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Paper 1

Degeneracy Cutting: A Local and Efficient Post-Processing for Belief Propagation Decoding of Quantum Low-Density Parity-Check Codes

Kento Tsubouchi, Hayata Yamasaki, Shiro Tamiya

Year

2025

Journal

arXiv preprint

DOI

arXiv:2510.08695

arXiv

2510.08695

Quantum low-density parity-check (qLDPC) codes are promising for realizing scalable fault-tolerant quantum computation due to their potential for low-overhead protocols. A common approach to decoding qLDPC codes is to use the belief propagation (BP) decoder, followed by a post-processing step to enhance decoding accuracy. For real-time decoding, the post-processing algorithm is desirable to have a small computational cost and rely only on local operations on the Tanner graph to facilitate parallel implementation. To address this requirement, we propose degeneracy cutting (DC), an efficient post-processing technique for the BP decoder that operates on information restricted to the support of each stabilizer generator. DC selectively removes one variable node with the lowest error probability for each stabilizer generator, significantly improving decoding performance while retaining the favorable computational scaling and structure amenable to parallelization inherent to BP. We further extend our method to realistic noise models, including phenomenological and circuit-level noise models, by introducing the detector degeneracy matrix, which generalizes the notion of stabilizer-induced degeneracy to these settings. Numerical simulations demonstrate that BP+DC achieves decoding performance approaching that of BP followed by ordered statistics decoding (BP+OSD) in several settings, while requiring significantly less computational cost. Our results present BP+DC as a promising decoder for fault-tolerant quantum computing, offering a valuable balance of accuracy, efficiency, and suitability for parallel implementation.

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Paper 2

To break, or not to break: Symmetries in adaptive quantum simulations, a case study on the Schwinger model

Karunya Shailesh Shirali, Kyle Sherbert, Yanzhu Chen, Adrien Florio, Andreas Weichselbaum, Robert D. Pisarski, Sophia E. Economou

Year

2025

Journal

arXiv preprint

DOI

arXiv:2510.03083

arXiv

2510.03083

We investigate the role of symmetries in constructing resource-efficient operator pools for adaptive variational quantum eigensolvers. In particular, we focus on the lattice Schwinger model, a discretized model of $1+1$ dimensional electrodynamics, which we use as a proxy for spin chains with a continuum limit. We present an extensive set of simulations comprising a total of $11$ different operator pools, which all systematically and independently break or preserve a combination of discrete translations, the conservation of charge (magnetization) and the fermionic locality of the excitations. Circuit depths are the primary bottleneck in current quantum hardware, and we find that the most efficient ansätze in the near-term are obtained by pools that $\textit{break}$ translation invariance, conserve charge, and lead to shallow circuits. On the other hand, we anticipate the shot counts to be the limiting factor in future, error-corrected quantum devices; our findings suggest that pools $\textit{preserving}$ translation invariance could be preferable for such platforms.

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