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Autonomous error correction with pair-cat codes

Invited

Abstract

We introduce a driven-dissipative two-mode bosonic system whose reservoir causes simultaneous loss of two photons in each mode and whose steady states are superpositions of pair-coherent/Barut-Girardello coherent states. We show how quantum information encoded in a steady-state subspace of this system is exponentially immune to phase drifts (cavity dephasing) in both modes. Additionally, it is possible to protect information from arbitrary photon loss in either (but not simultaneously both) of the modes by continuously monitoring the difference between the expected photon numbers of the logical states. Despite employing more resources, the two-mode scheme enjoys two advantages over its one-mode cat-qubit counterpart with regards to implementation using current circuit QED technology. First, monitoring the photon number difference can be done without turning off the currently implementable dissipative stabilizing process. Second, a lower average photon number per mode is required to enjoy a level of protection at least as good as that of the cat-codes. We discuss circuit QED proposals and current experiments to stabilize the code states, perform gates, and protect against photon loss via either active syndrome measurement or an autonomous procedure. We introduce quasiprobability distributions allowing us to represent two-mode states of fixed photon number difference in a two-dimensional complex plane, instead of the full four-dimensional two-mode phase space.

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Presenters

  • Victor Albert

    NIST / QUICS @ UMD College Park, NIST/QUICS, UMD College Park, National Institute of Standards and Technology

Authors

  • Victor Albert

    NIST / QUICS @ UMD College Park, NIST/QUICS, UMD College Park, National Institute of Standards and Technology

  • Shantanu O Mundhada

    Quantum Circuits Inc., Yale University, Yale University, QCI

  • Alex Grimm

    Paul Scherrer Institute

  • Steven Touzard

    Natl University of Singapore, Department of physics, National University of Singapore, Yale University, Nat. Univ. of Singapore

  • Michel Devoret

    Yale University, Applied Physics Department, Yale University, Yale, Department of Applied Physics and Physics, Yale University, Applied Physics, Yale University, Departments of Applied Physics and Physics, Yale University

  • Liang Jiang

    University of Chicago, Department of Molecular Engineering, The University of Chicago, Pritzker School of Molecular Engineering, University of Chicago, Yale University, Pritzker school of molecular engineering, The University of Chicago