Knill error correction reduces circuit-level decoding for quantum LDPC codes to the simpler code-capacity decoder while remaining fault-tolerant under locally decaying noise.
High-threshold, low-overhead and single-shot decodable fault-tolerant quantum memory
4 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We present a new family of quantum low-density parity-check codes, which we call radial codes, obtained from the lifted product of a specific subset of classical quasi-cyclic codes. The codes are defined using a pair of integers $(r,s)$ and have parameters $[\![2r^2s,2(r-1)^2,\leq2s]\!]$, with numerical studies suggesting average-case distance linear in $s$. In simulations of circuit-level noise, we observe comparable error suppression to surface codes of similar distance while using approximately five times fewer physical qubits. This is true even when radial codes are decoded using a single-shot approach, which can allow for faster logical clock speeds and reduced decoding complexity. We describe an intuitive visual representation, canonical basis of logical operators and optimal-length stabiliser measurement circuits for these codes, and argue that their error correction capabilities, tunable parameters and small size make them promising candidates for implementation on near-term quantum devices.
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quant-ph 4representative citing papers
HAL heuristic produces explicit layouts for bivariate bicycle, tile, radial, and Tanner qLDPC codes on multilayer superconducting hardware, demonstrating that open-boundary designs reduce hardware demands with only moderate loss in logical efficiency.
CAbLECAR provides a robotics-inspired shuttle scheduler that enables QLDPC codes on tileable spin-qubit hardware, yielding up to 86% faster schedules and orders-of-magnitude gains in encoding efficiency and logical error rates over surface codes.
A family of quantum LDPC codes with encoding rates exceeding 1/2 achieves logical error rates of 10^{-13} per round on atom arrays under 0.1% circuit noise using hierarchical decoding.
citing papers explorer
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Simplified circuit-level decoding using Knill error correction
Knill error correction reduces circuit-level decoding for quantum LDPC codes to the simpler code-capacity decoder while remaining fault-tolerant under locally decaying noise.
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Placing and routing quantum LDPC codes in multilayer superconducting hardware
HAL heuristic produces explicit layouts for bivariate bicycle, tile, radial, and Tanner qLDPC codes on multilayer superconducting hardware, demonstrating that open-boundary designs reduce hardware demands with only moderate loss in logical efficiency.
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CAbLECAR: efficiently scheduling QLDPC codes on a tileable spin qubit chip with shuttling
CAbLECAR provides a robotics-inspired shuttle scheduler that enables QLDPC codes on tileable spin-qubit hardware, yielding up to 86% faster schedules and orders-of-magnitude gains in encoding efficiency and logical error rates over surface codes.
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Towards Ultra-High-Rate Quantum Error Correction with Reconfigurable Atom Arrays
A family of quantum LDPC codes with encoding rates exceeding 1/2 achieves logical error rates of 10^{-13} per round on atom arrays under 0.1% circuit noise using hierarchical decoding.