Discrete-time quantum walks as fermions of lattice gauge theory

Pablo Arnault , Armando Pérez , Pablo Arrighi (1, 2) , Terry Farrelly

1 LIS - Laboratoire d'Informatique et des Systèmes (LIS) (Marseille, Toulon)
2 IXXI - Institut Rhône-Alpin des systèmes complexes

It is shown that discrete-time quantum walks can be used to digitize, i.e., to time discretize fermionic models of continuous-time lattice gauge theory. The resulting discrete-time dynamics is thus not only manifestly unitary, but also ultralocal, i.e., the particle's speed is upper bounded, as in standard relativistic quantum field theories. The lattice chiral symmetry of staggered fermions, which corresponds to a translational invariance, is lost after the requirement of ultralocality of the evolution; this fact is an instance of Meyer's 1996 no-go results stating that no nontrivial scalar quantum cellular automaton can be translationally invariant [D. A. Meyer, J. Stat. Phys. 85, 551 (1996)JSTPBS0022-471510.1007/BF02199356; Phys. Lett. A 223, 337 (1996)PYLAAG0375-960110.1016/S0375-9601(96)00745-1]. All results are presented in a single-particle framework and for a (1+1)-dimensional space-time.

Mots clés: 03.67.-a; 11.15.Ha; 11.30.Rd; 03.75.-b; 47.11.Qr; Quantum walks; Quantum cellular automata; Quantum simulation; Lattice gauge theories; Wilson fermions; Staggered fermions; Chiral symmetries; Lattice gas automata; Fundamental concepts; fermion: lattice field theory; fermion: staggered; fermion: model; field theory: relativistic; symmetry: chiral; time: discrete; space-time: dimension: 2; cellular automaton; dimension: 1; unitarity; lattice

Domaines: Physique Générale [physics.gen-ph]

Pablo Arnault, Armando Pérez, Pablo Arrighi, Terry Farrelly. Discrete-time quantum walks as fermions of lattice gauge theory. Phys.Rev.A, 2019, 99 (3), pp.032110. ⟨10.1103/PhysRevA.99.032110⟩. ⟨hal-01861936⟩