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This research proposes a specialized quantum error correction scheme for cat qubits that exploits their inherent noise bias to protect only against bit-flip errors using modified Reed-Solomon codes. By implementing a two-layer "Tornado" concatenation architecture, the authors demonstrate significantly improved logical error scaling compared to standard repetition or standalone RS codes in Monte-Carlo simulations. The work provides concrete circuit constructions and overhead analysis relevant for fault-tolerant architectures leveraging biased-noise qubits.
Biased-Noise Quantum Reed--Solomon Codes and a Tornado Concatenation for Cat Qubits
arXiv:2607.13105v2 Announce Type: replace Abstract: Dissipative cat qubits exponentially suppress one Pauli error channel with the mean photon number, leaving the conjugate bit-flip error as the dominant failure mode. This strong noise bias makes the full machinery of general quantum error correction unnecessary: a code need only protect against a single error type, and any classical linear code can be promoted to a Clifford stabilizer code that does exactly this. We use this observation to build a \emph{bit-flip-only} quantum Reed--Solomon (RS) code. Starting from the maximum-distance-separable RS code $[7,3,5]$ over $\GF(2^3)$, we binary-expand it to the linear code $[21,9,6]$ over $\GF(2)$ and realize it as a $[[21,9,d_X=6,d_Z=1]]$ bit-flip code whose stabilizers are products of $Z$ operators. Because no phase-flip correction is attempted, the construction discards the redundancy that standard quantum RS codes spend on correcting $Z$ errors -- which a strongly biased cat qubit renders unnecessary -- and yields a shallow Clifford circuit that samples directly in Stim. Errors are decoded by an optimal bounded-distance syndrome-lookup table. We then introduce a \emph{Tornado} architecture: a two-layer concatenation that wraps every position of the outer RS code in an inner distance-three repetition code, yielding a $[[63,9,18]]$ code decoded by a two-stage inner majority vote and outer lookup decoder. Monte-Carlo simulation shows that at a physical bit-flip rate $p=0.1$ the Tornado code reaches a logical error rate $\pL \approx 5.3\times10^{-3}$, below both parent codes, and that its logical error rate scales as $\pL \propto p^{6}$ at low $p$, in contrast to $p^{2}$ for the repetition code and $p^{3}$ for the standalone RS code. We give the exact construction, the error and circuit model, an asymptotic scaling analysis, and an honest account of the overhead cost and single-shot assumptions.
Abstract:Dissipative cat qubits exponentially suppress one Pauli error channel with the mean photon number, leaving the conjugate bit-flip error as the dominant failure mode. This strong noise bias makes the full machinery of general quantum error correction unnecessary: a code need only protect against a single error type, and any classical linear code can be promoted to a Clifford stabilizer code that does exactly this. We use this observation to build a \emph{bit-flip-only} quantum Reed--Solomon (RS) code. Starting from the maximum-distance-separable RS code $[7,3,5]$ over $\GF(2^3)$, we binary-expand it to the linear code $[21,9,6]$ over $\GF(2)$ and realize it as a $[[21,9,d_X=6,d_Z=1]]$ bit-flip code whose stabilizers are products of $Z$ operators. Because no phase-flip correction is attempted, the construction discards the redundancy that standard quantum RS codes spend on correcting $Z$ errors -- which a strongly biased cat qubit renders unnecessary -- and yields a shallow Clifford circuit that samples directly in Stim. Errors are decoded by an optimal bounded-distance syndrome-lookup table. We then introduce a \emph{Tornado} architecture: a two-layer concatenation that wraps every position of the outer RS code in an inner distance-three repetition code, yielding a $[[63,9,18]]$ code decoded by a two-stage inner majority vote and outer lookup decoder. Monte-Carlo simulation shows that at a physical bit-flip rate $p=0.1$ the Tornado code reaches a logical error rate $\pL \approx 5.3\times10^{-3}$, below both parent codes, and that its logical error rate scales as $\pL \propto p^{6}$ at low $p$, in contrast to $p^{2}$ for the repetition code and $p^{3}$ for the standalone RS code. We give the exact construction, the error and circuit model, an asymptotic scaling analysis, and an honest account of the overhead cost and single-shot assumptions.
All authors contributed equally. 12 pages, 3 figures, 2 tables. Winning project of MIT iQuHACK 2026, Alice & Bob Track
Quantum Physics (quant-ph); Information Theory (cs.IT)
arXiv:2607.13105 [quant-ph]
(or arXiv:2607.13105v2 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2607.13105 Focus to learn more arXiv-issued DOI via DataCite
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