2025/05/12 by Bakircioglu, Dogukan, Arnault, Pablo, Arrighi, Pablo · 1 citation
#FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2505.07900
A Quantum Cellular Automaton (QCA) is essentially an operator driving the evolution of particles on a lattice, through local unitaries. Because Δx=Δt=ε, QCAs constitute a privileged framework to cast the digital quantum simulation of relativistic quantum particles and their interactions with gauge fields, e.g., (3+1)D Quantum Electrodynamics (QED). But before they can be adopted, simulation schemes for high-energy physics need prove themselves against specific numerical issues, of which the most infamous is Fermion Doubling (FD). FD is well understood in particular in the discrete-space but continuous-time settings of real-time/Hamiltonian Lattice Gauge Theories (LGTs), as the appearance of spurious solutions for all Δx=ε≠ 0. We rigorously extend this analysis to the real-time discrete-space and discrete-time schemes that QCAs are. We demonstrate the existence of FD issues in QCAs. By applying a covering map on the Brillouin zone, we provide a flavoring-without-staggering way of fixing FD that does not break chiral symmetry. We explain how this method coexists with the Nielsen-Ninomiya no-go theorem, and illustrate this with a neutrino-like QCA.