Quantum rainbow codes

APA

Pesah, A. (2024). Quantum rainbow codes. Perimeter Institute for Theoretical Physics. https://pirsa.org/24040115

MLA

Pesah, Arthur. Quantum rainbow codes. Perimeter Institute for Theoretical Physics, Apr. 24, 2024, https://pirsa.org/24040115

BibTex

          @misc{ scivideos_PIRSA:24040115,
            doi = {10.48660/24040115},
            url = {https://pirsa.org/24040115},
            author = {Pesah, Arthur},
            keywords = {Quantum Information},
            language = {en},
            title = {Quantum rainbow codes},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2024},
            month = {apr},
            note = {PIRSA:24040115 see, \url{https://scivideos.org/pirsa/24040115}}
          }
          

Arthur Pesah University College London

Source RepositoryPIRSA

Abstract

With the recent construction of quantum low-density parity-check (LDPC) codes with optimal asymptotic parameters, finding methods to perform low-overhead computation using those constructions has become a central problem of quantum error-correction. In particular, triorthogonal codes---which admit transversal non-Clifford operations---are of particular interest, but few examples of these codes are presently known. In our work, we introduce a new family of codes, the quantum rainbow codes, a generalization of pin codes and color codes, that can be constructed from any chain complex. When applied to the hypergraph product of three complexes, we show that those codes can implement transversal non-Clifford gates and have improved parameters compared to pin codes. Considering expander graphs with large girth as the input complexes, we can for instance obtain families of triorthogonal codes with parameters [[n,Θ(n^{2/3}),Θ(log(n))]].

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