Robust Encoding of a Qubit in a Molecule
Abstract
We construct quantum error-correcting codes that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of rotational states of a rigid body. These codes, which protect against both drift in the body's orientation and small changes in its angular momentum, may be well suited for robust storage and coherent processing of quantum information using rotational states of a polyatomic molecule. Extensions of such codes to rigid bodies with a symmetry axis are compatible with rotational states of diatomic molecules as well as nuclear states of molecules and atoms. We also describe codes associated with general non-Abelian groups and develop orthogonality relations for coset spaces, laying the groundwork for quantum information processing with exotic configuration spaces.
Additional Information
© 2020 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. Received 18 November 2019; revised 27 May 2020; accepted 21 July 2020; published 1 September 2020. We thank Rafael N. Alexander, Benjamin L. Augenbraun, Stephen Bartlett, Juani Bermejo-Vega, Giacomo Bighin, Igor N. Cherepanov, David DeMille, Christa Flühmann, Steven M. Girvin, Alexey V. Gorshkov, Nick Hutzler, Joe Iverson, Arian Jadbabaie, Dominik Jüstel, Alexei Yu. Kitaev, Roman Korol, Roman Krems, Richard Kueng, Dietrich Leibfried, Mikhail Lemeshko, Angelo Lucia, Kang-Kuen Ni, Igor Pak, Hannes Pichler, Shruti Puri, Gil Refael, Grant Salton, Eugene Tang, and Jun Ye for useful suggestions and discussions. We gratefully acknowledge support from ARO-LPS (W911NF-18-1-0103), NSF (PHY-1733907), the Walter Burke Institute for Theoretical Physics, and the Division of Physics, Mathematics, and Astronomy (PMA) at Caltech. The Institute for Quantum Information and Matter is an NSF Physics Frontiers Center. Our figures were drawn using Mathematica 12.Attached Files
Published - PhysRevX.10.031050.pdf
Submitted - 1911.00099.pdf
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Additional details
- Eprint ID
- 102499
- Resolver ID
- CaltechAUTHORS:20200413-094120710
- Army Research Office (ARO)
- W911NF-18-1-0103
- NSF
- PHY-1733907
- Walter Burke Institute for Theoretical Physics, Caltech
- Caltech Division of Physics, Mathematics and Astronomy
- Created
-
2020-04-13Created from EPrint's datestamp field
- Updated
-
2021-11-16Created from EPrint's last_modified field
- Caltech groups
- Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics