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Paper 1
Relation Between Surface Codes and Hypermap-Homology Quantum Codes
Pradeep Sarvepalli
- Year
- 2013
- Journal
- arXiv preprint
- DOI
- arXiv:1312.6344
- arXiv
- 1312.6344
Recently, a new class of quantum codes based on hypermaps were proposed. These codes are obtained from embeddings of hypergraphs as opposed to surface codes which are obtained from the embeddings of graphs. It is natural to compare these two classes of codes and their relation to each other. In this context two related questions are addressed in this paper: Can the parameters of hypermap-homology codes be superior to those of surface codes and what is precisely the relation between these two classes of quantum codes? We show that a canonical hypermap code is identical to a surface code while a noncanonical hypermap code can be transformed to a surface code by CNOT gates alone. Our approach is constructive; we construct the related surface code and the transformation involving CNOT gates.
Open paperPaper 2
Estimating and decoding coherent errors of QEC experiments with detector error models
Evangelia Takou, Kenneth R. Brown
- Year
- 2025
- Journal
- arXiv preprint
- DOI
- arXiv:2510.23797
- arXiv
- 2510.23797
Decoders of quantum error correction (QEC) experiments make decisions based on detected errors and the expected rates of error events, which together comprise a detector error model. Here we show that the syndrome history of QEC experiments is sufficient to detect and estimate coherent errors, removing the need for prior device benchmarking experiments. Importantly, our method shows that experimentally determined detector error models work equally well for both stochastic and coherent noise regimes. We model fully-coherent or fully-stochastic noise for repetition and surface codes and for various phenomenological and circuit-level noise scenarios, by employing Majorana and Monte Carlo simulators. We capture the interference of coherent errors, which appears as enhanced or suppressed physical error rates compared to the stochastic case, and also observe hyperedges that do not appear in the corresponding Pauli-twirled models. Finally, we decode the detector error models undergoing coherent noise and find different thresholds compared to detector error models built based on the stochastic noise assumption.
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