Fermionic quantum cellular automata and generalized matrix-product unitaries
نویسندگان
چکیده
We study matrix product unitary operators (MPUs) for fermionic one-dimensional (1D) chains. In stark contrast with the case of 1D qudit systems, we show that (i) MPUs do not necessarily feature a strict causal cone and (ii) all Quantum Cellular Automata (QCA) can be represented as MPUs. then introduce natural generalization latter, obtained by allowing an additional operator acting on their auxiliary space. characterize family such generalized are locality-preserving, that, up to appending inert ancillary degrees freedom, any representative this is QCA viceversa. Finally, prove index theorem MPUs, recovering recently derived classification in one dimension. As technical tool our analysis, also graded canonical form states, proving its uniqueness similarity transformations.
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ژورنال
عنوان ژورنال: Journal of Statistical Mechanics: Theory and Experiment
سال: 2021
ISSN: ['1742-5468']
DOI: https://doi.org/10.1088/1742-5468/abd30f