Abstract Biological radical-pair systems operate at decoherence rates γeff = 3.25–4.55, far exceeding the entanglement-breaking threshold γc ≈ 0.3 (channel-model-dependent). Standard quantum error correction provably fails (Q1 = 0). We identify three escape routes: (i) motional narrowing from protein tumbling reduces γeff to 0.19–0.27 < γc; (ii) decoherence-free subspace encoding achieves F = 0.99 with 27 enzyme copies (assuming collective noise fraction fcoll ≥ 0.94); (iii) the Petz recovery map with a noisy nuclear-spin reference preserves concurrence C = 0.46 as an information-theoretic bound. Radical-pair quantum reservoir computing (QRC) performance degrades monotonically with noise and correlates with quantum resources (rQFI = −0.52); motional narrowing rescues QRC by 6×, though a classical echo-state network retains an advantage at current simulation scales. These results reframe the quantum brain hypothesis: not quantum computation, but quantum reservoir dynamics enhanced by biologically natural motional narrowing.
Abstract Biological radical-pair systems operate at decoherence rates γeff = 3.25–4.55, far exceeding the entanglement-breaking threshold γc ≈ 0.3 (channel-model-dependent). Standard quantum error correction provably fails (Q1 = 0). We identify three escape routes: (i) motional narrowing from protein tumbling reduces γeff to 0.19–0.27 < γc; (ii) decoherence-free subspace encoding achieves F = 0.99 with 27 enzyme copies (assuming collective noise fraction fcoll ≥ 0.94); (iii) the Petz recovery map with a noisy nuclear-spin reference preserves concurrence C = 0.46 as an information-theoretic bound. Radical-pair quantum reservoir computing (QRC) performance degrades monotonically with noise and correlates with quantum resources (rQFI = −0.52); motional narrowing rescues QRC by 6×, though a classical echo-state network retains an advantage at current simulation scales. These results reframe the quantum brain hypothesis: not quantum computation, but quantum reservoir dynamics enhanced by biologically natural motional narrowing.
Abstract Organisms continually commit to actions and occasionally cancel them before they occur. Whether quantum coherence could shape such decisions is debated, and the proposed radical-pair substrate in the brain has been read optimistically: biological noise was treated as a computational resource, coherence times as milliseconds, and error-corrected coherence as preserved deliberation. However, each of these readings is, on inspection, the opposite of what a careful open-systems analysis gives. Here we study the three-layer radical-pair hypothesis under a single revised theory anchored on cryptochrome, importing two established physics tools—open-system quantum error correction and the drift-to-bound theory of decisions—into the living-decision problem. We show that at biological rates the radical-pair channel is entanglement-breaking, that motional narrowing (protein tumbling acting as natural dynamical decoupling) is what restores a correctable regime, and that decoherence-free encoding with concatenation then reaches fidelity F = 0.996. Used as a reservoir, the system gives no advantage for static classification but a temporal-prediction error that tracks quantum resources (rQFI = −0.52). Strikingly, when the reservoir drives a decision, error correction does not enlarge the window in which the action can be vetoed; by preserving the decision signal it reaches the motor threshold sooner and advances the point of no return toward the action, a result we reproduce as a fidelity rescue on IBM superconducting hardware (an analog of the mechanism, not of the biology). We distill this into the principle of error-correction–advanced commitment: a more coherent decision is faster and less revisable, not freer—sharpening, rather than resolving, the question of quantum agency.
Abstract Whether quantum coherence plays a functional role in neural information processing remains contested, largely because biological environments are deemed too noisy for quantum states to sur- vive at relevant timescales. We construct a three-layer model—nuclear spin memory, radical pair interface, classical electrochemistry—and identify five quantum error correction (QEC) paradigms that map onto known biophysical mechanisms: decoherence-free subspaces (DFS) via 31P singlet states, dynamical decoupling (DD) via protein motional narrowing, purification QEC (PQEC) ex- ploiting enzymatic redundancy (∼104 copies/cell), gauging symmetry protection via radical-pair spin conservation, and catalytic coherence recovery (ICEC) at enzyme active sites. We parametrize the model for two molecular systems: monoamine oxidase A (MAO-A; γeff = 4.55, radical pair un- confirmed) and Drosophila cryptochrome (CRY; γeff = 3.25, radical pair experimentally confirmed, |J| < 1 MHz). We quantify each mechanism individually: DFS provides complete protection against collective dephasing (F = 1.000), DD yields a B−2 0 -dependent relaxation suppression (4.6×107-fold at Earth field vs X-band), and PQEC achieves near-unity fidelity using 64 of ∼104 available copies. We integrate gauging, PQEC, and covariant recovery into a unified three-layer stabilizer and benchmark it on pattern classification, time-series prediction, and quantum-coherent decision dynamics. For MAO-A, the stabilizer significantly outperforms standard covariant QEC in classification (accuracy 85.2% vs 80.0%, p = 0.017, Cohen’s d = 1.19) and coherence preservation (+40% at moderate noise), while for time-series prediction the improvement is not statistically significant (p = 0.79). CRY yields statistically equivalent stabilizer performance (MNIST 86.2% vs 85.2%, p = 0.67; spike median MSE 7.31 vs 7.65, Mann–Whitney p = 0.99), demonstrating that the QEC framework is robust across molecular substrates. CRY’s decisive advantages are experimental: a confirmed radical pair and immunity to homeostatic neurotransmitter buffering. Four falsifiable experiments are proposed.
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 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 magnitude threshold whenever the target's coherent modes are preserved. In an effective model of the recovery map, fidelity exceeds 0.99 across 200 noise configurations spanning d = 4-64; the catalyst cost drops from the constructive bound n* ~ d^4 e^(2 gamma) to 32 copies at matched fidelity (10^4- to 10^9-fold) via a pipeline of dynamical decoupling, Clifford twirling, and recursive swap-test purification. A first explicitly CPTP, exactly covariant joint-channel implementation validates genuine recovery under dephasing at small dimension (0.54 -> 0.77) while showing that shallow circuits consume the catalyst, quantifying the model-vs-channel gap. These results turn an abstract resource-theoretic statement into a concrete protocol candidate complementary to stabilizer- and purification-based QEC; an open-source package reproducing the benchmarks accompanies this work (arXiv:2603.25774, https://github.com/deeptell-inc/cqec).
Abstract Whether the electron--nuclear spin coherence behind radical-pair magnetoreception could also support biological \emph{computation} has been conjectured for decades but never made quantitative. We treat a cryptochrome-type radical pair as a reservoir computer, solving the radical-pair master equation with electronic decoherence and driving it as a real turnover does---by the birth of a spin-correlated pair whose singlet character encodes the input. Three results follow, none of them the expected one. The reservoir is \emph{readable by ordinary chemistry}: the nuclear polarisation the product carries away gives an out-of-sample information-processing capacity of 4.7 against its own memoryless floor of 2.0, with no spectroscopy. There is no quantum advantage: a classical network matched channel-for-channel exceeds the five-spin reservoir by 49--123%. And the memory horizon is set not by the microsecond pair lifetime but by the turnover interval, because the nuclear register survives recombination in the diamagnetic product---so the binding constraint is chemical rather than temporal, namely that the \emph{same} register be reused between turnovers. Predicting the register's relaxation instead of assuming it makes that constraint testable: at the geomagnetic field a proton on the intact protein relaxes in milliseconds, not seconds, capping the horizon below the neural band unless the register's dipolar vector reorients about two and a half times faster than the protein (τeff≲6~ns). What survives is a smaller claim on firmer ground: a criterion whose two constants can be measured in vitro, in place of one whose central relaxation time was never measured at all.
This work presents a rigorous, cross-domain review of mechanisms in living systems that exhibit mathematical parallels with quantum error correction (QEC). Rather than relying on metaphor or loose analogy, the paper traces concrete isomorphisms between stabilizer codes, decoherence-free subspaces, dynamical decoupling, and the specific molecular architectures that sustain high-fidelity biological information. The review synthesizes evidence across three domains—genomic stability, neural information processing, and metabolic coherence—and examines proton tunneling, tautomer suppression, nuclear spin protection, microtubule lattice codes, excitonic transport, ENAQT, vibronic stabilizers, and the radical-pair magnetoreception model. By comparing these biological processes to formal properties of QEC (Knill–Laflamme conditions, threshold theorems, syndrome extraction, and topological protection), the work argues that biological robustness can be understood as an evolved form of error-correcting architecture. The conclusion highlights the role of noise-structured environments, energetic cost constraints, and threshold behavior, and proposes that QEC-style mechanisms may be universal to life operating near the quantum–classical boundary.
We analyze quantum state preservation in open quantum systems using quantum error-correcting (QEC) codes explicitly embedded in microscopic system-bath models. Rather than assuming abstract quantum channels, we consider multi-qubit registers coupled to bosonic thermal environments, derive a second-order master equation for the reduced dynamics, and use it to benchmark the five-qubit, Steane, and toric codes under local and collective noise. We compute state fidelities as functions of system-bath coupling strength, bath temperatures, and the number of correction cycles. In the low-temperature regime, repeated error correction with the five-qubit code significantly suppresses decoherence and relaxation for weak-to-moderate couplings. In the high-temperature regime, thermal excitations reduce the effectiveness of all codes, although within the parameter range studied, the five-qubit code still yields the highest fidelities among the three codes. For two-qubit Werner states, we identify a critical evolution time associated with an early-time crossover, before which the overhead of QEC does not compensate for the noise-induced degradation; this critical time increases with entanglement, reflecting the greater fragility of strongly entangled states. Overall, our results provide a microscopic master-equation-based framework for benchmarking QEC performance in realistic open-system environments and for assessing code behavior in near-term noisy quantum architectures.