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Paper 1
Noisy-Syndrome Decoding of Hypergraph Product Codes
Venkata Gandikota, Elena Grigorescu, Vatsal Jha, S. Venkitesh
- Year
- 2025
- Journal
- arXiv preprint
- DOI
- arXiv:2510.07602
- arXiv
- 2510.07602
Hypergraph product codes are a prototypical family of quantum codes with state-of-the-art decodability properties. Recently, Golowich and Guruswami (FOCS 2024) showed a reduction from quantum decoding to syndrome decoding for a general class of codes, which includes hypergraph product codes. In this work we consider the "noisy" syndrome decoding problem for hypergraph product codes, and show a similar reduction in the noisy setting, addressing a question posed by Golowich and Guruswami. Our results hold for a general family of codes wherein the code and the dual code are "simultaneously nice"; in particular, for codes admitting good syndrome decodability and whose duals look "similar". These include expander codes, Reed-Solomon codes, and variants.
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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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