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

• URL: http://arxiv.org/abs/2007.01425v2
• Date: Tue, 24 Nov 2020 15:03:00 GMT
• Title: Continuous Time Limit of the DTQW in 2D+1 and Plasticity
• Authors: Michael Manighalam and Giuseppe Di Molfetta
• Abstract summary: We show that discrete time quantum walks can admit plasticity, showing the resulting Hamiltonians. This dependence on $varepsilon$ encapsulates all functions of $varepsilon$ for which a Taylor series expansion in $varepsilon$ is well defined.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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