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Reviews in Theoretical Science

An Introduction to Quantum Cellular Automata Technology and Its Defects

Zohre Beiki, Ali Shahidinejad

Published Jan 31, 2014• 11 citations
Publisher

Abstract

An Introduction to Quantum Cellular Automata Technology and Its Defects
DOI
10.1166/rits.2014.1028

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We investigate realizations of (1+1)-dimensional fusion category symmetries on tensor-product Hilbert spaces, allowing for mixing with quantum cellular automata (QCAs). It was argued recently that any such realizable symmetry must be weakly integral. We develop a systematic analysis of QCA-refined realizations of fusion categories and prove two statements. First, we show that, under certain physical assumptions on defects, any QCA-refined realization has QCA and symmetry-operator indices determined by the categorical data, up to the freedom of redefining the symmetry operators. Second, we construct a lattice model that provides a QCA-refined realization for any weakly integral fusion category symmetry on a tensor product Hilbert space. We also compute indices of the QCAs in our lattice model and show agreement with the first result. As an application of the general construction, we give an explicit QCA-refined realization of general Tambara-Yamagami categorical symmetries.