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Quantum Variational Learning of the Entanglement Hamiltonian

Kokail, Christian and Sundar, Bhuvanesh and Zache, Torsten V. and Elben, Andreas and Vermersch, Benoît and Dalmonte, Marcello and van Bijnen, Rick and Zoller, Peter (2021) Quantum Variational Learning of the Entanglement Hamiltonian. Physical Review Letters, 127 (17). Art. No. 170501. ISSN 0031-9007. doi:10.1103/PhysRevLett.127.170501.

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Learning the structure of the entanglement Hamiltonian (EH) is central to characterizing quantum many-body states in analog quantum simulation. We describe a protocol where spatial deformations of the many-body Hamiltonian, physically realized on the quantum device, serve as an efficient variational ansatz for a local EH. Optimal variational parameters are determined in a feedback loop, involving quench dynamics with the deformed Hamiltonian as a quantum processing step, and classical optimization. We simulate the protocol for the ground state of Fermi-Hubbard models in quasi-1D geometries, finding excellent agreement of the EH with Bisognano-Wichmann predictions. Subsequent on-device spectroscopy enables a direct measurement of the entanglement spectrum, which we illustrate for a Fermi Hubbard model in a topological phase.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Sundar, Bhuvanesh0000-0002-8867-360X
Zache, Torsten V.0000-0003-3549-7160
Elben, Andreas0000-0003-1444-6356
Vermersch, Benoît0000-0001-6781-2079
Dalmonte, Marcello0000-0001-5338-4181
van Bijnen, Rick0000-0002-0979-2521
Zoller, Peter0000-0003-4014-1505
Additional Information:© 2021 American Physical Society. Received 12 May 2021; revised 20 August 2021; accepted 1 September 2021; published 22 October 2021. We thank L. K. Joshi, R. Kaubrügger, J. Carrasco, J. Yu, and B. Kraus for valuable discussions. We thank Ana Maria Rey and Murray Holland for a careful reading of the manuscript. We acknowledge funding from the European Union’s Horizon 2020 research and innovation programme under Grant Agreement No. 817482 (Pasquans) and No. 731473 (QuantERA via QT-FLAG). Furthermore, this work was supported by the Simons Collaboration on Ultra-Quantum Matter, which is a grant from the Simons Foundation (651440, P. Z.), and LASCEM by AFOSR No. 64896-PH-QC. M. D. is partly supported by the ERC under Grant No. 758329 (AGEnTh). A. E. acknowledges funding by the German National Academy of Sciences Leopoldina under the Grant No. LPDS 2021-02. B. V. acknowledges funding from the Austrian Science Foundation (FWF, P 32597 N), and the French National Research Agency (ANR-20-CE47-0005, JCJC project QRand). The computational results presented here have been achieved (in part) using the LEO HPC infrastructure of the University of Innsbruck.
Group:Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
European Research Council (ERC)817482
European Research Council (ERC)731473
Simons Foundation651440
Air Force Office of Scientific Research (AFOSR)64896-PH-QC
European Research Council (ERC)758329
Deutsche Akademie der Naturforscher LeopoldinaLPDS 2021-02
FWF Der WissenschaftsfondsP 32597 N
Agence Nationale pour la Recherche (ANR)ANR-20-CE47-0005
Issue or Number:17
Record Number:CaltechAUTHORS:20211108-205323673
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111791
Deposited By: Tony Diaz
Deposited On:08 Nov 2021 21:25
Last Modified:08 Nov 2021 21:25

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