Logical gates at any Clifford-hierarchy level can be encoded as Pauli logicals of an auxiliary tensor-product code, and boundary deformations in that auxiliary code yield new constant-depth logical gates in toric and fracton codes.
High-rate qLDPC processors
8 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
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 ${\sim}10^{-11}$ per round at $0.1\%$ physical error rate (PER), while the $[\![ 975,195,\leq 24 ]\!]$ code reaches ${\sim}10^{-8}$ 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 ${\sim}10^{10}$ 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.
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quant-ph 8years
2026 8roles
background 2representative citing papers
R-linear chain maps between a QLDPC code and a copy of itself define fast, block-addressable surgery, and on the [[90,8,10]] and [[198,8,16]] radial codes every same-Pauli-type logical subspace is measurable in a single syndrome round.
A black-box post-processor estimates per-class truncated free energies from stochastic decoder samples and improves decoding thresholds on toric, color, and bivariate-bicycle codes relative to the same-pool minimum-weight baseline.
Parity Twine Networks are adapted to neutral-atom platforms with CZ, CZSWAP, and iSWAP gates, achieving up to 1000x estimated fidelity improvement for the 30-qubit QFT over competing approaches.
A multi-agent search over balanced-product quantum LDPC codes finds new finite-length instances, including [[288,16,18]], [[288,18,18]], and [[234,28,18]], with leading rate-distance scores under fixed weight constraints.
GALA codes are a new construction family of rate-1/2 quantum LDPC codes with AOD-compatible moves and certified distances up to 16, including compact instances like [[132,30,12]].
A search over non-abelian groups yields new moderate-blocklength quantum Tanner code instances whose randomized distance bounds exceed 20, with decoder pseudo-thresholds comparable to shorter codes.
citing papers explorer
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Computing with qLDPC Codes by Climbing the Chain Map Hierarchy
Logical gates at any Clifford-hierarchy level can be encoded as Pauli logicals of an auxiliary tensor-product code, and boundary deformations in that auxiliary code yield new constant-depth logical gates in toric and fracton codes.
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Lifted surgery: Fast processing with QLDPC codes
R-linear chain maps between a QLDPC code and a copy of itself define fast, block-addressable surgery, and on the [[90,8,10]] and [[198,8,16]] radial codes every same-Pauli-type logical subspace is measurable in a single syndrome round.
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Approximate maximum-likelihood decoding via truncated free energies
A black-box post-processor estimates per-class truncated free energies from stochastic decoder samples and improves decoding thresholds on toric, color, and bivariate-bicycle codes relative to the same-pool minimum-weight baseline.
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Optimizing Atom Transport, Gate-Count and Depth with Parity Twine
Parity Twine Networks are adapted to neutral-atom platforms with CZ, CZSWAP, and iSWAP gates, achieving up to 1000x estimated fidelity improvement for the 30-qubit QFT over competing approaches.
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Multi-agent discovery of practical quantum LDPC codes
A multi-agent search over balanced-product quantum LDPC codes finds new finite-length instances, including [[288,16,18]], [[288,18,18]], and [[234,28,18]], with leading rate-distance scores under fixed weight constraints.
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Designer Codes from GALA: Compact, Self-Dual, and Rate-1/2 QEC on Reconfigurable Atom Arrays
GALA codes are a new construction family of rate-1/2 quantum LDPC codes with AOD-compatible moves and certified distances up to 16, including compact instances like [[132,30,12]].
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Quantum Tanner Codes at Moderate Blocklength
A search over non-abelian groups yields new moderate-blocklength quantum Tanner code instances whose randomized distance bounds exceed 20, with decoder pseudo-thresholds comparable to shorter codes.
- Quantum error correction at ultra-low overhead