Two-component Dirac-like Hamiltonian for generating quantum walk on one-, two- and three-dimensional lattices
arXiv:1309.3911 · doi:10.1038/srep02829
Abstract
From the unitary operator used for implementing two-state discrete-time quantum walk on one-, two- and three- dimensional lattice we obtain a two-component Dirac-like Hamiltonian. In particular, using different pairs of Pauli basis as position translation states we obtain three different form of Hamiltonians for evolution on one-dimensional lattice. We extend this to two- and three-dimensional lattices using different Pauli basis states as position translation states for each dimension and show that the external coin operation, which is necessary for one-dimensional walk is not a necessary requirement for a walk on higher dimensions but can serve as an additional resource to control the dynamics. The two-component Hamiltonian we present here for quantum walk on different lattices can serve as a general framework to simulate, control, and study the dynamics of quantum systems governed by Dirac-like Hamiltonian.
14 pages, 5 figures ; Published version ; It includes some parts of arxiv:1103.2704
References in corpus (17)
- Environment-Assisted Quantum Walks in Photosynthetic Energy Transfer
- Quantum walks of correlated particles
- Exponential algorithmic speedup by quantum walk
- Quantum Walk in Position Space with Single Optically Trapped Atoms
- Exploring Topological Phases With Quantum Walks
- Realization of quantum walks with negligible decoherence in waveguide lattices
- Discrete single-photon quantum walks with tunable decoherence
- Decoherence in quantum walks - a review
- Optimizing the discrete time quantum walk using a SU(2) coin
- Relationship Between Quantum Walk and Relativistic Quantum Mechanics
- Limit distributions of two-dimensional quantum walks
- Mimicking the probability distribution of a two-dimensional Grover walk with a single-qubit coin
- The Dirac equation as a quantum walk: higher dimensions, observational convergence
- Disordered quantum walk-induced localization of a Bose-Einstein condensate
- Quantum phase transition using quantum walks in an optical lattice
- Decoherence on a two-dimensional quantum walk using four- and two-state particle
- Localization and Fractality in Inhomogeneous Quantum Walks with Self-Duality
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