2020
DOI: 10.1103/physrevlett.125.190402
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Quantum Cellular Automata, Tensor Networks, and Area Laws

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Cited by 51 publications
(42 citation statements)
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“…It is straightforward to see that U e , U o can be represented as two-site shift invariant matrix product operators (MPO) with D ¼ 2 [62], so that the evolution can be computed by applying a sequence of MPOs to jΨð0Þi. Note that this representation is completely general, since any quantum cellular automaton can be expressed exactly as an MPO with finite bond dimension [63][64][65].…”
mentioning
confidence: 99%
“…It is straightforward to see that U e , U o can be represented as two-site shift invariant matrix product operators (MPO) with D ¼ 2 [62], so that the evolution can be computed by applying a sequence of MPOs to jΨð0Þi. Note that this representation is completely general, since any quantum cellular automaton can be expressed exactly as an MPO with finite bond dimension [63][64][65].…”
mentioning
confidence: 99%
“…The dynamics we report, moreover, can be compared with the scenario considered in Ref. [9], in which a single quantum cellular automaton (QCA) application is discussed. In fact, we can cast our problem in terms of the dynamics of a continuous-time QCA over an infinitesimal time.…”
Section: A Quantum Blinkersmentioning
confidence: 96%
“…Recent works analysed the spreading of entanglement generated by quantum cellular automata [5,8], in Ref. [9] an explicit relation is identified between quantum cellular automata and tensor networks, showing that the entanglement entropy satisfies an area law bound that can be generated at each dynamical step of the quantum cellular automata.…”
Section: Introductionmentioning
confidence: 99%
“…Because after a period the state of the ancillas is unchanged, this evolution belongs to the QC a class of quantum circuits augmented by ancillas. This class is equivalent to quantum cellular automata [70][71][72][73] . We note that in this case there is no fundamental obstruction to realizing the evolution as a low-depth local circuit, merely a technical inconvenience (the three-qubit gates would have to act on triplets of qubits separated by several lattice spacings, as opposed to the present case where all interactions take place around a plaquette).…”
Section: Appendix A: Examples Of Correlationsmentioning
confidence: 99%