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arXiv:2005.12361 · Physical Review A

Decoherence scaling transition in the dynamics of quantum information scrambling

Federico D. Domínguez, María Cristina Rodríguez, Robin Kaiser, Dieter Suter, Gonzalo A. Álvarez

Published Jul 1, 2021• 30 citations
arXivHTMLPDF

Abstract

Reliable processing of quantum information for developing quantum technologies requires precise control of out-of-equilibrium many-body systems. This is a highly challenging task because the fragility of quantum states to external perturbations increases with the system size. Here, we report on a series of experimental quantum simulations that quantify the sensitivity of a controlled Hamiltonian evolution to perturbations that drive the system away from the targeted evolution. Based on out-of-time ordered correlations, we demonstrate that the decay rate of the process fidelity increases with the effective number $K$ of correlated qubits as ${K}^{\ensuremath{\alpha}}$. As a function of the perturbation strength, we observe a decoherence scaling transition of the exponent $\ensuremath{\alpha}$ between two distinct dynamical regimes. In the limiting case below the critical perturbation strength, the exponent $\ensuremath{\alpha}$ drops sharply below 1, and there is no inherent limit to the number of qubits that can be controlled. This resilient quantum feature of the controlled dynamics of quantum information is promising for reliable control of large quantum systems.

DOI
10.1103/physreva.104.012402

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Quantum simulation elucidates properties of quantum many-body systems by mapping its Hamiltonian to a better-controlled system. Being less stringent than a universal quantum computer, noisy small- and intermediate-scale quantum simulators have successfully demonstrated qualitative behavior such as phase transition, localization and thermalization which are insensitive to imperfections in the engineered Hamiltonian. For more complicated features like quantum information scrambling, higher controllability will be desired to simulate both the forward and the backward time evolutions and to diagnose experimental errors, which has only been achieved for discrete gates. Here, we study the verified scrambling in a 1D spin chain by an analogue superconducting quantum simulator with the signs and values of individual driving and coupling terms fully controllable. We measure the temporal and spatial patterns of out-of-time ordered correlators (OTOC) by engineering opposite Hamiltonians on two subsystems, with the Hamiltonian mismatch and the decoherence extracted quantitatively from the scrambling dynamics. Our work demonstrates the superconducting system as a powerful quantum simulator.
The manipulation of quantum information in large systems requires precise control of quantum systems that are out of equilibrium. As the size of the system increases, its fragility in response to external perturbations and intrinsic decoherence processes also increases. The degradation of the system response makes accurate measurements a challenging and time-consuming task. However, quantum information lifetime enhancement can be achieved by dynamical decoupling techniques, where an external drive with a frequency much higher than the system's internal evolution renders signal acquisition with decay times greater than 1000-fold. In this study, we demonstrate that the system response during a prethermal period, subject to Floquet control, can be utilized to probe the multiple quantum evolution of dense and highly connected spin systems. This approach exhibits an enhanced sensitivity at a reduced experimental time. The enhanced signal-to-noise ratio achieved enabled the use of numerical inversion strategies to model the evolution of the excited multiple quantum coherences, which describe the number of correlated spins within a cluster. We observed that the increase in the number of correlated spins with multiple quantum evolution is accompanied by an increase in the distribution of spin cluster sizes, which follows a quadratic law.
In closed generic many-body systems, unitary evolution disperses local quantum information into highly nonlocal objects, resulting in thermalization. Such a process is called information scrambling, whose swiftness is quantified by the operator size growth. However, the impact of couplings to the environment on the process of information scrambling remains unexplored for quantum systems embedded within an environment. Here we predict a dynamical transition in quantum systems with all-to-all interactions accompanied by an environment, which separates two phases. In the dissipative phase, information scrambling halts as the operator size decays with time, while in the scrambling phase, dispersion of information persists, and the operator size grows and saturates to an O(N) value in the long-time limit with N the number of degrees of freedom of the systems. The transition is driven by the competition between the system's intrinsic and environment propelled scramblings and the environment-induced dissipation. Our prediction is derived from a general argument based on epidemiological models and demonstrated analytically via solvable Brownian Sachdev-Ye-Kitaev models. We provide further evidence which suggests that the transition is generic to quantum chaotic systems when coupled to an environment. Our study sheds light on the fundamental behavior of quantum systems in the presence of an environment.