The $γ_c$-Peak: Covariant Recovery on Four Organic Qubit Platforms

Abstract

The Petz recovery map (1986) provably reverses a noisy quantum channel on a reference state, but its algorithmic relevance to real, dissipation-dominated platforms has remained unclear. Using the open-source \texttt{organic-qc-bench} simulation package, we benchmark a Petz-style covariant-purification quantum error correction (CQEC) protocol across four engineered organic qubit platforms operated \emph{without any magnetic field}: a flavin-nitroxide radical-pair reservoir (P1); perchlorotriphenylmethyl radicals in a covalent organic framework (P2); the SVILC qubit [Wakaura2017] on $κ$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]Br (P3, conditional on SVILC confirmation); and a Su-Schrieffer-Heeger soliton on \emph{trans}-polyacetylene (P4). Across five quantum algorithms (QKAN, qDRIFT, control-free QPE, Shor-Regev, Bernstein-Vazirani) and two ML tasks, CQEC gains are significant ($p\!<\!10^{-5}$; Wilcoxon, Bonferroni $α\!=\!0.05/44$) for all sixteen path$\times$algorithm pairs. The central finding is the \emph{$γ_c$-peak}: the fidelity gain $ΔF$ is maximised \emph{at} the entanglement-breaking threshold $γ_c$, with $ΔF_{\rm max}\!=\!+0.303$ at $d\!=\!64$ and a linear $\log_2 d$ scaling over $d=2$-$64$ -- algorithmically confirming the prediction [Wakaura2026LQBH] that Petz recovery preserves coherence beyond this threshold. Bernstein-Vazirani also yields a $7.6$-$31\times$ provable quantum advantage at $n\!=\!3$-$5$, diarylethene-photoswitch CZ fidelities reach $F_{CZ}\!\ge\!0.987$ for P2-P4, and projected manufacturing costs are 10-40$\times$ lower with 10-200$\times$ less operating power than superconducting platforms. The $γ_c$-peak establishes Petz-style recovery as a practically relevant primitive at the dissipation-coherence boundary and identifies PTM-COF (P2) as the highest-priority experimental target.