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Paper 1
The surface code beyond Pauli channels: Logical noise coherence, information-theoretic measures, and errorfield-double phenomenology
Jan Behrends, Benjamin Béri
- Year
- 2024
- Journal
- arXiv preprint
- DOI
- arXiv:2412.21055
- arXiv
- 2412.21055
We consider the surface code under errors featuring both coherent and incoherent components and study the coherence of the corresponding logical noise channel and how this impacts information-theoretic measures of code performance, namely coherent information and quantum relative entropy. Using numerical simulations and developing a phenomenological field theory, focusing on the most general single-qubit X-error channel, we show that, for any nonzero incoherent noise component, the coherence of the logical noise is exponentially suppressed with the code distance. We also find that the information-theoretic measures require this suppression to detect optimal thresholds for Pauli recovery; for this they thus require increasingly large distances for increasing error coherence and ultimately break down for fully coherent errors. To obtain our results, we develop a statistical mechanics mapping and a corresponding matrix-product-state algorithm for approximate syndrome sampling. These methods enable the large scale simulation of these non-Pauli errors, including their maximum-likelihood thresholds, away from the limits captured by previous approaches.
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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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