Muzhou Ma - Quantum Science and Engineering Seminar

High-Rate qLDPC Processors

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. In this work, we introduce mitten codes, a family of qLDPC processor codes with encoding rate 20% and check weight 9, constructed from non-abelian groups. The non-abelian structure evades stringent distance bounds suffered by their abelian counterparts, allowing mitten codes to reach distance 18 and beyond with only a few hundred data qubits. All logical operators of a mitten code are related by the underlying group action, and this symmetry yields a modular, low-overhead logical toolkit: full Clifford operations follow from bridging just two reusable seed surgery gadgets of tens of qubits each, or from a single fixed extractor.  Furthermore, qLDPC processors based on mitten codes support parallel magic-state injection into all logical qubits at once and high-rate surgery that executes many logical measurements in parallel. Under circuit-level depolarizing noise, our fast decoder shows, without extrapolation, that the [[300,60,14]] code attains 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. Directly decoding 15 billion surgery experiments on the [[540,108,18]] code at 0.1% PER, we observe only two logical failures, thereby demonstrating a qLDPC processor capable of running ~10^{10} logical operations. Our decoder achieves this accuracy while being 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.

Bio: Muzhou (Richard) Ma is a PhD student at Caltech, advised by Prof. John Preskill and Prof. Hsin-Yuan (Robert) Huang. His research is in quantum information theory, with a particular interest in understanding what the information-theoretical interpretations of Nature are, and how they shape the capabilities and limitations of computation.