Exact solution of the Rule 150 reversible cellular automaton

Wilkinson, Joseph W. P.; Prosen, Tomaž; Garrahan, Juan P.

doi:10.48550/arxiv.2110.15085

Cited by 5 publications

(6 citation statements)

References 58 publications

(101 reference statements)

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“…For a recent analysis, see Ref. [57]. For the ZFEV model, there are many symmetries which preserve the integrability [14].…”

Section: Classical Scamentioning

confidence: 99%

See 1 more Smart Citation

Integrable nonunitary quantum circuits

Su¹,

Martin²

2022

Preprint

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We show that the integrable Lindblad superoperators found recently can be used to build integrable nonunitary quantum circuits with two-site gates by demonstrating that the Ř-matrices are completely positive and trace preserving. Using the bond-site transformation, we obtain the corresponding integrable nonunitary quantum circuits with three-site gates. When restricted to the diagonals of the density matrix, these quantum models reduce to integrable classical cellular automata. This approach may pave the way for a systematic construction of integrable nonunitary quantum circuits.

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“…For a recent analysis, see Ref. [57]. For the ZFEV model, there are many symmetries which preserve the integrability [14].…”

Section: Classical Scamentioning

confidence: 99%

“…Appendix A: RCA150 and RCA105 RCA150 and RCA105 are two 3-to-1 cellular automata that preserve the spin reflection symmetry [47,49,57]. They belong to the category of "exclusive one-spin facilitated" Fredrickson-Andersen (XOR-FA) models [62].…”

mentioning

confidence: 99%

Integrable nonunitary quantum circuits

Su¹,

Martin²

2022

Preprint

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“…Therefore, the dynamics can be understood using freely moving domain walls. In the specific case of N = 2 this model is the so-called Rule150 model [8], which was studied recently in [61,31,62].…”

Section: Extension To 3 → 1 Modelsmentioning

confidence: 99%

Superintegrable cellular automata and dual unitary gates from Yang-Baxter maps

Gombor,

Pozsgay

2021

Preprint

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We consider one dimensional block cellular automata, where the local update rules are given by Yang-Baxter maps, which are set theoretical solutions of the Yang-Baxter equations. We show that such systems are superintegrable: they possess an exponentially large set of conserved local charges, such that the charge densities propagate ballistically on the chain. For these quantities we observe a complete absence of "operator spreading". In addition, the models can also have other local charges which are conserved only additively. We discuss concrete models up to local dimensions N ≤ 4, and show that they give rise to rich physical behaviour, including non-trivial scattering of particles and the coexistence of ballistic and diffusive transport. We find that the local update rules are classical versions of the "dual unitary gates" if the Yang-Baxter maps are non-degenerate. We discuss consequences of dual unitarity, and we also discuss a family of dual unitary gates obtained by a non-integrable quantum mechanical deformation of the Yang-Baxter maps.

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“…ministic cellular automata [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44] (for a review see [45]). Recently, cellular automata circuits have been also used to study Fredkin-like systems [46,47], revealing a new "universality class" of hydrodynamics.…”

Section: Introductionmentioning

confidence: 99%

Slow dynamics and large deviations in classical stochastic Fredkin chains

2022

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The Fredkin spin chain serves as an interesting theoretical example of a quantum Hamiltonian whose ground state exhibits a phase transition between three distinct phases, one of which violates the area law. Here we consider a classical stochastic version of the Fredkin model, which can be thought of as a simple exclusion process subject to additional kinetic constraints, and study its classical stochastic dynamics. The ground state phase transition of the quantum chain implies an equilibrium phase transition in the stochastic problem, whose properties we quantify in terms of numerical matrix product states (MPS). The stochastic model displays slow dynamics, including power law decaying autocorrelation functions and hierarchical relaxation processes due to exponential localization. Like in other kinetically constrained models, the Fredkin chain has a rich structure in its dynamical large deviations -which we compute accurately via numerical MPS -including an active-inactive phase transition, and a hierarchy of trajectory phases connected to particular equilibrium states of the model. We also propose, via its height field representation, a generalization of the Fredkin model to two dimensions in terms of constrained dimer coverings of the honeycomb lattice.

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Exact solution of the Rule 150 reversible cellular automaton

Cited by 5 publications

References 58 publications

Integrable nonunitary quantum circuits

Integrable nonunitary quantum circuits

Superintegrable cellular automata and dual unitary gates from Yang-Baxter maps

Slow dynamics and large deviations in classical stochastic Fredkin chains

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