• Open Access

Generalization of group-theoretic coherent states for variational calculations

Tommaso Guaita, Lucas Hackl, Tao Shi, Eugene Demler, and J. Ignacio Cirac
Phys. Rev. Research 3, 023090 – Published 3 May 2021

Abstract

We introduce families of pure quantum states that are constructed on top of the well-known Gilmore-Perelomov group-theoretic coherent states. We do this by constructing unitaries as the exponential of operators quadratic in Cartan subalgebra elements and by applying these unitaries to regular group-theoretic coherent states. This enables us to generate entanglement not found in the coherent states themselves, while retaining many of their desirable properties. Most importantly, we explain how the expectation values of physical observables can be evaluated efficiently. Examples include generalized spin-coherent states and generalized Gaussian states, but our construction can be applied to any Lie group represented on the Hilbert space of a quantum system. We comment on their applicability as variational families in condensed matter physics and quantum information.

  • Figure
  • Received 22 January 2021
  • Accepted 12 April 2021

DOI:https://doi.org/10.1103/PhysRevResearch.3.023090

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & TechnologyCondensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Authors & Affiliations

Tommaso Guaita1,2,*, Lucas Hackl3,4,†, Tao Shi5,6, Eugene Demler7, and J. Ignacio Cirac1,2

  • 1Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany
  • 2Munich Center for Quantum Science and Technology, Schellingstr. 4, 80799 Munich, Germany
  • 3School of Mathematics and Statistics & School of Physics, The University of Melbourne, Parkville, VIC 3010, Australia
  • 4QMATH, Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
  • 5CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
  • 6CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100049, China
  • 7Lyman Laboratory, Department of Physics, Harvard University, 17 Oxford St., Cambridge, Massachusetts 02138, USA

  • *tommaso.guaita@mpq.mpg.de
  • lucas.hackl@unimelb.edu.au

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Vol. 3, Iss. 2 — May - July 2021

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