Quantum Variational Learning of the Entanglement Hamiltonian
Abstract
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.
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.Attached Files
Published - PhysRevLett.127.170501.pdf
Accepted Version - 2105.04317.pdf
Supplemental Material - SM.pdf
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Additional details
- Eprint ID
- 111791
- Resolver ID
- CaltechAUTHORS:20211108-205323673
- 817482
- European Research Council (ERC)
- 731473
- European Research Council (ERC)
- 651440
- Simons Foundation
- 64896-PH-QC
- Air Force Office of Scientific Research (AFOSR)
- 758329
- European Research Council (ERC)
- LPDS 2021-02
- Deutsche Akademie der Naturforscher Leopoldina
- P 32597 N
- FWF Der Wissenschaftsfonds
- ANR-20-CE47-0005
- Agence Nationale pour la Recherche (ANR)
- Created
-
2021-11-08Created from EPrint's datestamp field
- Updated
-
2021-11-08Created from EPrint's last_modified field
- Caltech groups
- Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics