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arXiv · 2408.04493

Classification of qubit cellular automata on hypercubic lattices

Andrea Pizzamiglio·Alessandro Bisio·Paolo Perinotti
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Abstract

We classify quantum cellular automata whose cells are qubits, on hypercubic lattices $\mathbb Z^s$, with the von Neumann neighborhood scheme, in terms of realizability as finite-depth quantum circuits. We show the most general structure of such automata and use its characterisation to simulate a few steps of evolution and evaluate the rate of entanglement production between one cell and its surroundings.

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Andrea Pizzamiglio, Alessandro Bisio, Paolo Perinotti. 2024-08-08. Classification of qubit cellular automata on hypercubic lattices. https://doi.org/10.1103/physrevlett.134.240601

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