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Magnon-condensation, which emerges in pumped bosonic systems at room temperature, continues to garner great interest for its long-lived coherence. While traditionally formulated in terms of Bose-Einstein condensation, which typically occurs at ultra-low temperatures, it could potentially also be explained by Fr\"ohlich-condensation, a hypothesis of Bose-Einstein-like condensation in living systems at ambient temperatures. This prompts general questions relating to fundamental differences between coherence phenomena in open and isolated quantum systems. To that end, we introduce a simple model of bosonic condensation in an open quantum system (OQS) formulation, wherein bosons dissipatively interact with an oscillator (phonon) bath. Our derived equations of motion for expected boson occupations turns out to be similar in form to the rate equations governing Fr\"ohlich-condensation. Provided that specific system parameters result in correlations that amplify or diminish the condensation effects, we thereby posit that our treatment offers a better description of high-temperature condensation compared to traditional formulations obtained using equilibrium thermodynamics. By comparing our OQS derivation with the original uncorrelated and previous semi-classical rate equations, we furthermore highlight how both classical anti-correlations and quantum correlations alter the bosonic occupation distribution., Comment: 7 pages, 2 figures, plus supplementary material (8 pages)

Understanding the intricate quantum spin dynamics of radical pair reactions is crucial for unraveling the underlying nature of chemical processes across diverse scientific domains. In this work, we leverage Trotterization to map coherent radical pair spin dynamics onto a digital gate-based quantum simulation. Our results demonstrated agreement between the idealized noiseless quantum circuit simulation and established master equation approaches for homogeneous radical pair recombination, identifying approximately 15 Trotter steps to be sufficient for faithfully reproducing the coupled spin dynamics of a prototypical system. By utilizing this computational technique to study the dynamics of spin systems of biological relevance, our findings underscore the potential of digital quantum simulation (DQS) of complex radical pair reactions and builds the groundwork towards more utilitarian investigations into their intricate reaction dynamics. We further investigate the effect of realistic error models on our DQS approach, and provide an upper limit for the number of Trotter steps that can currently be applied in the absence of error mitigation techniques before losing simulation accuracy to deleterious noise effects., Comment: 10 pages, 9 figures

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 Cram\'er--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 plateaus 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.

We realize arbitrary waveform-based control of spin-selective recombination reactions of radical pairs in the low magnetic field regime. To this end, we extend the Gradient Ascent Pulse Engineering (GRAPE) paradigm to allow for optimizing reaction yields. This overcomes drawbacks of previously suggested time-local optimization approaches for the reaction control of radical pairs, which were limited to high biasing fields. We demonstrate how efficient time-global optimization of the recombination yields can be realized by gradient based methods augmented by time-blocking, sparse sampling of the yield, and evaluation of the central single time-step propagators and their Fr\'echet derivatives using iterated Trotter-Suzuki splittings. Results are shown for both a toy model, previously used to demonstrate coherent control of radical pair reactions in the simpler high-field scenario, and furthermore for a realistic exciplex-forming donor-acceptor system comprising 16 nuclear spins. This raises prospects for the spin-control of actual radical pair systems in ambient magnetic fields, by suppressing or boosting radical reaction yields using purpose-specific radio-frequency waveforms, paving the way for reaction-yield-dependent quantum magnetometry and potentially applications of quantum control to biochemical radical pair reactions. We demonstrate the latter aspect for two radical pairs implicated in quantum biology., Comment: 17 pages, 9 figures, plus supplementary material (8 pagese, 8 figures)

A popular hypothesis ascribes magnetoreception to a magnetosensitive recombination reaction of a pair of radicals in the protein cryptochrome. Many theoretical studies of this model have ignored inter-radical interactions, particularly the electron-electron dipolar coupling (EED), which have a detrimental effect on the magnetosensitivity. Here, we set out to elucidate if a radical pair allowed to undergo internal motion can yield enhanced magneto-sensitivity. Our model considers the effects of diffusive motion of one radical partner along a one-dimensional reaction coordinate. Such dynamics could in principle be realized either via actual diffusion of a mobile radical through a protein channel, or via bound radical pairs subjected to protein structural rearrangements and fluctuations. We demonstrate that the suppressive effect of the EED interactions can be alleviated in these scenarios as a result of the quantum Zeno effect and intermittent reduction of the EED coupling during the radical's diffusive excursions. Our results highlight the importance of the dynamic environment entwined with the radical pair and ensuing magnetosensitivity under strong EED coupling, where it had not previously been anticipated, and demonstrate that a triplet-born radical pair can develop superior sensitivity over a singlet-born one., Comment: 13 pages, 6 figures

The Posner molecule (calcium phosphate trimer), has been hypothesized to function as a biological quantum information processor due to its supposedly long-lived entangled $^{31}$P nuclear spin states. This hypothesis was challenged by our recent finding that the molecule lacks a well-defined rotational axis of symmetry -- an essential assumption in the proposal for Posner-mediated neural processing -- and exists as an asymmetric dynamical ensemble. Following up, we investigate here the spin dynamics of the molecule's entangled $^{31}$P nuclear spins within the asymmetric ensemble. Our simulations show that entanglement between two nuclear spins prepared in a Bell state in separate Posner molecules decays on a sub-second timescale -- much faster than previously hypothesized, and not long enough for super-cellular neuronal processing. Calcium phosphate dimers however, are found to be surprisingly resilient to decoherence and are able to preserve entangled nuclear spins for hundreds of seconds, suggesting that neural processing might occur through them instead.

Adult hippocampal neurogenesis and hippocampus-dependent cognition in mice have been found to be adversely affected by hypomagnetic field exposure. The effect concurred with a reduction of reactive oxygen species in the absence of the geomagnetic field. A recent theoretic study suggests a mechanistic interpretation of this phenomenon in the framework of the Radical Pair Mechanism. According to this model, a flavin-superoxide radical pair, born in the singlet spin configuration, undergoes magnetic field-dependent spin dynamics such that the pair's recombination is enhanced as the applied magnetic field is reduced. This model has two ostensible weaknesses: a) the assumption of a singlet initial state is irreconcilable with known reaction pathways generating such radical pairs, and b) the model neglects the swift spin relaxation of free superoxide, which abolishes any magnetic sensitivity in geomagnetic/hypomagnetic fields. We here suggest that a model based on a radical triad and the assumption of a secondary radical scavenging reaction can, in principle, explain the phenomenon without unnatural assumptions, thus providing a coherent explanation of hypomagnetic field effects in biology., Comment: 26 pages, 3 figures

The mechanism underlying magnetoreception has long eluded explanation. A popular hypothesis attributes this sense to the quantum coherent spin dynamics of spin-selective recombination reactions of radical pairs in the protein cryptochrome. However, concerns about the validity of the hypothesis have been raised as unavoidable inter-radical interactions, such as strong electron-electron dipolar coupling, appear to suppress its sensitivity. We demonstrate that this can be overcome by driving the spin system through a modulation of the inter-radical distance. It is shown that this dynamical process markedly enhances geomagnetic field sensitivity in strongly coupled radical pairs via a Landau-Zener type transition between singlet and triplet states. These findings suggest that a "live" harmonically driven magnetoreceptor can be more sensitive than its "dead" static counterpart., Comment: 7 pages, 4 figures, in addition to Supporting Material of 15 pages and 12 figures

It is hypothesised that the avian compass relies on spin dynamics in a recombining radical pair. Quantum coherence has been suggested as a resource to this process that nature may utilise to achieve increased compass sensitivity. To date, the true functional role of coherence in these natural systems has remained speculative, lacking insights from sufficiently complex models. Here, we investigate realistically large radical pair models with up to 21 nuclear spins, inspired by the putative magnetosensory protein cryptochrome. By varying relative radical orientations, we reveal correlations of several coherence measures with compass fidelity. Whilst electronic coherence is found to be an ineffective predictor of compass sensitivity, a robust correlation of compass sensitivity and a global coherence measure is established. The results demonstrate the importance of realistic models, and appropriate choice of coherence measure, in elucidating the quantum nature of the avian compass., Comment: 10 pages, 4 figures

The Posner molecule, $\text{Ca}_9(\text{PO}_4)_6$, has long been recognized to have biochemical relevance in various physiological processes. It has found recent attention for its possible role as a biological quantum information processor, whereby the molecule purportedly maintains long-lived nuclear spin coherences among its ${^{31}\text{P}}$ nuclei (presumed to be symmetrically arranged), allowing it to function as a room temperature qubit. The structure of the molecule has been of much dispute in the literature, although the $\text{S}_6$ point group symmetry has often been assumed and exploited in calculations. Using a variety of simulation techniques (including ab initio molecular dynamics and structural relaxation), rigorous data analysis tools and by exploring thousands of individual configurations, we establish that the molecule predominantly assumes low symmetry structures ($\text{C}_\text{s}$ and $\text{C}_\text{i}$) at room temperature, as opposed to the higher symmetry configurations explored previously. Our findings have important implications on the viability of this molecule as a qubit., Comment: Posner Molecule, Symmetry, Biological Qubit, Density Functional Theory

We adapt the Monte-Carlo wavefunction (MCWF) approach to treat the open-system spin dynamics of radical pairs subject to spin-selective recombination reactions. For these systems, non-Lindbladian master equations are widely employed, which account for recombination via the non trace-preserving Haberkorn superoperator in combination with reaction-dependent exchange and singlet-triplet dephasing terms. We show that this type of master equation can be accommodated in the MCWF approach, by introducing a second type of quantum jump that accounts for the reaction simply by suitably terminating the propagation. In this way, we are able to evaluate approximate solutions to the time-dependent radical pair survival probability for systems that have been considered untreatable with the master equation approach until now. We explicate the suggested approach with calculations for radical pair reactions that have been suggested to be relevant for the quantum compass of birds and related phenomena., Comment: 13 pages, 6 figures

The Radical Pair Mechanism is a canonical model for the magnetosensitivity of chemical reaction processes. The key ingredient of this model is the hyperfine interaction that induces a coherent mixing of singlet and triplet electron spin states in pairs of radicals, thereby facilitating magnetic field effects (MFEs) on reaction yields through spin-selective reaction channels. We show that the hyperfine interaction is not a categorical requirement to realize the sensitivity of radical reactions to weak magnetic fields. We propose that, in systems comprising three instead of two radicals, dipolar interactions provide an alternative pathway for MFEs. By considering the role of symmetries and energy level crossings, we present a model that demonstrates a directional sensitivity to fields weaker than the geomagnetic field and remarkable spikes in the reaction yield as a function of the magnetic field intensity; these effects can moreover be tuned by the exchange interaction. Our results further the current understanding of the effects of weak magnetic fields on chemical reactions, could pave the way to a clearer understanding of the mysteries of magnetoreception and other biological MFEs and motivate the design of quantum sensors. Further still, this phenomenon will affect spin systems used in quantum information processing in the solid state and may also be applicable to spintronics., Comment: 5 pages, 4 figures, Supporting Material

Birds have a remarkable ability to obtain navigational information from the Earth's magnetic field. The primary detection mechanism of this compass sense is uncertain but appears to involve the quantum spin dynamics of radical pairs formed transiently in cryptochrome proteins. We propose here a new version of the current model in which spin-selective recombination of the radical pair is not essential. One of the two radicals is imagined to react with a paramagnetic scavenger via spin-selective electron transfer. By means of simulations of the spin dynamics of cryptochrome-inspired radical pairs, we show that the new scheme offers two clear and important benefits. The sensitivity to a 50 {\mu}T magnetic field is greatly enhanced and, unlike the current model, the radicals can be more than 2 nm apart in the magnetoreceptor protein. The latter means that animal cryptochromes that have a tetrad (rather than a triad) of tryptophan electron donors can still be expected to be viable as magnetic compass sensors. Lifting the restriction on the rate of the spin-selective recombination reaction also means that the detrimental effects of inter-radical exchange and dipolar interactions can be minimised by placing the radicals much further apart than in the current model., Comment: 24 pages, 12 figures, including supporting information

We present a new method for calculating the product yield of a radical pair recombination reaction in the presence of a weak time-dependent magnetic field. This method successfully circumvents the computational difficulties presented by a direct solution of the Liouville-von Neumann equation for a long-lived radical pair containing many hyperfine-coupled nuclear spins. Using a modified formulation of Floquet theory, treating the time-dependent magnetic field as a perturbation, and exploiting the slow radical pair recombination, we show that one can obtain a good approximation to the product yield by considering only nearly-degenerate sub-spaces of the Floquet space. Within a significant parameter range, the resulting method is found to give product yields in good agreement with exact quantum mechanical results for a variety of simple model radical pairs. Moreover it is considerably more efficient than the exact calculation, and it can be applied to radical pairs containing significantly more nuclear spins. This promises to open the door to realistic theoretical investigations of the effect of radiofrequency electromagnetic radiation on the photochemically induced radical pair recombination reactions in the avian retina which are believed to be responsible for the magnetic compass sense of migratory birds., Comment: 11 pages, 7 figures