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Fermionic and bosonic quantum field theories from quantum cellular automata in three spatial dimensions

Leonard Mlodinow and Todd A. Brun
Phys. Rev. A 103, 052203 – Published 7 May 2021

Abstract

In the past decade or so, there has been a growing number of papers postulating a correspondence relating quantum cellular automata (QCAs) to quantum field theories (QFTs). If valid, this would relate two important but seemingly unconnected physical systems and offer the potential for a deeper understanding of both. For example, it could lead to algorithms for simulating QFTs on a quantum computer. Moreover, it is possible that nature actually obeys a QCA model and it is the corresponding QFT that is a mere approximation. However, verifying the QCA/QFT correspondence beyond the single-particle case has proven challenging, especially in more than one spatial dimension. Here we construct quantum cellular automata that, in the long-wavelength limit, yield a multiparticle theory for free fermions and bosons in three spatial dimensions: the Dirac and Maxwell field theories, i.e., free QED.

  • Received 17 November 2020
  • Accepted 9 April 2021

DOI:https://doi.org/10.1103/PhysRevA.103.052203

©2021 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Leonard Mlodinow* and Todd A. Brun

  • Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089, USA

  • *lmlodinow@gmail.com
  • tbrun@usc.edu

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Issue

Vol. 103, Iss. 5 — May 2021

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