TY - JOUR

T1 - Unpredictability and entanglement in open quantum systems

AU - Weimer, Hendrik

AU - Kazemi, Javad

N1 - Funding Information: The authors acknowledge fruitful discussion with R van Bijnen on variational quantum simulation. This work was funded by the Volkswagen Foundation, by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) within SFB 1227 (DQ-mat, project A04), SPP 1929 (GiRyd), and under Germanys Excellence Strategy—EXC-2123 QuantumFrontiers - 390837967.

PY - 2023/9/15

Y1 - 2023/9/15

N2 - We investigate dynamical many-body systems capable of universal computation, which leads to their properties being unpredictable unless the dynamics is simulated from the beginning to the end. Unpredictable behavior can be quantitatively assessed in terms of a data compression of the states occurring during the time evolution, which is closely related to their Kolmogorov complexity. We analyze a master equation embedding of classical cellular automata and demonstrate the existence of a phase transition between predictable and unpredictable behavior as a function of the random noise introduced by the embedding. We then turn to have this dynamics competing with a second process inducing quantum fluctuations and dissipatively driving the system to a highly entangled steady state. Strikingly, for intermediate strength of the quantum fluctuations, we find that both unpredictability and quantum entanglement can coexist even in the long time limit. Finally, we show that the required many-body interactions for the cellular automaton embedding can be efficiently realized within a variational quantum simulator platform based on ultracold Rydberg atoms with high fidelity.

AB - We investigate dynamical many-body systems capable of universal computation, which leads to their properties being unpredictable unless the dynamics is simulated from the beginning to the end. Unpredictable behavior can be quantitatively assessed in terms of a data compression of the states occurring during the time evolution, which is closely related to their Kolmogorov complexity. We analyze a master equation embedding of classical cellular automata and demonstrate the existence of a phase transition between predictable and unpredictable behavior as a function of the random noise introduced by the embedding. We then turn to have this dynamics competing with a second process inducing quantum fluctuations and dissipatively driving the system to a highly entangled steady state. Strikingly, for intermediate strength of the quantum fluctuations, we find that both unpredictability and quantum entanglement can coexist even in the long time limit. Finally, we show that the required many-body interactions for the cellular automaton embedding can be efficiently realized within a variational quantum simulator platform based on ultracold Rydberg atoms with high fidelity.

KW - quant-ph

KW - cond-mat.stat-mech

KW - elementary cellular automata

KW - computational unpredictability

KW - variational quantum simulation

UR - http://www.scopus.com/inward/record.url?scp=85173092534&partnerID=8YFLogxK

U2 - 10.1088/1367-2630/acf151

DO - 10.1088/1367-2630/acf151

M3 - Article

VL - 25

JO - New Journal of Physics

JF - New Journal of Physics

SN - 1367-2630

IS - 9

M1 - 093034

ER -