase Shift
arXiv:2105.01730 · doi:10.1016/j.physleta.2021.127674
Abstract
We investigate the role of a time and spin-dependent phase shift on the evolution of one-dimensional discrete-time quantum walks. By employing Floquet engineering, a time and spin-dependent phase shift () is imprinted onto the walker's wave function while it shifts from one lattice site to another. For a quantum walk driven by the standard protocol we show with our numerical simulations that complete revivals with equal periods occur in the probability distribution of the walk for rational values of the phase factor, i.e., . For an irrational value of our results show partial revivals in the probability distribution with unpredictable periods, and the walker remains localized in a small region of the lattice. We further investigate revivals in a split-step quantum walk with a time and spin-dependent phase shift for rational values of . In contrast to the case of standard protocol, the split-step quantum walk shows partial revivals in the probability distribution. Furthermore, in view of an experimental realization we investigate the robustness of revivals against noise in the phase shift. Our results show that signatures of revivals persist for smaller values of the noise parameter, while revivals vanish for larger values. Our work is important in the context of quantum computation where quantum walks with a time and spin-dependent phase shift can be used to control and manipulate a desired quantum state on demand.
arXiv comment10 pages, 4 figures
References in corpus (52)
- The Physical Implementation of Quantum Computation
- Quantum random walks - an introductory overview
- Quantum Computation and Decision Trees
- Universal computation by quantum walk
- Quantum walks of correlated particles
- Quantum walks: a comprehensive review
- Exponential algorithmic speedup by quantum walk
- Spatial search by quantum walk
- Quantum Walk in Position Space with Single Optically Trapped Atoms
- Observation of topologically protected bound states in a one dimensional photonic system
- Photons Walking the Line: A quantum walk with adjustable coin operations
- Two-particle bosonic-fermionic quantum walk via 3D integrated photonics
- Exploring Topological Phases With Quantum Walks
- Realization of a quantum walk with one and two trapped ions
- Universal quantum computation using the discrete time quantum walk
- Quantum walk of a trapped ion in phase space
- Discrete single-photon quantum walks with tunable decoherence
- Chiral symmetry and bulk--boundary correspondence in periodically driven one-dimensional systems
- Bulk--Boundary Correspondence for Chiral Symmetric Quantum Walks
- Detecting topological invariants in nonunitary discrete-time quantum walks
- Symmetries, Topological Phases and Bound States in the One-Dimensional Quantum Walk
- Ideal negative measurements in quantum walks disprove theories based on classical trajectories
- Electric quantum walks with individual atoms
- Quantum random walks with decoherent coins
- Decoherence in the quantum walk on the line
- Asymptotic evolution of quantum walks with random coin
- Experimental quantum-walk revival with a time-dependent coin
- Quantum Walk of Two Interacting Bosons
- Propagation and spectral properties of quantum walks in electric fields
- Quantum walk on a line for a trapped ion
- Disordered Quantum Walks in one lattice dimension
- Unveiling hidden topological phases of a one-dimensional Hadamard quantum walk
- Quantum Walk with a time-dependent coin
- Scattering theory of topological phases in discrete-time quantum walks
- Robustness of topologically protected edge states in quantum walk experiments with neutral atoms
- Localization, delocalization, and topological phase transitions in the one-dimensional split-step quantum walk
- Remarks on the Atiyah-Hitchin metric
- Bulk-edge correspondence of one-dimensional quantum walks
- Edge-state enhanced transport in a 2-dimensional quantum walk
- Creating anomalous Floquet Chern insulators with magnetic quantum walks
- Decoherence Models for Discrete-Time Quantum Walks and their Application to Neutral Atom Experiments
- Quantum walks in external gauge fields
- Effects of long-range hopping and interactions on quantum walk in ordered and disordered lattices
- Controlling quantum random walk with a step-dependent coin
- Revivals in Quantum Walks with quasi-periodically time-dependent coin
- Quantum walks in weak electric fields and Bloch oscillations
- Singular continuous Cantor spectrum for magnetic quantum walks
- Bloch-like super-oscillations and unidirectional motion of phase driven quantum walkers
- Discrete-Time Quantum Walk - Dynamics and Applications
- Interacting quantum walkers: Two-body bosonic and fermionic bound states
- One-Dimensional Quantum Walks with a Position-Dependent Coin
- Localization and Fractality in Inhomogeneous Quantum Walks with Self-Duality