Loschmidt echo and scrambling of systematic errors in tomography-A quantum signature of chaos
Year: 2026
Authors: Sahu A., Varikuti N.D., Madhok V.
Autors Affiliation: Indian Inst Technol Madras, Dept Phys, Chennai 600036, India; Indian Inst Technol Madras, Ctr Quantum Informat Commun & Comp, Chennai 600036, India; CNR, Pitaevskii BEC Ctr, INO, Via Sommar 14, I-38123 Trento, Italy; Univ Trento, Dept Phys, Via Sommar 14, I-38123 Trento, Italy; INFN, Trento Inst Fundamental Phys & Applicat, TIFPA, Via Sommar 14, I-38123 Trento, Italy.
Abstract: How does quantum chaos lead to rapid scrambling of information as well as systematic errors across a system when one introduces perturbations in the dynamics’ What are its consequences for the reliability of quantum simulations and quantum information processing’ We employ continuous measurement quantum tomography as a paradigm to study these questions. The measurement record is generated as a sequence of expectation values of a Hermitian observable evolving under repeated application of the Floquet map of the quantum kicked top. We construct a quantity to capture the scrambling of systematic errors, an out-of-time-ordered correlator (OTOC), which serves as a signature of chaos and quantifies the spread of errors. We show that the spread of errors, as quantified by the OTOC, is related to the operator Loschmidt echo, which is defined as the Hilbert-Schmidt inner product of the operators O n, and O ’ n generated from repeated application of the Floquet map for ideal (unperturbed) dynamics and the true (perturbed) dynamics, respectively. This also gives us an operational interpretation of Loschmidt echo (LE) for operators by connecting it to the performance of quantum tomography. We show how our results demonstrate not only a link between LE and scrambling of errors different than previous studies, but also that such a link can have operational consequences in quantum information processing.
Journal/Review: CHAOS
Volume: 36 (3) Pages from: 33129-1 to: 33129-10
More Information: We are grateful to Arul Lakshminarayan for useful discussions. We thank Sreeram PG for the helpful discussions. We thank B. S. Datta Vikas for his inputs during the initial stage of this work. The authors would like to acknowledge HPCE, IIT Madras, for providing the computational facility for numerical simulations. This work was supported, in part, by Grant No. DST/ICPS/QusT/Theme-3/2019/Q69 and New Faculty Seed Grant from IIT Madras. The authors were supported, in part, by a grant fro m Mphasis to the Centre for Quantum Information, Communication, and Computing (CQuICC) at IIT Madras.KeyWords: Dynamics; TrajectoriesDOI: 10.1063/5.0289048
