Covariant quantum error correction in a three-layer quantum brain model: computational analysis of layer-specific coherence dynamics

Quantum brain proposals require coherence on behaviorally relevant timescales, yet the gap between spin coherence times and neural decision windows has remained a quantitative obstacle. We evaluate approximate covariant quantum error correction (CQEC) – a purification protocol constrained by the Eastin-Knill theorem – across two radical-pair proteins parameterized by $\mathit{\text{ab}}\mathit{\text{initio}}$ spin Hamiltonians: monoamine oxidase~A (MAO-A) and cryptochrome (CRY, PDB~4I6G). Both share a three-layer architecture (${}^{31}$P nuclear spin memory, electron spin interface, classical electrochemistry) and identical hyperfine coupling ($A=200$~MHz), but differ 16-fold in nuclear $T_2$: 3.2~ms (MAO-A) versus 52~ms (CRY). We test whether CQEC preserves coherence over the 200~ms Schultze-Kraft veto window by mapping each protein’s $T_2$ gap onto a simulation decoherence rate (${\gamma }_{\mathrm{v}\mathrm{e}\mathrm{t}\mathrm{o}}=T_2\text{ gap}\mathrm{/}2T_{\mathrm{s}\mathrm{i}\mathrm{m}}$): 3.08 for MAO-A, 0.19 for CRY. At ${\gamma }_{\mathrm{v}\mathrm{e}\mathrm{t}\mathrm{o}}=0.19$, CQEC maintains tunneling coherence of 0.83 (95% CI [0.76, 0.79]; versus 0.12 without correction, $\times$6.9 improvement). At ${\gamma }_{\mathrm{v}\mathrm{e}\mathrm{t}\mathrm{o}}=3.08$, coherence collapses to 0.012 even with CQEC. A $T_2$ sensitivity analysis confirms robustness: at $T_2=26$~ms (half the CRY estimate), CQEC-protected coherence remains 0.69. A classical Markov baseline produces only monotonic relaxation, confirming that CQEC-maintained oscillatory dynamics are genuinely quantum. However, no single protein optimizes both layers: CRY’s shorter $T_2^e$ (0.53~ns versus 1.1~ns) worsens Layer~2 fidelity. This layer-protein tradeoff, together with unresolved challenges in state preparation and entanglement distribution, defines the next targets for quantum brain research.