Qudit-native measurement protocol for dynamical correlations using Hadamard tests

Year: 2025

Authors: Popov P.P., Geier K.T., Kasper V., Lewenstein M., Hauke P.

Autors Affiliation: Barcelona Inst Sci & Technol, Inst Ciencies Foton, Avinguda Carl Friedrich Gauss 3, Castelldefels 08860, Barcelona, Spain; Univ Trento, Pitaevskii BEC Ctr, CNR INO, I-38123 Trento, Italy; Univ Trento, Dipartimento Fis, I-38123 Trento, Italy; INFN, Trento Inst Fundamental Phys & Applicat, I-38123 Trento, Italy; Technol Innovat Inst, Quantum Res Ctr, POB 9639, Abu Dhabi, U Arab Emirates; Kipu Quantum GmbH, Greifswalderstr 226, D-10405 Berlin, Germany; ICREA, Passeig Lluis Co 23, Barcelona 08010, Spain.

Abstract: Dynamical correlations reveal important out-of-equilibrium properties of the underlying quantum many-body system, yet they are notoriously difficult to measure in experiments. While measurement protocols for dynamical correlations based on Hadamard tests for qubit quantum devices exist, they do not straightforwardly extend to qudits. Here, we propose a modified protocol to overcome this limitation by decomposing qudit observables into unitary operations that can be implemented and probed in a quantum circuit. We benchmark our algorithm numerically at the example of quench dynamics in a spin-1 XXZ chain with finite shot noise and demonstrate advantages in terms of the signal-to-noise ratio over established protocols based on linear response. Our scheme can readily be implemented on various platforms and offers a wide range of applications like variational quantum optimization and probing thermalization in many-body systems.

Journal/Review: PHYSICAL REVIEW A

Volume: 111 (4)      Pages from: 42604-1  to: 42604-10

More Information: The ICFO group acknowledges support from ERC AdG NOQIA; MCIN/AEI [PGC2018-0910.13039/501100011033, CEX2019-000910-S/10.13039/501100011033, Plan National FIDEUA PID2019-106901GB-I00, the Plan National STAMEENA PID2022-139099NB-I00 project funded by MCIN/AEI/10.13039/501100011033 and by the European Union NextGenerationEU/PRTR (PRTR-C17.I1) , FPI] ; QUANTERA MAQS PCI2019-111828-2; QUANTERA DYNAMITE PCI2022-132919 (QuantERA II Programme cofunded by the European Union’s Horizon 2020 program under Grant Agreement No. 101017733) , Ministry of Economic Affairs and Digital Transformation of the Spanish Government, through the QUANTUM ENIA project call – Quantum Spain project, and the European Union through the Recovery, Transformation, and Resilience Plan – NextGenerationEU within the framework of the Digital Spain 2026 Agenda; Fundacio Cellex; Fundacio Mir-Puig; Generalitat de Catalunya (European Social Fund FEDER and CERCA program, AGAUR Grant No. 2021 SGR 01452, QuantumCAT U16-011424, cofunded by ERDF Operational Program of Catalonia 2014-2020) ; Barcelona Supercomputing Center MareNostrum (FI-2023-1-0013) ; EU Quantum Flagship (PASQuanS2.1, 101113690) ; EU Horizon 2020 FET-OPEN OPTOlogic (Grant No. 899794) ; the EU Horizon Europe Program (Grant Agreement No. 101080086-NeQST) , ICFO Internal QuantumGaudi project; the European Union’s Horizon 2020 program under Marie Sklodowska-Curie Grant Agreement No. 847648; and La Caixa Junior Leaders fellowships, La Caixa Foundation (ID No. 100010434) : CF/BQ/PR23/11980043. This project received funding from the European Union’s Horizon Europe research and innovation program under Grant Agreement No. 101080086 NeQST, the European Union under NextGenerationEU PRIN 2022 Prot. No. 2022ATM8FY (CUP: E53D23002240006) , the Italian Ministry of University and Research (MUR) through the FARE grant for the project DAVNE (Grant No. R20PEX7Y3A) , the National Recovery and Resilience Plan (NRRP) , Mission 4 Component 2 Investment 1.4-Call for tender No. 1031 of the Italian Ministry for University and Research funded by the European Union – NextGenerationEU (Project No. CN_00000013) , and Project DYNAMITE QUANTERA2_00056 funded by the Ministry of University and Research through t he ERANET COFUND QuantERA II – 2021 call and cofunded by the European Union (H2020, Grant Agreement No. 101017733) . This work benefited from Q@TN, the joint laboratory between the University of Trento, Fondazione Bruno Kessler (FBK) , National Institute for Nuclear Physics (INFN) , and National Research Council (CNR) . We acknowledge support from Provincia Autonoma di Trento. P.P.P. also acknowledges support from the Secretaria d’Universitats i Recerca del Departament de Recerca i Universitats de la Generalitat de Catalunya under Grant No. 2024 FI-3 00390, as well as the European Social Fund Plus. Views and opinions expressed are, however, those of the author (s) only and do not necessarily reflect those of the Euro-pean Union, the European Commission, or the Italian Ministry of University and Research. Neither the European Union nor the granting authority can be held responsible for them.
KeyWords: Statistical-mechanics; Quantum; Thermalization; Chaos
DOI: 10.1103/PhysRevA.111.042604