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Paper 1

Hierarchical quantum decoders

Nirupam Basak, Ankith Mohan, Andrew Tanggara, Tobias Haug, Goutam Paul, Kishor Bharti

Year

2026

Journal

arXiv preprint

DOI

arXiv:2601.21715

arXiv

2601.21715

Decoders are a critical component of fault-tolerant quantum computing. They must identify errors based on syndrome measurements to correct quantum states. While finding the optimal correction is NP-hard and thus extremely difficult, approximate decoders with faster runtime often rely on uncontrolled heuristics. In this work, we propose a family of hierarchical quantum decoders with a tunable trade-off between speed and accuracy while retaining guarantees of optimality. We use the Lasserre Sum-of-Squares (SOS) hierarchy from optimization theory to relax the decoding problem. This approach creates a sequence of Semidefinite Programs (SDPs). Lower levels of the hierarchy are faster but approximate, while higher levels are slower but more accurate. We demonstrate that even low levels of this hierarchy significantly outperform standard Linear Programming relaxations. Our results on rotated surface codes and honeycomb color codes show that the SOS decoder approaches the performance of exact decoding. We find that Levels 2 and 3 of our hierarchy perform nearly as well as the exact solver. We analyze the convergence using rank-loop criteria and compare the method against other relaxation schemes. This work bridges the gap between fast heuristics and rigorous optimal decoding.

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Paper 2

Active multiplexing for scalable generation and manipulation of photonic quantum states.

Kaneda F, Yabuno M.

Year

2026

Journal

Nano Converg

DOI

10.1186/s40580-026-00540-6

arXiv

-

No abstract.

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