Unraveling the emergence of quantum state designs in systems with symmetry

Year: 2024

Authors: Varikuti N.D., Bandyopadhyay S.

Autors Affiliation: Indian Inst Technol Madras, Dept Phys, Chennai 600036, India; Indian Inst Technol Madras, Ctr Quantum Informat Commun & Comp CQuICC, Chennai 600036, India; Univ Trento, Pitaevskii BEC Ctr, CNR INO & Dipartimento Fis, Via Sommarive 14, I-38123 Trento, Italy; Trento Inst Fundamental Phys & Applicat, INFN TIFPA, Via Sommarive 14, I-38123 Trento, Italy.

Abstract: Quantum state designs, by enabling an efficient sampling of random quantum states, play a quintessential role in devising and bench- marking various quantum protocols with broad applications ranging from circuit designs to black hole physics. Symmetries, on the other hand, are expected to reduce the randomness of a state. Despite being ubiquitous, the effects of symmetry on quantum state designs remain an outstanding question. The recently introduced projected ensemble framework generates efficient approximate state tdesigns by hinging on projective measurements and many-body quantum chaos. In this work, we examine the emergence of state designs from the random generator states exhibiting symmetries. Leveraging on translation symmetry, we analytically establish a sufficient condition for the measurement basis leading to the state t-designs. Then, by making use of the trace distance measure, we numerically investigate the convergence to the designs. Subsequently, we inspect the violation of the sufficient condition to identify bases that fail to converge. We further demonstrate the emergence of state designs in a physical system by studying the dynamics of a chaotic tilted field Ising chain with translation symmetry. We find faster convergence of the trace distance during the early time evolution in comparison to the cases when the symmetry is broken. To delineate the general applicability of our results, we extend our analysis to other symmetries. We expect our findings to pave the way for further exploration of deep thermalization and equilibration of closed and open quantum many-body systems.

Journal/Review: QUANTUM

Volume: 8      Pages from: 1456-1  to: 1456-29

More Information: We gratefully acknowledge useful discussions with Vaibhav Madhok, Arul Lakshminarayan, Philipp Hauke, and N. Ramadas. We thank Andrea Legramandi for reading the manuscript and providing useful suggestions. N.D.V. acknowledges fund ing from the Department of Science and Technology, Govt of India, under Grant No. DST/ICPS/QusT/Theme-3/2019/Q69, and partial support by a grant from Mphasis to the Centre for Quantum Information, Communication, and Computing (CQuICC) at IIT Madras. S.B. acknowledges funding from the European Union under NextGenerationEU Prot. n. 2022ATM8FY (CUP: E53D23002240006) , European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 804305) , Provincia Autonoma di Trento, Q@TN, the joint lab between University of Trento, FBK-Fondazione Bruno Kessler, INFN-National Institute for Nuclear Physics and CNR-National Research Council. Views and opinions ex-pressed are however those of the author (s) only and do not necessarily reflect those of the European Union or European Commission. Neither the European Union nor the granting authority can be held responsible for them. S.B. acknowledges CINECA for the use of HPC resources under ISCRA-C projects ISSYK-2 (HP10CP8XXF) and DISYK (HP10CGNZG9) .
KeyWords: Statistical-mechanics; Thermalization; Simulations; Chaos
DOI: 10.22331/q-2024-08-29-1456