Quantum and Classical Temporal Correlations in (1+1)D Quantum Cellular Automata

Gillman, Edward; Carollo, Federico; Lesanovsky, Igor

Abstract

We employ (1 + 1)-dimensional quantum cellular automata to study the evolution of entangle-ment and coherence near criticality in quantum systems that display non-equilibrium steady-state phase transitions. This construction permits direct access to the entire space-time structure of the underlying non-equilibrium dynamics, and allows for the analysis of unconventional correlations, such as entanglement in the time direction between the "present" and the "past". We show how the uniquely quantum part of these correlations-the coherence-can be isolated and that, close to criti-cality, its dynamics displays a universal power-law behaviour on approach to stationarity. Focussing on quantum generalizations of classical non-equilibrium systems: the Domany-Kinzel cellular automaton and the Bagnoli-Boccara-Rechtman model, we estimate the universal critical exponents for both the entanglement and coherence. As these models belong to the one-dimensional directed percolation universality class, the latter provides a key new critical exponent, one that is unique to quantum systems. Introduction. Cellular automata (CA) are paradig-matic models for the study of non-equilibrium processes [1-3] that also serve as models of computation [4, 5]. An important class of CA are so-called (1 + 1)-dimensional CA [6]. These are 2-dimensional (2D) lattice models whose evolution is such that the state of a given row depends only on the row above it. This results in the emergence of an effective time dimension, see Fig. 1(a). The dynamics of CA follow simple local update rules which propagate the state along the time dimension. This allows the implementation of a whole host of non-equilibrium processes, including some that display phase transitions into absorbing states. In the classical setting this construction has enabled the accurate study of non-equilibrium universality classes, such as that of directed percolation (DP) [7]. Here, sampling the dynamics of a suitably chosen order parameter enables the extraction of critical exponents. Importantly, these exponents are universal and also apply to other physical processes. For example, DP universality is also found in water percolating through sand [6], the dynamics of epidemic spreading [8] or even electro-convection in nematic liquid crystals [9] and the transition to turbulence [10]. Very recently, it was shown that also other quantities, that are not accessible by sampling-such as entropies-show critical behavior and are found to obey universal power-law scaling [11]. This raises the question as to whether there might be additional exponents, beyond the ones of the order parameter or correlation functions, that characterize universality classes.

Citation

Gillman, E., Carollo, F., & Lesanovsky, I. (2021). Quantum and Classical Temporal Correlations in (1+1)D Quantum Cellular Automata. Physical Review Letters, 127(23), Article 230502. https://doi.org/10.1103/PhysRevLett.127.230502

• Journal Article Type: Article
• Acceptance Date: Nov 5, 2021
• Online Publication Date: Dec 1, 2021
• Publication Date: Dec 3, 2021
• Deposit Date: Nov 18, 2021
• Publicly Available Date: Dec 1, 2021
• Journal: Physical Review Letters
• Print ISSN: 0031-9007
• Electronic ISSN: 1079-7114
• Peer Reviewed: Peer Reviewed
• Volume: 127
• Issue: 23
• Article Number: 230502
• DOI: https://doi.org/10.1103/PhysRevLett.127.230502
• Public URL: https://nottingham-repository.worktribe.com/output/6729158
• Publisher URL: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.127.230502