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Fermion doubling in Dirac quantum walks

Chaitanya Gupta* and Anthony J. Short†

  • *Contact author: chai.gupta@bristol.ac.uk
  • †Contact author: Tony.Short@bristol.ac.uk
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Phys. Rev. A 114, 012208 – Published 15 July, 2026

DOI: https://doi.org/10.1103/kkz3-fthm

Abstract

We consider discrete spacetime models known as quantum walks, which can be used to simulate Dirac particles. In particular, we look at fermion doubling in these models, in which high-momentum states yield additional low-energy solutions which behave like Dirac particles. The presence of doublers carries over to the "second-quantized" version of the walks represented by quantum cellular automata, which may lead to spurious solutions when introducing interactions. Moreover, we also consider pseudodoublers, which have high energy but behave like low-energy Dirac particles, and cause potential problems regarding the stability of the vacuum. To address these issues, we propose a family of quantum walks that are free of these doublers and pseudodoublers but still simulate the Dirac equation in the continuum limit. However, there remain a small number of additional low-energy solutions which do not directly correspond to Dirac particles. While the conventional Dirac walk always has a zero probability for the walker staying at the same point after a single time step, we obtain the family of walks by allowing this probability to be nonzero.

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Phys. Rev. A 114, 012208– Published 15 July, 2026
  • Received 3 March 2026
  • Accepted 1 July 2026
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