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Bures and Sjöqvist metrics over thermal state manifolds for spin qubits and superconducting flux qubits

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Abstract

The interplay among differential geometry, statistical physics, and quantum information science has been increasingly gaining theoretical interest in recent years. In this paper, we present an explicit analysis of the Bures and Sjöqvist metrics over the manifolds of thermal states for specific spin qubit and the superconducting flux qubit Hamiltonian models. While the two metrics equally reduce to the Fubini-Study metric in the asymptotic limiting case of the inverse temperature approaching infinity for both Hamiltonian models, we observe that the two metrics are generally different when departing from the zero-temperature limit. In particular, we discuss this discrepancy in the case of the superconducting flux Hamiltonian model. We conclude the two metrics differ in the presence of a nonclassical behavior specified by the noncommutativity of neighboring mixed quantum states. Such a noncommutativity, in turn, is quantified by the two metrics in different manners. Finally, we briefly discuss possible observable consequences of this discrepancy between the two metrics when using them to predict critical and/or complex behavior of physical systems of interest in quantum information science.

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Acknowledgements

C.C. is grateful to the United States Air Force Research Laboratory (AFRL) Summer Faculty Fellowship Program for providing support for this work. C. C. acknowledges helpful discussions with Orlando Luongo, Cosmo Lupo, Stefano Mancini, and Hernando Quevedo. P.M.A. acknowledges support from the Air Force Office of Scientific Research (AFOSR). Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the Air Force Research Laboratory (AFRL).

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Authors and Affiliations

  1. SUNY Polytechnic Institute, Albany, NY, 12203, USA

    Carlo Cafaro

  2. Air Force Research Laboratory, Information Directorate, Rome, NY, 13441, USA

    Paul M. Alsing

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  1. Carlo Cafaro
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Correspondence to Carlo Cafaro.

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Cafaro, C., Alsing, P.M. Bures and Sjöqvist metrics over thermal state manifolds for spin qubits and superconducting flux qubits. Eur. Phys. J. Plus 138, 655 (2023). https://doi.org/10.1140/epjp/s13360-023-04267-9

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