This repository contains the computational framework, simulation code, and raw data used in the manuscript "Quantum Entanglement and Information Theory in Radical Pair Navigation." We built the simulation framework using Python and the Quantum Toolbox in Python (QuTiP v4.7). The code models the open quantum system dynamics of the FAD•−/Trp•+ radical pair mechanism (RPM) implicated in avian magnetoreception. The repository includes scripts to compute the following: Spin Hamiltonian Dynamics: Construction of the two-electron spin Hamiltonian, incorporating Zeeman interactions and the dominant hyperfine couplings for both the FAD•− and Trp•+ radicals. Open System Evolution: Integration of the Lindblad master equation to track the time evolution of the singlet and triplet state populations under biological decoherence channels (spin relaxation, environmental dephasing, and radical recombination). Quantum Fisher Information (QFI): Calculation of the symmetric logarithmic derivative and QFI to determine the fundamental angular sensitivity limits of the radical pair compass. Information Theory: Computation of the Shannon mutual information and channel capacity between the Earth's magnetic field orientation and the molecular signaling states.
This repository contains the computational framework, simulation code, and raw data used in the manuscript "Quantum Entanglement and Information Theory in Radical Pair Navigation." We built the simulation framework using Python and the Quantum Toolbox in Python (QuTiP v4.7). The code models the open quantum system dynamics of the FAD•−/Trp•+ radical pair mechanism (RPM) implicated in avian magnetoreception. The repository includes scripts to compute the following: Spin Hamiltonian Dynamics: Construction of the two-electron spin Hamiltonian, incorporating Zeeman interactions and the dominant hyperfine couplings for both the FAD•− and Trp•+ radicals. Open System Evolution: Integration of the Lindblad master equation to track the time evolution of the singlet and triplet state populations under biological decoherence channels (spin relaxation, environmental dephasing, and radical recombination). Quantum Fisher Information (QFI): Calculation of the symmetric logarithmic derivative and QFI to determine the fundamental angular sensitivity limits of the radical pair compass. Information Theory: Computation of the Shannon mutual information and channel capacity between the Earth's magnetic field orientation and the molecular signaling states.
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.
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.
The simulation of open quantum dynamics on quantum circuits has attracted wide interests recently with a variety of quantum algorithms developed and demonstrated. Among these, one particular design of a unitary-dilation-based quantum algorithm is capable of simulating general and complex physical systems. In this paper, we apply this quantum algorithm to simulating the dynamics of the radical pair mechanism in the avian compass. This application is demonstrated on the IBM QASM quantum simulator. This work is the first application of any quantum algorithm to simulating the radical pair mechanism in the avian compass, which not only demonstrates the generality of the quantum algorithm but also opens new opportunities for studying the avian compass with quantum computing devices.
• Published in AIP Publishing's APL Quantum, fully applying digital quantum simulation (DQS) to spin biology. • Successfully implemented the quantum spin dynamics of the radical pair mechanism utilizing the 'Trotterization' technique. • Analyzed the noise limits of actual quantum hardware and demonstrated the potential of utilizing quantum computing for the future development of new drugs targeting complex biomolecules. [Quantum Biology Society] In the emerging field of quantum biology, simulating spin-chemistry systems with actual biological complexity has posed computational limitations that are difficult to overcome with conventional classical computers. This is because as the number of elements constituting the spin system increases, the dimension of the Hilbert space required for computation grows exponentially. Recently, a study simulating biological phenomena using an actual digital quantum computer was published to resolve this problem, drawing the attention of the academic community. A paper titled "Simulating spin biology using a digital quantum computer: Prospects on a near-term quantum hardware emulator" was published on August 19 in APL Quantum, a journal of AIP Publishing. This research was led by a multinational joint research team including Pedro H. Alvarez and Clarice D. Aiello. ■ Mapping the Radical Pair Mechanism via Trotterization The radical pair mechanism (RPM), represented by the magnetic field sensing (magnetoreception) ability of migratory birds, centers on the quantum entanglement and coherence phenomena of electron spins in vivo. The research team introduced the Trotterization technique to directly apply gate-based digital quantum simulation (DQS) to biological systems. Through this technique, they successfully mapped the coherent spin dynamics of radical pairs onto quantum circuits. In ideal, noise-free quantum circuit simulations, they obtained accurate spin dynamics results consistent with the conventional classical Haberkorn master equation approach using only about 15 Trotter steps. ■ Analysis of Quantum Hardware Noise Limits and Future Prospects Furthermore, going beyond ideal environments, the research team conducted an in-depth analysis of the impact of realistic error models on simulations using a near-term (NISQ) quantum hardware emulator that mimics the noise profile of an IBM quantum device (e.g., ibmq_jakarta). The analysis revealed that realistic limitations were observed due to the constrained performance and noise (such as phase damping and amplitude damping) of current quantum hardware, including a shift in singlet yield and a decreased ability to sense magnetic field anisotropy. However, the researchers showed that by fitting an analytical model to the measured noisy data, the overall dynamical shape depending on the magnetic field angle could be successfully derived. In addition, they presented a practical upper limit for the number of Trotter steps that can be directly run on quantum devices if error mitigation techniques are introduced in the future. Unlike conventional classical computing methods that face exponential limits, the DQS approach possesses the potential to efficiently model biological spin systems simply through linear resource scaling by adding qubits. This study is evaluated as a groundbreaking first step demonstrating that digital quantum simulation can be utilized as an innovative tool for new drug development targeting complex biomolecules and ultra-precise biosensing modeling by directly calculating the entanglement and coherence of biological phenomena.
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.
The radical pair mechanism (RPM) in the chemical magnetic compass model is considered to be one of the most promising candidates for the avian magnetic navigation, and quantum needle phenomenon further boosts the navigation precision to a new high level. It is well known that there are also a variety of methods in the field of magnetic field sensing in laboratory, e.g. Ramsey protocol of NV centers in diamond. Here, we compare the RPM model and Ramsey-like model under laboratory conditions and under in vivo conditions respectively. The results are both surprising and reasonable. Under laboratory conditions, if we have precise control over time and a reasonably accurate prior knowledge of the magnetic field direction, the Ramsey-like model will outperform the RPM model. However, when such information is unavailable, as under in vivo conditions, the RPM model stands out. The RPM model achieves greater practicality at the cost of reduced accuracy.