Abstract
A Plastic quantum walk admits both continuous time and continuous spacetime. The model has been recently proposed by one of the authors in Di Molfetta and Arrighi (Quant Inf Process 19(2): 47, 2020), 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 functions 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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