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.

中文翻译：

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量子细胞自动机在三个空间维度上的费米子和玻色子量子场理论

在过去的十年左右的时间里，越来越多的论文提出了将量子细胞自动机（QCA）与量子场论（QFT）相关的对应关系。如果有效，它将与两个重要但看似未连接的物理系统相关联，并为更深入地了解这两个系统提供了潜力。例如，它可能导致用于在量子计算机上模拟QFT的算法。此外，自然界实际上可能会遵循QCA模型，而相应的QFT仅仅是一个近似值。然而，在单粒子情况之外验证QCA / QFT对应性已被证明具有挑战性，尤其是在一个以上的空间维度上。在这里，我们构造了量子细胞自动机，该自动机在长波长范围内产生了三个空间维度上的自由费米子和玻色子的多粒子理论：