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arXiv · 2007.01425

Continuous Time Limit of the DTQW in 2D+1 and Plasticity

Michael Manighalam·Giuseppe Di Molfetta
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Abstract

A Plastic Quantum Walk admits both continuous time and continuous spacetime. The model has been recently proposed by one of the authors in \cite{molfetta2019quantum}, leading to a general quantum simulation scheme for simulating fermions in the relativistic and non relativistic regimes. The extension to two physical dimensions is still missing and here, as a novel result, we demonstrate necessary and sufficient conditions concerning which discrete time quantum walks can admit plasticity, showing the resulting Hamiltonians. We consider coin operators as general $4$ parameter unitary matrices, with parameters which are function of the lattice step size $\varepsilon$. This dependence on $\varepsilon$ encapsulates all functions of $\varepsilon$ for which a Taylor series expansion in $\varepsilon$ is well defined, making our results very general.

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Michael Manighalam, Giuseppe Di Molfetta. 2020-11-24. Continuous Time Limit of the DTQW in 2D+1 and Plasticity. https://arxiv.org/abs/2007.01425

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