Twisted quantum walks, generalised Dirac equation and Fermion doubling

TL;DR

This paper introduces twisted quantum walks that, in the continuous limit, lead to a generalized Dirac equation with a dispersion term, effectively regularizing Fermion doubling and expanding quantum simulation capabilities.

Contribution

It presents a new family of quantum walks called twisted walks, which incorporate a dispersion term in the Dirac operator, addressing Fermion doubling issues.

Findings

The twisted quantum walks converge to a generalized Dirac equation with a dispersion term.

The dispersion term acts as an effective mass, regularizing Fermion doubling.

The approach broadens the applicability of quantum walks in simulating quantum field theories.

Abstract

Quantum discrete-time walkers have, since their introduction, demonstrated applications in algorithmic and in modeling and simulating a wide range of transport phenomena. They have long been considered the discrete-time and discrete space analogue of the Dirac equation and have been used as a primitive to simulate quantum field theories precisely because of some of their internal symmetries. In this paper we introduce a new family of quantum walks, said twisted, which admits, as continuous limit, a generalized Dirac operator equipped with a dispersion term. Moreover, this quadratic term in the energy spectrum acts as an effective mass, leading to a regularization of the well known Fermion doubling problem.