PIRSA:22040103

Quantum error correction meets continuous symmetries: fundamental trade-offs and case studies

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}}
          }

Sisi Zhou Perimeter Institute for Theoretical Physics

Talk number PIRSA:22040103
DOI 10.48660/22040103
Collection
Talk Type Scientific Series
Subject

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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