This proposal studies the practical fault tolerance of quantum low-density parity-check (qLDPC) codes through joint design of logical protocols, decoders, and code constructions.
The central claim is that overhead is governed by cross-layer compatibility: useful codes must support low-overhead syndrome extraction, fast decoding with guarantees, and efficient logical operations. My completed work supports this view via adaptive syndrome extraction and single-shot code-switching protocols, generalized matching decoders for 2D translationally-invariant codes with provable performance, and code-design tools based on effective distance, weight reduction, and automorphism structure. Building on these results, I will (i) formalize morphing-circuit syndrome extraction and mid-cycle logical symmetries, (ii) extend efficient decoding to larger structured 2D/3D families, and (iii) develop qLDPC constructions with improved connectivity and logical-gate support, including routes to high-rate non-Clifford logical operations. The expected outcome is a framework for architecture-aware co-design that lowers fault-tolerance overhead both in terms of asymptotic and finite-size performance.
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