Optimizing the spatial spread of a quantum walk

Abstract

We devise a protocol to build 1D time-dependent quantum walks in 1D maximizing the spatial spread throughout the procedure. We allow only one of the physical parameters of the coin-tossing operator to vary, i.e. the angle $\theta$, such that for $\theta =0$ we have the ${\hat{\sigma }}_z$, while for $\theta =\pi /4$ we obtain the Hadamard gate. The optimal $\theta$ sequences present non-trivial patterns, with mostly $\theta \approx 0$ alternated with $\theta \approx \pi /4$ values after increasingly long periods. We provide an analysis of the entanglement properties, quasi-energy spectrum and survival probability, providing a full physical picture.

References in corpus (33)

• Environment-Assisted Quantum Walks in Photosynthetic Energy Transfer
• A Quantum Random Walk Search Algorithm
• Long-lived quantum coherence in photosynthetic complexes at physiological temperature
• Universal computation by quantum walk
• Quantum walks: a comprehensive review
• Two-particle bosonic-fermionic quantum walk via 3D integrated photonics
• Realization of quantum walks with negligible decoherence in waveguide lattices
• Universal quantum computation using the discrete time quantum walk
• Quantum walk of a trapped ion in phase space
• Experimental Implementation of Discrete Time Quantum Random Walk on an NMR Quantum Information Processor
• Quantum physics meets biology
• Decoherence can be useful in quantum walks
• The quantum to classical transition for random walks
• Quantum Walks driven by many coins
• Optimizing the discrete time quantum walk using a SU(2) coin
• Observing Topological Invariants Using Quantum Walk in Superconducting Circuits
• Relationship Between Quantum Walk and Relativistic Quantum Mechanics
• Decoherence vs entanglement in coined quantum walks
• Entangling Power of Disordered Quantum Walks
• Dynamic-Disorder-Induced Enhancement of Entanglement in Photonic Quantum Walks
• Finding spin-glass ground states using quantum walks
• Dynamics and energy spectra of aperiodic discrete-time quantum walks
• Aperiodic space-inhomogeneous quantum walks: localization properties, energy spectra and enhancement of entanglement
• Discrete spacetime, quantum walks and relativistic wave equations
• Connecting velocity and entanglement in quantum walks
• Weak disorder enhancing the production of entanglement in quantum walks
• Replica symmetry breaking in trajectories of a driven Brownian particle
• Trojan Quantum Walks
• The quantum walk search algorithm: Factors affecting efficiency
• Universal nature of replica symmetry breaking in quantum systems with Gaussian disorder
• Tunneling effects in a one-dimensional quantum walk
• On the spreading of quantum walks starting from local and delocalized states
• Engineering large end-to-end correlations in finite fermionic chains

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• Directionality and quantum backfire in continuous-time quantum walks from delocalized states: Exact results
• Enhanced spreading in continuous-time quantum walks using aperiodic temporal modulation of defects