Facilitated quantum cellular automata as simple models with nonthermal eigenstates and dynamics

Gopalakrishnan, Sarang; Zakirov, Bahti

doi:10.48550/arxiv.1802.07729

Cited by 9 publications

(16 citation statements)

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“…Model.-The model we consider was recently introduced in Ref. [35]; the system is a spin-1/2 chain, subject to repeated application of the unitary x t ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ L = 20 where W (even → odd) consists of the following rule, applied to each odd spin n: apply the Pauli operator σ x n unless the two neighboring even sites, n − 1 and n + 1, are both in the | ↓ state. This rule can be composed from the gate sequence Toffoli…”

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confidence: 99%

Operator growth and eigenstate entanglement in an interacting integrable Floquet system

2018

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We analyze a simple model of quantum dynamics, which is a discrete-time deterministic version of the Frederickson-Andersen model. We argue that this model is integrable, with a quasiparticle description related to the classical hard-rod gas. Despite the integrability of the model, commutators of physical operators grow as in generic chaotic models, with a diffusively broadening front, and local operators obey the eigenstate thermalization hypothesis (ETH). However, large subsystems violate ETH; as a function of subsystem size, eigenstate entanglement first increases linearly and then saturates at a scale that is parametrically smaller than half the system size.

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confidence: 99%

Operator growth and eigenstate entanglement in an interacting integrable Floquet system

2018

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“…Clifford circuits are efficiently simulable on classical computers, [17][18][19] because they map each Pauli operator to a single other Pauli operator. Pure Clifford circuits have been used to construct analytically tractable ETH Hamiltonians, 20 and related quantum cellular automaton models have been used to study hydrodynamics. 21,22 Circuits with few non-Clifford gates (or many gates that are nearly Clifford) are also classically simulable.…”

Section: Introductionmentioning

confidence: 99%

Mana and thermalization: probing the feasibility of near-Clifford Hamiltonian simulation

J.¹,

White²

2022

Preprint

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Quantum hydrodynamics is the emergent classical dynamics governing transport of conserved quantities in generic strongly-interacting quantum systems. Recent matrix product operator methods 1,2 have made simulations of quantum hydrodynamics in 1+1d tractable, but they do not naturally generalize to 2+1d or higher, and they offer limited guidance as to the difficulty of simulations on quantum computers. Near-Clifford simulation algorithms are not limited to one dimension, and future error-corrected quantum computers will likely be bottlenecked by non-Clifford operations. We therefore investigate the non-Clifford resource requirements for simulation of quantum hydrodynamics using "mana", a resource theory of non-Clifford operations. For ifinite-temperature starting states we find that the mana of subsystems quickly approaches zero, while for starting states with energy above some threshold the mana approaches a nonzero value. Surprisingly, in each case the finite-time mana is governed by the governed by the subsystem entropy, not the thermal state mana; we argue that this is because mana is a sensitive diagnostic of finite-time deviations from canonical typicality.

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“…Our work introduces a new aspect to ongoing attempts towards extending the concept of a cellular automaton into the quantum domain -for a few examples see Refs. [15][16][17][18][19][20][21] -and also connects to quantum generalizations of perceptrons in neural networks [22,23]. Our proposed setting provides further-more a natural testbed for assessing the capabilities of current Rydberg lattice quantum simulators: it possesses non-trivial features, such as a phase transition and longranged quantum correlations, but yet can be efficiently solved.…”

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confidence: 99%

“…The rule (1) can be considered as imposing a kinetic constraint in the dynamics, reminiscent of facilitated models of glasses [24], such that local evolution only occurs if a certain condition is met. Constrained dynamics can give rise to complex evolution both in classical [25] and in both closed and open quantum systems [21,[26][27][28][29][30][31]. In particular, a rule akin to (1), of at least one nearest neighbour in the excited state required to allow for local evolution, is known in classical facilitated models to lead to an effective dynamics of the reaction-diffusion kind [32,33], with the concomitant competition between active and inactive dynamical states.…”

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Non-equilibrium absorbing state phase transitions in discrete-time quantum cellular automaton dynamics on spin lattices

Lesanovsky

Macieszczak

Garrahan

2019

Quantum Sci. Technol.

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We introduce a discrete-time quantum dynamics on a two-dimensional lattice that describes the evolution of a 1 + 1-dimensional spin system. The underlying quantum map is constructed such that the reduced state at each time step is separable. We show that for long times this state becomes stationary and displays a continuous phase transition in the density of excited spins. This phenomenon can be understood through a connection to the so-called Domany-Kinzel automaton, which implements a classical non-equilibrium process that features a transition to an absorbing state. Near the transition density-density correlations become long-ranged, but interestingly the same is the case for quantum correlations despite the separability of the stationary state. We quantify quantum correlations through the local quantum uncertainty and show that in some cases they may be determined experimentally solely by measuring expectation values of classical observables. This work is inspired by recent experimental progress in the realization of Rydberg lattice quantum simulators, which -in a rather natural way -permit the realization of conditional quantum gates underlying the discrete-time dynamics discussed here.

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Facilitated quantum cellular automata as simple models with nonthermal eigenstates and dynamics

Cited by 9 publications

References 0 publications

Operator growth and eigenstate entanglement in an interacting integrable Floquet system

Operator growth and eigenstate entanglement in an interacting integrable Floquet system

Mana and thermalization: probing the feasibility of near-Clifford Hamiltonian simulation

Non-equilibrium absorbing state phase transitions in discrete-time quantum cellular automaton dynamics on spin lattices

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