Researchers from the California Institute of Technology (Caltech) and Oratomic, Inc. have introduced mitten codes, a new family of non-abelian quantum low-density parity-check (qLDPC) error-correcting codes. Published on arXiv under the title “High-rate qLDPC processors,” the research addresses the long-standing challenge of creating fault-tolerant quantum processors that simultaneously achieve high encoding rates, low logical gadget overheads, hardware compatibility, and fast, accurate decoding.
Mitten codes achieve a constant 20% encoding rate with a low check weight of 9. They are constructed as lifted product codes using classical base matrices over non-abelian groups such as C5×S3, C4×D10, and C13⋊C15. By leveraging non-abelian group structures, the design evades the severe distance bounds—often capped at distance 6—that limit abelian codes of the same base-matrix shape. This structural breakthrough allows mitten codes to reach code distances of 18 to 24 and beyond using only a few hundred physical data qubits.
A central architectural feature of mitten codes is their canonical logical basis, where the logical operators for all encoded logical qubits are related by the underlying non-abelian group action. Because every logical operator can be mapped to any other through group operations, the processor supports a modular and highly reusable logical toolkit. Universal Clifford operations can be executed using just five reusable graph surgery gadgets generated from two small seed gadgets. The architecture also enables high-throughput instruction sets—including parallel lattice surgery that measures multiple logical qubit pairs simultaneously—and parallel magic-state injection across all logical qubits to deliver non-Clifford resources.
To evaluate processing capacity under circuit-level noise, the authors developed a telescoping decoder that combines GPU-accelerated Belief Propagation kernels with exact integer-programming solvers. In memory simulations at a 0.1% physical error rate under circuit-level depolarizing noise, a 300-data-qubit mitten code achieved a block logical error rate of approximately 10−11 per syndrome extraction round. At a 0.4% physical error rate, a 975-data-qubit code encoding 195 logical qubits reached an error rate of 10−8 per round, outperforming a benchmark stack of 195 rotated surface codes comprising over 100,000 physical qubits by nearly two orders of magnitude in both physical qubit count and logical error rate. Furthermore, directly decoding 15 billion surgery experiments on a 540-data-qubit code yielded only two logical failures, demonstrating capacity for over 10 billion logical operations with sub-millisecond average per-cycle decoding latency.
The authors mapped mitten codes onto both neutral atom arrays and superconducting qubit platforms. On neutral atom systems, non-local check measurements are executed by shuttling ancilla atoms via crossed Acousto-Optic Deflectors, where group product factorizations allow atom movements to decompose into clean row shifts and column swaps with estimated cycle times between 5 and 15 milliseconds. On superconducting chips, mitten codes were proven to have a planar thickness of 3, achieving hardware layout complexity scores on multi-chip stackups comparable to bivariate bicycle codes while encoding substantially more qubits per block. The entire mitten code family was discovered using an automated discovery pipeline built around sQetch, a GPU-accelerated distance estimator operating up to 800,000 times faster than conventional distance estimation tools.
Review the full pre-print study on arXiv here, and examine our previous coverage of qLDPC Code Architectures and Fault-Tolerant Processing here.
August 3, 2026
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