Bivariate bicycle code
One of several Abelian 2BGA codes which admit time-optimal syndrome measurement circuits that can be implemented in a two-layer architecture, a generalization of the square-lattice architecture optimal for the surface codes.
The qubit connectivity graph is not quite a 2D grid and is instead decomposable into two planar subgraphs of degree three. There are \(n\) \(X\) and \(Z\) check operators, with each one of weight six.
- Kitaev surface code — Bivariate bicycle codes are on par with the surface code in terms of threshold, but admit a much higher ancilla-added encoding rate at the expense of having non-geometrically local weight-six check operators.
- S. Bravyi et al., “High-threshold and low-overhead fault-tolerant quantum memory”, (2023) arXiv:2308.07915
- P. Panteleev and G. Kalachev, “Degenerate Quantum LDPC Codes With Good Finite Length Performance”, Quantum 5, 585 (2021) arXiv:1904.02703 DOI
- A. G. Fowler, A. M. Stephens, and P. Groszkowski, “High-threshold universal quantum computation on the surface code”, Physical Review A 80, (2009) arXiv:0803.0272 DOI
- L. Z. Cohen et al., “Low-overhead fault-tolerant quantum computing using long-range connectivity”, Science Advances 8, (2022) arXiv:2110.10794 DOI
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“Bivariate bicycle code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/qcga