2026/07/14 by Cheng-You Ho, Daniel Wang, Simba Shi +2
#quant-ph #cs.IT #math.IT
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 bit-flip-only quantum Reed-Solomon (RS) code. Starting from the maximum-distance-separable RS code [7, 3, 5] over GF(23), we binary-expand it to the linear code [21, 9, 6] over GF(2) and realize it as a [[21, 9, dX = 6, dZ = 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 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 ≈ 5.3 × 10-3, below both parent codes, and that its logical error rate scales as pL ∝ p6 at low p, in contrast to p2 for the repetition code and p3 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.