Continuous Time Limit of the DTQW in 2D+1 and Plasticity
Abstract
A Plastic Quantum Walk admits both continuous time and continuous spacetime. The model has been recently proposed by one of the authors in 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 . This dependence on encapsulates all functions of for which a Taylor series expansion in is well defined, making our results very general.