PIRSA:24050045

Emergent symmetries and their application to logical gates in quantum LDPC codes

APA

Zhu, G. (2024). Emergent symmetries and their application to logical gates in quantum LDPC codes. Perimeter Institute. https://pirsa.org/24050045

MLA

Zhu, Guanyu. Emergent symmetries and their application to logical gates in quantum LDPC codes. Perimeter Institute, May. 31, 2024, https://pirsa.org/24050045

BibTex

          @misc{ pirsa_PIRSA:24050045,
            doi = {10.48660/24050045},
            url = {https://pirsa.org/24050045},
            author = {Zhu, Guanyu},
            keywords = {Quantum Information},
            language = {en},
            title = {Emergent symmetries and their application to logical gates in quantum LDPC codes},
            publisher = {Perimeter Institute},
            year = {2024},
            month = {may},
            note = {PIRSA:24050045 see, \url{https://pirsa.org}}
          }
          

Guanyu Zhu IBM (United States)

Abstract

In this talk, I’ll discuss the deep connection between emergent k-form symmetries and transversal logical gates in quantum low-density parity-check (LDPC) codes. I’ll then present a parallel fault-tolerant quantum computing scheme for families of homological quantum LDPC codes defined on 3-manifolds with constant or almost-constant encoding rate using the underlying higher symmetries in our recent work. We derive a generic formula for a transversal T gate on color codes defined on general 3-manifolds, which acts as collective non-Clifford logical CCZ gates on any triplet of logical qubits with their logical-X membranes having a Z2 triple intersection at a single point. The triple intersection number is a topological invariant, which also arises in the path integral of the emergent higher symmetry operator in a topological quantum field theory (TQFT): the (Z2) 3 gauge theory. Moreover, the transversal S gate of the color code corresponds to a higher-form symmetry supported on a codimension-1 submanifold, giving rise to exponentially many addressable and parallelizable logical CZ gates. Both symmetries are related to gauged SPT defects in the (Z2) 3 gauge theory. We have then developed a generic formalism to compute the triple intersection invariants for general 3- manifolds. We further develop three types of LDPC codes supporting such logical gates with constant or almost-constant encoding rate and logarithmic distance. Finally, I’ll point out a connection between the gauged SPT defects in the 6D color code and a recently discovered non-Abelian self-correcting quantum memory in 5D. Reference: arXiv:2310.16982, arXiv:2208.07367, arXiv:2405.11719.