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arXiv:2112.11204

Verifying quantum information scrambling dynamics in a fully controllable superconducting quantum simulator

J. -H. Wang, T. -Q. Cai, X. -Y. Han, Y. -W Ma, Z. -L Wang, Z. -H Bao, Y. Li, H. -Y Wang, H. -Y Zhang, L. -Y Sun, Y. -K. Wu, Y. -P. Song, Duan, L. -M.

Published Dec 21, 2021• 2 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2112.11204

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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.
Quantum information scrambling has received tremendous attention owing to its key concept in the fields of quantum chaos and quantum gravity. Here, with exploiting a fully controllable superconducting quantum processor, we study the verified scrambling in a 1D spin chain by an analog superconducting quantum simulator with the signs and values of individual driving and coupling terms fully controllable. By engineering opposite Hamiltonians on two subsystems, we measure the temporal and spatial patterns of out-of-time ordered correlators (OTOC), with the Hamiltonian mismatch and the decoherence extracted quantitatively from the scrambling dynamics, providing a benchmarking tool for probing not only the spatial but the temporal patterns of scrambling dynamics in many-body systems. Our work demonstrates the superconducting system with strong controllability as a powerful quantum simulator.
A closed quantum system never forgets its initial state, but the encoded information can get scrambled and become inaccessible without measuring a large fraction of all the system degrees of freedom. This scrambling can be diagnosed by studying the spatial spreading of initially local operators under the Heisenberg time evolution, and the decay of the out-of-time-ordered correlators (OTOC). What insights can OTOCs provide to understand the dynamics of quantum many-body systems? What are the characteristic behaviors of OTOCs during the time evolution? How is information scrambling affected by the dissipation in open quantum many-body systems? We first study slow scrambling in many-body localized systems via calculating various correlators, two-point retarded correlators and OTOCs. Comparing with retarded correlators, OTOCs provide more information about the dynamics. We find that disorder slows and partially halts the onset of information scrambling. Instead of ballistic spreading, propagation of information forms a logarithmic light cone. Next, we study the finite-size scaling of OTOCs at late times in generic thermalizing quantum many-body systems. When energy is conserved, the late-time saturation value of the OTOC of generic traceless local operators scales as an inverse polynomial in the system size. This is in contrast to the inverse exponential scaling expected for chaotic dynamics without energy conservation. We also study information scrambling in open quantum many-body systems. We define a dissipative version of OTOC and study its behaviors in a prototypical chaotic quantum chain with dissipation. We find that dissipation leads to not only the overall decay of the scrambled information due to leaking, but also structural changes so that the information light cone can only reach a finite distance even when the effect of overall decay is removed. Finally, we construct a family of local Hamiltonians for understanding the asymmetric information scrambling. Our models live on a one-dimensional lattice and exhibit asymmetric butterfly light cone between the left and right spatial directions.
In ergodic many-body quantum systems, locally encoded quantum information becomes, in the course of time evolution, inaccessible to local measurements. This concept of "scrambling" is currently of intense research interest, entailing a deep understanding of many-body dynamics such as the processes of chaos and thermalization. Here, we present first experimental demonstrations of quantum information scrambling on a 10-qubit trapped-ion quantum simulator representing a tunable long-range interacting spin system, by estimating out-of-time ordered correlators (OTOCs) through randomized measurements. We also analyze the role of decoherence in our system by comparing our measurements to numerical simulations and by measuring Rényi entanglement entropies.
Developing quantum technologies requires the control and understanding of the nonequilibrium dynamics of quantum information in many-body systems. Local information propagates in the system by creating complex correlations known as information scrambling, as this process prevents extracting the information from local measurements. In this paper, we develop a model adapted from solid-state NMR methods, to quantify the information scrambling. The scrambling is measured via time-reversal Loschmidt echo (LE) and multiple quantum coherences experiments that intrinsically contain imperfections. Considering these imperfections, we derive expressions for out-of-time order correlators (OTOCs) to quantify the observable information scrambling based on measuring the number of active spins where the information was spread. Based on the OTOC expressions, decoherence effects arise naturally by the effects of the nonreverted terms in the LE experiment. Decoherence induces localization of the measurable degree of information scrambling. These effects define a localization cluster size for the observable number of active spins that determines a dynamical equilibrium. We contrast the model's predictions with quantum simulations performed with solid-state NMR experiments, that measure the information scrambling with time-reversal echoes with controlled imperfections. An excellent quantitative agreement is found with the dynamics of quantum information scrambling and its localization effects determined from the experimental data. The presented model and derived OTOCs set tools for quantifying the quantum information dynamics of large quantum systems (more than 104{10}^{4}104 spins) consistent with experimental implementations that intrinsically contain imperfections.
Most experimental protocols for measuring scrambling require time evolution with a Hamiltonian and with the Hamiltonian's negative counterpart (backward time evolution). Engineering controllable quantum many-body systems for which such forward and backward evolution is possible is a significant experimental challenge. Furthermore, if the system of interest is quantum chaotic, one might worry that any small errors in the time reversal will be rapidly amplified, obscuring the physics of scrambling. This paper undermines this expectation: We exhibit a renormalization protocol that extracts nearly ideal out-of-time-ordered-correlator measurements from imperfect experimental measurements. We analytically and numerically demonstrate the protocol's effectiveness, up to the scrambling time, in a variety of models and for sizable imperfections. The scheme extends to errors from decoherence by an environment.
Out-of-time-order correlation (OTOC) functions provide a powerful theoretical tool for diagnosing chaos and the scrambling of information in strongly interacting, quantum systems.However, their direct and unambiguous experimental measurement remains an essential challenge.At its core, this challenge arises from the fact that the effects of both decoherence and experimental noise can mimic that of information scrambling, leading to decay of OTOCs.Here, we analyze a quantum teleportation protocol that explicitly enables one to differentiate between scrambling and decoherence.Moreover, we demonstrate that within this protocol, one can extract a precise "noise" parameter which quantitatively captures the nonscramblinginduced decay of OTOCs.Using this parameter, we prove explicit bounds on the true value of the OTOC.Our results open the door to experimentally measuring quantum scrambling with built-in verifiability.