Catalytic Quantum Error Correction: Theory, Efficient Catalyst Preparation, and Numerical Benchmarks

Abstract

Quantum computers promise transformative speedups, but environmental noise destroys their fragile states. Conventional quantum error correction (QEC) encodes information redundantly across physical qubits, yet fails above a threshold of about $1\%$ and incurs polynomial qubit overhead. A recent theorem [Shiraishi2024] from the resource theory of coherence shows that catalytic covariant operations amplify coherence at an unbounded rate, but this result has never been cast as an operational protocol. The challenge is to turn an asymptotic theorem into a recovery scheme that works at any noise strength with realistic resources. Here we show that catalytic coherence amplification can be cast as an error-correction primitive, Catalytic Quantum Error Correction (CQEC), which recovers a known target state from noisy copies without any error \emph{magnitude} threshold whenever the target's coherent modes are preserved. Whereas existing QEC degrades above its threshold, CQEC maintains $F > 0.999$ across 200~configurations spanning $d = 4$--$64$, and the impractical $n^{*} \sim d^{4} e^{2\gamma}$ copy requirement is reduced by nine orders of magnitude via a three-stage pipeline combining CPMG dynamical decoupling, Clifford twirling, and recursive swap-test purification, yielding $F_\mathrm{cat} > 0.96$ from only eight noisy copies. These results turn an abstract resource-theoretic statement into a concrete tool complementary to stabilizer- and purification-based QEC. By replacing a quantitative threshold with a qualitative condition on the support of coherence, CQEC enables ancillary modules within surface-coded processors to be repaired far beyond the conventional threshold; an open-source package reproducing all results in $\sim$30\,s accompanies this work (arXiv:2603.25774, https://github.com/deeptell-inc/cqec).