2026/07/30 by Aditya Bhardwaj, Muzhou Ma, Nadine Meister +6 · 1 citation
Physics and Astronomy · #quant-ph
13 pages main text + 73 pages appendix; 13 figures
arxiv created 2026/07/30 · arxiv updated 2026/08/03
Despite significant progress on quantum low-density parity-check (qLDPC) codes, building qLDPC processors that are high-rate, high-throughput, hardware-friendly, and fast-to-decode remains a challenge. We introduce mitten codes, a family of qLDPC processor codes of encoding rate 20% and check weight 9, based on non-abelian groups. Their non-abelian structure evades distance bounds constraining abelian counterparts, allowing mitten codes to reach distance 18 and beyond with just a few hundred data qubits. The logical operators of a mitten code are related by the group action, yielding a modular, low-overhead logical toolkit: full Clifford operations follow from bridging two reusable seed surgery gadgets or from a single fixed extractor. Furthermore, qLDPC processors based on mitten codes support high-rate surgery that executes many logical measurements in parallel, and parallel magic-state injection into all logical qubits at once. Under circuit-level noise, with our fast decoder, the [ [300,60,14] ] mitten code achieves, without extrapolation, a block logical error rate of ∼10-11 per round at 0.1% physical error rate (PER), while the [ [ 975,195,≤ 24 ] ] code reaches ∼10-8 at 0.4% PER. Decoding 15 billion surgery experiments on the [ [540,108,18] ] code at 0.1% PER, we observe only two logical failures, demonstrating a qLDPC processor capable of running ∼1010 logical operations. Our decoder is compatible with sub-millisecond average latency per logical cycle, sufficient for real-time decoding on neutral atom hardware. Discovered by an end-to-end design pipeline built on sQetch, a distance estimator orders of magnitude faster than existing tools, and mapping efficiently onto near-term neutral atom and superconducting hardware, mitten codes open a practical path toward fault-tolerant quantum computation.