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Symmetry breaking and error correction in open quantum systems

Published

Author(s)

Simon K. Lieu, Ron Belyansky, Jeremy T. Young, Rex Lundgren, Victor Albert, Alexey Gorshkov

Abstract

Symmetry-breaking transitions are a well-understood phenomenon of closed quantum systems in quantum optics, condensed matter, and high energy physics. However, symmetry breaking in open systems is less thoroughly understood, in part due to the richer steady-state and symmetry structure that such systems possess. For the prototypical open system---a Lindbladian---a unitary symmetry can be imposed in a ''weak'' or a ''strong'' way. We characterize the possible $\mathbbZ}_n$ symmetry breaking transitions for both cases. In the case of $\mathbbZ}_2$, a weak-symmetry-broken phase guarantees at most a classical bit steady-state structure, while a strong-symmetry-broken phase admits a partially-protected steady-state qubit. Viewing photonic cat qubits through the lens of strong-symmetry breaking, we show how to dynamically recover the logical information after any gap-preserving strong-symmetric error; such recovery becomes perfect exponentially quickly in the number of photons. Our study forges a connection between driven-dissipative phase transitions and error correction.
Citation
Physical Review Letters

Keywords

open quantum systems, non-equilibrium phase transitions, quantum error correction

Citation

Lieu, S. , Belyansky, R. , Young, J. , Lundgren, R. , Albert, V. and Gorshkov, A. (2020), Symmetry breaking and error correction in open quantum systems, Physical Review Letters, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=930889 (Accessed May 10, 2021)
Created December 7, 2020, Updated February 23, 2021