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
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