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- W3092795509 abstract "Quantum walks on lattices can give rise to one-particle relativistic wave equations in the long-wavelength limit. In going to multiple particles, quantum cellular automata (QCA) are natural generalizations of quantum walks. In one spatial dimension, the quantum walk can be promoted to a QCA that, in the long-wavelength limit, gives rise to the Dirac quantum field theory (QFT) for noninteracting fermions. This QCA/QFT correspondence has both theoretical and practical applications, but there are obstacles to similar constructions in two or more spatial dimensions. Here we show that a method of construction employing distinguishable particles confined to the completely antisymmetric subspace yields a QCA in two spatial dimensions that gives rise to the 2D Dirac QFT. Generalizing to 3D will entail some additional complications, but no conceptual barriers. We examine how this construction evades the no go results in earlier work." @default.
- W3092795509 created "2020-10-22" @default.
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- W3092795509 date "2020-12-30" @default.
- W3092795509 modified "2023-09-26" @default.
- W3092795509 title "Quantum cellular automata and quantum field theory in two spatial dimensions" @default.
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- W3092795509 doi "https://doi.org/10.1103/physreva.102.062222" @default.
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