Toward simulation of topological phenomenas with one-, two- and three-dimensional quantum walks
arXiv:2005.08720 · doi:10.1103/PhysRevA.103.012201
Abstract
We study the simulation of the topological phases in three subsequent dimensions with quantum walks. We are mainly focused on the completion of a table for the protocols of the quantum walk that could simulate different family of the topological phases in one, two dimensions and take the first initiatives to build necessary protocols for three-dimensional cases. We also highlight the possible boundary states that can be observed for each protocol in different dimensions and extract the conditions for their emergences or absences. To further enrich the simulation of the topological phenomenas, we include step-dependent coins in the evolution operators of the quantum walks. Consequently, this leads to step-dependency of the simulated topological phenomenas and their properties which in turn introduce dynamicality as a feature to simulated topological phases and boundary states. This dynamicality provides the step-number of the quantum walk as a mean to control and engineer the number of topological phases and boundary states, their populations, types and even occurrences.
arXiv comment24 pages, 11 figures, 1 table; some typos are corrected. submitted for publication
References in corpus (44)
- Topological Insulators
- Topological insulators and superconductors
- Quantum Spin Hall Insulator State in HgTe Quantum Wells
- Weyl and Dirac Semimetals in Three Dimensional Solids
- Classification of topological insulators and superconductors in three spatial dimensions
- Topological Field Theory of Time-Reversal Invariant Insulators
- Classification of topological quantum matter with symmetries
- Topological insulators and superconductors: ten-fold way and dimensional hierarchy
- Weyl semimetal phase in non-centrosymmetric transition metal monophosphides
- Environment-Assisted Quantum Walks in Photosynthetic Energy Transfer
- Topological phases of fermions in one dimension
- Topological Semimetals
- Observation of topologically protected bound states in a one dimensional photonic system
- Exploring Topological Phases With Quantum Walks
- Universal quantum computation using the discrete time quantum walk
- Bulk-Boundary Correspondence in a Non-Hermitian System in One Dimension with Chiral-Inversion Symmetry
- Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons
- Topological phases and surface flat bands in superconductors without inversion symmetry
- Bulk--Boundary Correspondence for Chiral Symmetric Quantum Walks
- Simulating dynamic quantum phase transitions in photonic quantum walks
- Detecting topological invariants in nonunitary discrete-time quantum walks
- Symmetries, Topological Phases and Bound States in the One-Dimensional Quantum Walk
- Dynamical moments reveal a topological quantum transition in a photonic quantum walk
- Dispersion of Fermi arcs in Weyl semimetals and their evolutions to Dirac cones
- Dynamical classification of topological quantum phases
- Observing Topological Invariants Using Quantum Walk in Superconducting Circuits
- Direct Probe of Topological Invariants Using Bloch Oscillating Quantum Walks
- Two-dimensional topological quantum walks in the momentum space of structured light
- Unveiling hidden topological phases of a one-dimensional Hadamard quantum walk
- Measuring Topological Invariants in Disordered Discrete Time Quantum Walks
- Measuring a Dynamical Topological Order Parameter in Quantum Walks
- Localization, delocalization, and topological phase transitions in the one-dimensional split-step quantum walk
- Universal Nonlinear Disordered Wave Packet Subdiffusion: 12 Decades
- Higher winding number in a non-unitary photonic quantum walk
- Controlling quantum random walk with a step-dependent coin
- Eigenvalue Measurement of Topologically Protected Edge states in Split-Step Quantum Walks
- Boltzmann-Gibbs states in topological quantum walks and associated many-body systems: Fidelity and Uhlmann parallel transport analysis of Phase Transitions
- Edge states in a two-dimensional quantum walk with disorder
- Simulation of the multiphase configuration and phase transitions with quantum walks utilizing a step-dependent coin
- Topological Phases in a Weyl Semimetal Multilayer
- Controllable simulation of topological phases and edge states with quantum walk
- Diverse tunable dynamics of two quantum random walkers
- Spectral Magnetization Ratchets with Discrete Time Quantum Walks
- Theoretical Studies on Quantum Walks with a Time-varying Coin
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- Steered discrete-time quantum walks for engineering of quantum states
- Optical realization of one-dimensional generalized split-step quantum walks
- Complementarity in quantum walks