Simulating open quantum many-body systems using optimised circuits in digital quantum simulation

Jo, Minjae; Kim, Myungshik

doi:10.48550/arxiv.2203.14295

Cited by 5 publications

(5 citation statements)

References 56 publications

(81 reference statements)

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“…Analyzing their universal properties is particularly challenging since these investi-gations require the consideration of dissipative quantum dynamics of large systems at long times. Such dynamics, and that of similar dissipative models, such as those with kinetic constraints [48][49][50][51][52][53][54][55][56][57][58][59], serve as benchmark problems for numerics [60][61][62][63][64] and for quantum simulators [65][66][67][68]. Due to these difficulties, analytical predictions for the quantum analogue of the diffusion-limited regime (1) are currently still missing.…”

Section: (Classical Diffusion Limited)mentioning

confidence: 99%

Quantum reaction-limited reaction-diffusion dynamics of annihilation processes

Perfetto,

Carollo,

Garrahan

et al. 2023

Phys. Rev. E

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We investigate the quantum reaction-diffusion dynamics of fermionic particles which coherently hop in a one-dimensional lattice and undergo annihilation reactions. The latter are modelled as dissipative processes which involve losses of pairs 2A → ∅, triplets 3A → ∅, and quadruplets 4A → ∅ of neighbouring particles. When considering classical particles, the corresponding decay of their density in time follows an asymptotic power-law behavior. The associated exponent in one dimension is different from the mean-field prediction whenever diffusive mixing is not too strong and spatial correlations are relevant. This specifically applies to 2A → ∅, while the mean-field power-law prediction just acquires a logarithmic correction for 3A → ∅ and is exact for 4A → ∅. A mean-field approach is also valid, for all the three processes, when the diffusive mixing is strong, i.e., in the so-called reaction-limited regime. Here, we show that the picture is different for quantum systems. We consider the quantum reaction-limited regime and we show that for all the three processes power-law behavior beyond mean field is present as a consequence of quantum coherences, which are not related to space dimensionality. The decay in 3A → ∅ is further, highly intricate, since the power-law behavior therein only appears within an intermediate time window, while at long times the density decay is not power-law. Our results show that emergent critical behavior in quantum dynamics has a markedly different origin, based on quantum coherences, to that applying to classical critical phenomena, which is, instead, solely determined by the relevance of spatial correlations.

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Section: (Classical Diffusion Limited)mentioning

confidence: 99%

Quantum reaction-limited reaction-diffusion dynamics of annihilation processes

Perfetto,

Carollo,

Garrahan

et al. 2023

Phys. Rev. E

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“…Open quantum many-body systems constitute a fascinating subject of investigation [1,2]. The interplay between coherent and dissipative processes, combined with the large number of microscopic constituents forming the system, can give rise to interesting nonequilibrium stationary or dynamical phases [3][4][5][6][7][8][9][10][11][12] as well as to nonequilibrium critical dynamics [12][13][14][15][16]. An intriguing aspect of the formalism of open quantum systems is that it allows one to start from a purely classical stochastic dynamics (see, e.g., the reaction-diffusion processes considered in Ref.…”

Section: Introductionmentioning

confidence: 99%

Mean-field dynamics of open quantum systems with collective operator-valued rates: validity and application

Fiorelli¹,

Müller²,

Lesanovsky³

et al. 2023

Preprint

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We consider a class of open quantum many-body Lindblad dynamics characterized by an all-to-all coupling Hamiltonian and by dissipation featuring collective "state-dependent" rates.The latter encodes local incoherent transitions that depend on average properties of the system. This type of open quantum dynamics can be seen as a generalization of classical (mean-field) stochastic Markov dynamics, in which transitions depend on the instantaneous configuration of the system, to the quantum domain. We study the time evolution in the limit of infinitely large systems, and we demonstrate the exactness of the mean-field equations for the dynamics of average operators. We further derive the effective dynamical generator governing the time evolution of (quasi-)local operators. Our results allow for a rigorous and systematic investigation of the impact of quantum effects on paradigmatic classical models, such as quantum generalized Hopfield associative memories or (mean-field) kinetically-constrained models.

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“…Already in the classical domain these models are challenging to investigate and analytic solutions remain scarce [1]. They become even more complex when quantum effects, such as coherence and entanglement, are introduced, which makes them ideal benchmark problems for numerical methods [9,10] as well as for gauging the capabilities of quantum simulators [11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Signatures of a quantum stabilized fluctuating phase and critical dynamics in a kinetically constrained open many-body system with two absorbing states

et al. 2022

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We introduce and investigate an open many-body quantum system in which kinetically constrained coherent and dissipative processes compete. The form of the incoherent dissipative dynamics is inspired by that of epidemic spreading or cellular-automaton-based computation related to the density-classification problem. It features two non-fluctuating absorbing states as well as a Z2symmetric point in parameter space. The coherent evolution is governed by a kinetically constrained Z2-symmetric many-body Hamiltonian which is related to the quantum XOR-Fredrickson-Andersen model. We show that the quantum coherent dynamics can stabilize a fluctuating state and we characterize the transition between this active phase and the absorbing states. We also identify a rather peculiar behavior at the Z2-symmetric point. Here the system approaches the absorbing-state manifold with a dynamics that follows a power-law whose exponent continuously varies with the relative strength of the coherent dynamics. Our work shows how the interplay between coherent and dissipative processes as well as symmetry constraints may lead to a highly intricate non-equilibrium evolution and may stabilize phases that are absent in related classical problems.

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Simulating open quantum many-body systems using optimised circuits in digital quantum simulation

Cited by 5 publications

References 56 publications

Quantum reaction-limited reaction-diffusion dynamics of annihilation processes

Quantum reaction-limited reaction-diffusion dynamics of annihilation processes

Mean-field dynamics of open quantum systems with collective operator-valued rates: validity and application

Signatures of a quantum stabilized fluctuating phase and critical dynamics in a kinetically constrained open many-body system with two absorbing states

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