Fermionic quantum cellular automata and generalized matrix product unitaries
| Autor: | Piroli, Lorenzo, Turzillo, Alex, Shukla, Sujeet K., Cirac, J. Ignacio |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | J. Stat. Mech. (2021) 013107 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1742-5468/abd30f |
| Popis: | 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. Comment: 35 pages, no figures; v2: minor revision |
| Databáze: | arXiv |
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