Quantum Cellular Automata, Tensor Networks, and Area Laws

Piroli, Lorenzo; Cirac, J. I.

doi:10.1103/physrevlett.125.190402

Cited by 51 publications

(42 citation statements)

References 27 publications

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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].…”

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confidence: 99%

Exact Thermalization Dynamics in the “Rule 54” Quantum Cellular Automaton

2021

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We study the out-of-equilibrium dynamics of the quantum cellular automaton known as "Rule 54." For a class of low-entangled initial states, we provide an analytic description of the effect of the global evolution on finite subsystems in terms of simple quantum channels, which gives access to the full thermalization dynamics at the microscopic level. As an example, we provide analytic formulas for the evolution of local observables and Rényi entropies. We show that, in contrast to other known examples of exactly solvable quantum circuits, Rule 54 does not behave as a simple Markovian bath on its own parts, and displays typical nonequilibrium features of interacting integrable many-body quantum systems such as finite relaxation rate and interaction-induced dressing effects. Our study provides a rare example where the full thermalization dynamics can be solved exactly at the microscopic level.

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confidence: 99%

Exact Thermalization Dynamics in the “Rule 54” Quantum Cellular Automaton

2021

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“…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%

Entanglement in the Quantum Game of Life

Ney,

Notarnicola,

Montangero

et al. 2021

Preprint

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We investigate the quantum dynamics of a spin chain that implements a quantum analog of Conway's game of life. We solve the time-dependent Schrödinger equation starting with initial separable states and analyse the evolution of quantum correlations across the lattice. We report examples of evolutions leading to all-entangled chains and/or to time oscillating entangling structures and characterize them by means of entanglement and network measures. The quantum patterns result to be quite different from the classical ones, even in the dynamics of local observables. A peculiar instance is a structure behaving as the quantum analog of a blinker, but that has no classical counterpart.

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“…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%

Tri-unitary quantum circuits

Jonay,

Khemani,

Ippoliti

2021

Preprint

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We introduce a novel class of quantum circuits that are unitary along three distinct "arrows of time". These dynamics share some of the analytical tractability of "dual-unitary" circuits, while exhibiting distinctive and richer phenomenology. We find that two-point correlations in these dynamics are strictly confined to three directions in (1 + 1)-dimensional spacetime -the two light cone edges, δx = ±vδt, and the static worldline δx = 0. Along these directions, correlation functions are obtained exactly in terms of quantum channels built from the individual gates that make up the circuit. We prove that, for a class of initial states, entanglement grows at the maximum allowed speed up to an entropy density of at least one half of the thermal value, at which point it becomes model-dependent. Finally, we extend our circuit construction to 2 + 1 dimensions, where two-point correlation functions are confined to the one-dimensional edges of a tetrahedral light cone -a subdimensional propagation of information reminiscent of "fractonic" physics.

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Quantum Cellular Automata, Tensor Networks, and Area Laws

Cited by 51 publications

References 27 publications

Exact Thermalization Dynamics in the “Rule 54” Quantum Cellular Automaton

Exact Thermalization Dynamics in the “Rule 54” Quantum Cellular Automaton

Entanglement in the Quantum Game of Life

Tri-unitary quantum circuits

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