Abstract
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 \textit{ab initio} spin Hamiltonians: monoamine oxidase~A (MAO-A) and cryptochrome (CRY, PDB~4I6G). Both share a three-layer architecture (³¹P nuclear spin memory, electron spin interface, classical electrochemistry) and identical hyperfine coupling (A = 200~MHz), but differ 16-fold in nuclear T₂: 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 T₂ gap onto a simulation decoherence rate (γveto = T₂ gap/2Tsim): 3.08 for MAO-A, 0.19 for CRY. At γveto = 0.19, CQEC maintains tunneling coherence of 0.83 (95\% CI [0.76, 0.79]; versus 0.12 without correction, ×6.9 improvement). At γveto = 3.08, coherence collapses to 0.012 even with CQEC. A T₂ sensitivity analysis confirms robustness: at T₂ = 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 T₂^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.