Cryptochrome radical pairs as quantum reservoirs: information-processing capacity, classical baselines, and a microsecond memory bound on neural computation
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 ($\tau_{\rm eff}\lesssim6$~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.
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.
Migratory birds detect the Earth’s magnetic field with remarkable precision using a quantum process in retinal cryptochrome proteins. We review the observational and experimental evidence supporting the radical-pair mechanism and propose a simple dynamical model that augments the standard radical-pair Hamiltonian with a minimal geometric protection term. This term is modulated by consecutive Fibonacci numbers whose ratios converge to the golden ratio ϕ = (1 + √5)/2 ≈ 1.618. Numerical integration and analytical fixed-point analysis show that the protection term naturally stabilizes singlet–triplet coherence lifetimes and optimizes magnetic sensitivity at geomagnetic field strengths and inclinations observed in nature. The model is fully classical, self-contained, and provides a new quantitative explanation for the robustness of avian magnetoreception. It offers the first empirical hint of a universal geometric principle governing quantum coherence in biological systems.
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.
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 Quantum sensing enables the ultimate precision attainable in parameter estimation. Circumstantial evidence suggests that certain organisms, most notably migratory songbirds, also harness quantum-enhanced magnetic field sensing via a radical-pair-based chemical compass for the precise detection of the weak geomagnetic field. However, what underpins the acuity of such a compass operating in a noisy biological setting, at physiological temperatures, remains an open question. Here, we address the fundamental limits of inferring geomagnetic field directions from radical-pair spin dynamics. Specifically, we compare the compass precision, as derived from the directional dependence of the radical-pair recombination yield, to the ultimate precision potentially realisable by a quantum measurement on the spin system under steady-state conditions. To this end, we probe the quantum Fisher information and associated Cramér–Rao bound in spin models of realistic complexity, accounting for complex inter-radical interactions, a multitude of hyperfine couplings, and asymmetric recombination kinetics, as characteristic for the magnetosensory protein cryptochrome. We compare several models implicated in cryptochrome magnetoreception and unveil their optimality through the precision of measurements ostensibly accessible to nature. Overall, the comparison provides insight into processes honed by nature to realise optimality whilst constrained to operating with mere reaction yields. Generally, the inference of compass orientation from recombination yields approaches optimality in the limits of complexity, yet levels off short of the theoretical optimal precision bounds by up to one or two orders of magnitude, thus underscoring the potential for improving on design principles inherent to natural systems.
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.
Radical pairs are short-lived, spin-correlated intermediates that underpin processes in chemistry, biology, and emerging quantum technologies. Their behavior is governed by coupled electron-nuclear spin dynamics and is sensitive to weak magnetic fields, but full quantum treatments have been obstructed by the extreme computational cost of modeling many interacting spins. Here, this barrier is removed, demonstrating that open-system radical-pair dynamics can be resolved at nuclear-spin scales previously intractable, explicitly reaching regimes with tens of coupled nuclei and validated up to 60 spins. In biologically relevant flavin-tryptophan radical pairs, electron-transfer pathways and magnetic-field anisotropy are found to reshape spin evolution and, in turn, spin-selective reaction yields. The resulting directional responses expose a strong mechanistic link between the nuclear environment, magnetic geometry, and chemical outcome-a relationship central to hypotheses of avian magnetoreception and other magnetic-field effects in biology. This establishes a widely applicable simulation framework that removes a long-standing barrier in spin chemistry, quantum biology, and spin-based device science.