PIRSA:22040103 Scientific Series Quantum Information

DOI10.48660/22040103

Series: Colloquium

Zhou, S. (2022). Quantum error correction meets continuous symmetries: fundamental trade-offs and case studies. Perimeter Institute. https://pirsa.org/22040103

Zhou, Sisi. Quantum error correction meets continuous symmetries: fundamental trade-offs and case studies. Perimeter Institute, Apr. 13, 2022, https://pirsa.org/22040103 

@misc{ pirsa_PIRSA:22040103,
  doi = {10.48660/22040103},
  url = {https://pirsa.org/22040103},
  author = {Zhou, Sisi},
  keywords = {Quantum Information},
  language = {en},
  title = {Quantum error correction meets continuous symmetries: fundamental trade-offs and case studies},
  publisher = {Perimeter Institute},
  year = {2022},
  month = {apr},
  note = {PIRSA:22040103 see, \url{https://pirsa.org}}
}

Abstract

Quantum error correction and symmetries are two key notions in quantum information and physics. The competition between them has fundamental implications in fault-tolerant quantum computing, many-body physics and quantum gravity. We systematically study the competition between quantum error correction and continuous symmetries associated with a quantum code in a quantitative manner. We derive various forms of trade-off relations between the quantum error correction inaccuracy and three types of symmetry violation measures. We introduce two frameworks for understanding and establishing the trade-offs based on the notions of charge fluctuation and gate implementation error. From the perspective of fault-tolerant quantum computing, we demonstrate fundamental limitations on transversal logical gates. We also analyze the behaviors of two near-optimal codes: a parametrized extension of the thermodynamic code, and quantum Reed–Muller codes.

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