2020/07/02 by Manighalam, Michael, Di Molfetta, Giuseppe
#FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2007.01425
A Plastic Quantum Walk admits both continuous time and continuous spacetime. The model has been recently proposed by one of the authors in \citemolfetta2019quantum, 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 ε. This dependence on ε encapsulates all functions of ε for which a Taylor series expansion in ε is well defined, making our results very general.