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Symmetry Breaking and Error Correction in Open Quantum Systems.

Simon Lieu1,2, Ron Belyansky1,2, Jeremy T Young1

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We explore symmetry breaking in open quantum systems, distinguishing between weak and strong symmetry breaking. Strong symmetry breaking in Z2 systems protects quantum information in photonic cat qubits, enabling error correction.

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Area of Science:

  • Quantum physics
  • Quantum optics
  • Condensed matter physics

Background:

  • Symmetry breaking is understood in closed quantum systems.
  • Symmetry breaking in open quantum systems is less understood due to complex steady-state structures.

Purpose of the Study:

  • Characterize Z_n symmetry-breaking transitions in open quantum systems (Lindbladians).
  • Differentiate between weak and strong symmetry imposition.
  • Investigate implications for quantum information and error correction.

Main Methods:

  • Analysis of Lindbladian dynamics.
  • Characterization of Z_n symmetry breaking.
  • Application to photonic cat qubits.

Main Results:

  • Weak Z2 symmetry breaking leads to classical steady states.
  • Strong Z2 symmetry breaking allows for partially protected steady-state qubits.
  • Photonic cat qubits exhibit error recovery after strong symmetric errors, improving with photon number.

Conclusions:

  • Established a link between driven-dissipative phase transitions and quantum error correction.
  • Demonstrated the potential of strong symmetry breaking for protecting quantum information.