Related papers: Fermionic quantum cellular automata and generalized matrix product unitaries

Fermionic quantum cellular automata and generalized matrix product unitaries

URL: http://arxiv.org/abs/2007.11905v2
Date: Wed, 9 Dec 2020 08:10:47 GMT
Title: Fermionic quantum cellular automata and generalized matrix product unitaries
Authors: Lorenzo Piroli, Alex Turzillo, Sujeet K. Shukla, J. Ignacio Cirac
Abstract summary: We study matrix product unitary operators (MPUs) for fermionic one-dimensional (1D) chains. We show that (i) fermionic MPUs do not necessarily feature a strict causal cone and (ii) not all fermionic Quantum Cellular Automata (QCA) can be represented as fermionic MPUs.
Score: 0.688204255655161
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: 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) fermionic MPUs do not necessarily feature a strict causal cone and (ii) not all fermionic Quantum Cellular Automata (QCA) can be represented as fermionic MPUs. We then introduce a natural generalization of the latter, obtained by allowing for an additional operator acting on their auxiliary space. We characterize a family of such generalized MPUs that are locality-preserving, and show that, up to appending inert ancillary fermionic degrees of freedom, any representative of this family is a fermionic QCA and viceversa. Finally, we prove an index theorem for generalized MPUs, recovering the recently derived classification of fermionic QCA in one dimension. As a technical tool for our analysis, we also introduce a graded canonical form for fermionic matrix product states, proving its uniqueness up to similarity transformations.

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