Symmetry breaking and error correction in open quantum systems
- URL: http://arxiv.org/abs/2008.02816v1
- Date: Thu, 6 Aug 2020 18:00:11 GMT
- Title: Symmetry breaking and error correction in open quantum systems
- Authors: Simon Lieu, Ron Belyansky, Jeremy T. Young, Rex Lundgren, Victor V.
Albert, Alexey V. Gorshkov
- Abstract summary: We show how to recover the logical information after any gap-preserving strong-symmetric error.
Our study forges a connection between driven-dissipative phase transitions and error correction.
- Score: 0.9786690381850356
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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
$\mathbb{Z}_n$ symmetry breaking transitions for both cases. In the case of
$\mathbb{Z}_2$, 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.
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