Electric quantum walks in two dimensions

Abstract

We study electric quantum walks in two dimensions considering Grover, Alternate, Hadamard, and DFT quantum walks. In the Grover walk the behaviour under an electric field is easy to summarize: when the field direction coincides with the x or y axes, it produces a transient trapping of the probability distribution along the direction of the field, while when it is directed along the diagonals, a perfect 2D trapping is frustrated. The analysis of the alternate walk helps to understand the behaviour of the Grover walk as both walks are partially equivalent; in particular, it helps to understand the role played by the existence of conical intersections in the dispersion relations, as we show that when these are removed a perfect 2D trapping can occur for suitable directions of the field. We complete our study with the electric DFT and Hadamard walks in 2D, showing that the latter can exhibit perfect 2D trapping.

References added and minor typos corrected

References in corpus (8)

• Universal computation by quantum walk
• Spatial search and the Dirac equation
• A random walk approach to quantum algorithms
• Experimental quantum-walk revival with a time-dependent coin
• Mimicking the probability distribution of a two-dimensional Grover walk with a single-qubit coin
• Tailoring discrete quantum walk dynamics via extended initial conditions: Towards homogeneous probability distributions
• Two-dimensional quantum walk under artificial magnetic field
• Localization and Fractality in Inhomogeneous Quantum Walks with Self-Duality

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