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Paper 1
Transversal non-Clifford gates for quantum LDPC codes on sheaves
Ting-Chun Lin
- Year
- 2024
- Journal
- arXiv preprint
- DOI
- arXiv:2410.14631
- arXiv
- 2410.14631
A major goal in quantum computing is to build a fault-tolerant quantum computer. One approach involves quantum low-density parity-check (qLDPC) codes that support transversal non-Clifford gates. In this work, we provide a large family of such codes. The key insight is to interpret the logical operators of qLDPC codes as geometric surfaces and use the intersection number of these surfaces to define the non-Clifford operation. At a more abstract level, this construction is based on defining the cup product on the chain complex induced from a sheaf.
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Qubit-oscillator concatenated codes: decoding formalism & code comparison
Yijia Xu, Yixu Wang, En-Jui Kuo, Victor V. Albert
- Year
- 2022
- Journal
- arXiv preprint
- DOI
- arXiv:2209.04573
- arXiv
- 2209.04573
Concatenating bosonic error-correcting codes with qubit codes can substantially boost the error-correcting power of the original qubit codes. It is not clear how to concatenate optimally, given there are several bosonic codes and concatenation schemes to choose from, including the recently discovered GKP-stabilizer codes [Phys. Rev. Lett. 125, 080503 (2020)}] that allow protection of a logical bosonic mode from fluctuations of the mode's conjugate variables. We develop efficient maximum-likelihood decoders for and analyze the performance of three different concatenations of codes taken from the following set: qubit stabilizer codes, analog/Gaussian stabilizer codes, GKP codes, and GKP-stabilizer codes. We benchmark decoder performance against additive Gaussian white noise, corroborating our numerics with analytical calculations. We observe that the concatenation involving GKP-stabilizer codes outperforms the more conventional concatenation of a qubit stabilizer code with a GKP code in some cases. We also propose a GKP-stabilizer code that suppresses fluctuations in both conjugate variables without extra quadrature squeezing, and formulate qudit versions of GKP-stabilizer codes.
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