Identification of the external electromagnetic fields and internal hyperfine parameters which optimize the quantum singlet-triplet yield of simplified radical pairs modeled by Schrödinger system with spin Hamiltonians given by the sum of Zeeman interaction and hyperfine coupling interaction terms are analyzed. A method that combines sensitivity analysis with Tikhonov regularization is implemented. Numerical results demonstrate that the quantum singlet-triplet yield of the radical pair system can be significantly reduced if optimization is pursued simultaneously for both external magnetic fields and internal hyperfine parameters. The results may contribute towards understanding the structure-function relationship of a putative magnetoreceptor to manipulate and enhance quantum coherences at room temperature and leveraging biofidelic function to inspire novel quantum devices.
Identification of the external electromagnetic fields and internal hyperfine parameters which optimize the quantum singlet-triplet yield of simplified radical pairs modeled by Schrödinger system with spin Hamiltonians given by the sum of Zeeman interaction and hyperfine coupling interaction terms are analyzed. A method that combines sensitivity analysis with Tikhonov regularization is implemented. Numerical results demonstrate that the quantum singlet-triplet yield of the radical pair system can be significantly reduced if optimization is pursued simultaneously for both external magnetic fields and internal hyperfine parameters. The results may contribute towards understanding the structure-function relationship of a putative magnetoreceptor to manipulate and enhance quantum coherences at room temperature and leveraging biofidelic function to inspire novel quantum devices.
Abstract Optimal control of the external electromagnetic field input for the maximization of the quantum triplet-singlet yield of the radical pairs in biochemical reactions modeled by Schrödinger system with spin Hamiltonians given by the sum of Zeeman interaction and hyperfine coupling interaction terms are analyzed. Fréchet differentiability and Pontryagin Maximum Principle in Hilbert space is proved and the bang-bang structure of the optimal control is established. A closed optimality system of nonlinear differential equations for the identification of the bang-bang optimal control is revealed. Numerical methods for the identification of the bang-bang optimal control based on the Pontryagin maximum principle are developed. Numerical simulations are pursued, and the convergence and stability of the numerical methods are demonstrated. The results contribute towards understanding the structure-function relationship of the putative magnetoreceptor to manipulate and enhance quantum coherences at room temperature and leveraging biofidelic function to inspire novel quantum devices.
This paper aims to devise the shape of the external electromagnetic field that drives the spin dynamics of radical pairs to a quantum coherent state through maximization of the triplet-born singlet yield in biochemical reactions. The model is a Schrödinger system with spin Hamiltonians given by the sum of Zeeman interaction and hyperfine coupling interaction terms. We introduce a one-parameter family of optimal control problems by coupling the Schrödinger system to a control field through filtering equations for the electromagnetic field. Fréchet differentiability and the Pontryagin Maximum Principle in Hilbert space are proved, and the bang-bang structure of the optimal control is established. A new iterative Pontryagin Maximum Principle (IPMP) method for the identification of the bang-bang optimal control is developed. Numerical simulations based on IPMP and the gradient projection method (GPM) in Hilbert spaces are pursued, and the convergence, stability, and the regularization effect are demonstrated. Comparative analysis of filtering with regular optimal electromagnetic field versus non-filtering with bang-bang optimal field ( Abdulla et al, Quantum Sci. Technol., 9 , 4, 2024 ) demonstrates that the change of the maxima of the singlet yield is less than 1%. The results open a venue for a potential experimental work on magnetoreception as a manifestation of quantum biological phenomena.
The development of the radical pair mechanism has allowed for theoretical explanation of the fact that magnetic fields are observed to have an effect on chemical reactions. The mechanism describes how an external magnetic field can alter chemical yields by interacting with the spin state of a pair of radicals. In the field of quantum biology, there has been some interest in the application of the mechanism to biological systems. This paper takes an open quantum systems approach to a model of the radical pair mechanism in order to derive a master equation in the Born-Markov approximation for the case of two electrons, each interacting with an environment of nuclear spins as well as the external magnetic field, then placed in a dissipative bosonic bath. This model is used to investigate two different cases relating to radical pair dynamics. The first uses a collective coupling approach to simplify calculations for larger numbers of nuclei interacting with the radical pair. The second looks at the effects of different hyperfine configurations of the radical pair model, for instance the case in which one of the electrons interact with two nuclei with different hyperfine coupling constants. The results of these investigations are analysed to see if they offer any insights into the biological application of the radical pair mechanism in avian magnetoreception.
The Radical Pair Mechanism, a process by which magnetic fields modulate the kinetics of chemical reactions by influencing spin dynamics, is thought to underlie a variety of biological mechanisms and is inherently both quantum and noisy. Model simulations with limited electron-nuclear interactions have been conducted on classical devices resulting in experimentally verified final state results, however these simulations become too complex to simulate as the systems scale in size. This motivates us to propound the simulation of the relevant spin dynamics in a noisy quantum device to probe the currently unexplored open quantum systems aspects of the radical pair mechanism and to provide a novel theoretical tool for us to be able to tackle bottlenecks in simulating larger and more physically relevant biological spin systems. We employ a hybrid quantum machine learning approach where we evaluate a parametrized quantum circuit representing the evolution of the system on the quantum device and then update the parameters according to our objective cost function on a classical computer using a gradient optimizer and a noisy gradient free (SPSA) optimizer. We show that a 3 qubit circuit with a series of parametrized rotation gates representing the Hyperfine and Zeeman interactions can be optimized, resulting in a circuit that evolves a singlet state under different magnetic field angles. Moreover, we show that the noisy gradient free optimizer is better suited for optimizing on a noisy quantum device. However, the precision in the quantum circuit outputs is only sub-par at present, leaving room for further improvements.
Radical-pair reactions pertinent to biological magnetic field sensing are an ideal system for demonstrating the paradigm of quantum biology, the exploration of quantum coherence effects in complex biological systems.We here provide yet another fundamental connection between this biochemical spin system and quantum information science.We introduce and explore a formal measure quantifying the singlet-triplet coherence of radical pairs using the concept of quantum relative entropy.The ability to quantify singlet-triplet coherence opens up a number of possibilities in the study of magnetic sensing with radical pairs.We first use the explicit quantification of singlet-triplet coherence to affirmatively address the major premise of quantum biology, namely, that quantum coherence provides an operational advantage to magnetoreception.Second, we use the concept of incoherent operations to show that incoherent manipulations of nuclear spins can have a dire effect on singlet-triplet coherence when the radical pair exhibits electronic-nuclear entanglement.Finally, we unravel subtle effects related to exchange interactions and their role in promoting quantum coherence.
Electron spin-dependent chemical reactions in proteins, often discussed under the 'radical-pair mechanism', remain the leading microscopic proposal for magnetic field sensing in biology. Yet the essential physics is often obscured by the complexity of realistic models. In this work, we present a physicist-friendly primer on the simplest radical-pair Hamiltonian that already captures many of the mechanism's best-known qualitative features. The contributions of this work are fourfold. First, we place on record a complete analytical solution of this toy model, which has previously been studied extensively, mostly through numerical and partial analytical approaches. Working in the experimentally relevant singlet-triplet basis, we derive closed-form expressions for the instantaneous singlet population and for two related time-averaged singlet yields. Second, we introduce a new interpretation of these results that makes several familiar features of radical-pair physics transparent. In particular, we show that the dynamics admit a bright-dark decomposition (in the sense of spin mixing), similar to structures studied in atomic physics. Third, through this bright-dark perspective, we clarify experimentally relevant features of the toy model. In particular, we show that the so-called 'low-field effect' arises from a coherence term between bright and dark sectors, and that the special role of zero field is best understood as a phase-locking phenomenon rather than merely as enhanced mixing. Fourth, we import methods developed in the context of technological quantum sensing to obtain further insight into the model. This allows us to clarify the role of initial state preparation and the trade-off between coherent phase accumulation and time-averaging penalties. The resulting toy model serves both as an analytically tractable benchmark and as a conceptual starting point for future work.