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arXiv:2211.15427 · The Journal of Physical Chemistry Letters

Quantum Simulation of the Radical Pair Dynamics of the Avian Compass

Yiteng Zhang, Zixuan Hu, Yuchen Wang, Sabre Kais

Published Jan 19, 2023• 21 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1021/acs.jpclett.2c03617

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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.
There has been a recent interest in quantum algorithms for the modeling and prediction of nonunitary quantum dynamics using current quantum computers. The field of quantum biology is one area where these algorithms could prove to be useful as biological systems are generally intractable to treat in their complete form but amenable to an open quantum systems approach. Here, we present the application of a recently developed singular value decomposition (SVD) algorithm to two systems in quantum biology: excitonic energy transport through the Fenna-Matthews-Olson complex and the radical pair mechanism for avian navigation. We demonstrate that the SVD algorithm is capable of capturing accurate short- and long-time dynamics for these systems through implementation on a quantum simulator and conclude that while the implementation of this algorithm is beyond the reach of current quantum computers, it has the potential to be an effective tool for the future study of systems relevant to quantum biology.
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.
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 radical pair model has been successful in explaining behavioral characteristics of the geomagnetic compass believed to underlie the navigation capability of certain avian species. In this study, the spin dynamics of the radical pair model and decoherence therein are interpreted from a microscopic state transition point of view. This helps to elucidate the interplay between the hyperfine and Zeeman interactions that enables the avian compass and clarify the distinctive effects of nuclear and environmental decoherence on it. Three regimes have been identified for the strength of the hyperfine interaction with respect to that of the geomagnetic Zeeman. It is found that the compass is likely to function in the large hyperfine interaction regime. Using a quantum information theoretic quantifier of coherence, we find that nuclear decoherence induces new structure in the spin dynamics for intermediate hyperfine interaction strength. On the other hand, environmental decoherence-modeled by two different noise models-seems to disrupt the compass action.
• Published in ACS Physical Chemistry Au, introducing an SVD quantum algorithm for open quantum system approaches. • Applied to key quantum biological systems, including excitonic energy transport in the photosynthetic FMO complex and the avian compass radical pair mechanism. • Captures both short- and long-time dynamics accurately... Demonstrating potential as a future tool for simulating complex in vivo nonunitary quantum dynamics. [Quantum Biology Society] A new algorithmic approach capable of modeling and predicting complex nonunitary quantum dynamics inside living organisms using quantum computers has been successfully validated. A research paper titled "Singular Value Decomposition Quantum Algorithm for Quantum Biology" was published in the international journal ACS Physical Chemistry Au. A joint research team led by Professor Kade Head-Marsden from Washington University in St. Louis presented a groundbreaking mathematical framework to solve modeling challenges in quantum biology. ■ Breaking Through Simulation Limits with 'Open Quantum Systems' There has been growing academic interest in algorithms for predicting nonunitary quantum dynamics using current quantum computers. In the field of quantum biology, it is virtually impossible to treat large and complex biological systems entirely as quantum states. However, an open quantum systems approach, which considers continuous interaction with the environment and dissipation, can make these quantum algorithms highly useful. Accordingly, the researchers introduced the Singular Value Decomposition (SVD) quantum algorithm, which helps implement complex nonunitary operators on quantum circuits, and applied it to two major challenges in quantum biology. ■ Secrets of Photosynthesis and Avian Compass Captured by SVD Algorithm The systems the research team applied the SVD algorithm to are: 1) excitonic energy transport through the Fenna-Matthews-Olson (FMO) complex in the photosynthetic process of green sulfur bacteria, and 2) the radical pair mechanism (RPM) of avian navigation, where migratory birds find their way by sensing the Earth's magnetic field. The researchers implemented and analyzed this using the IBM QASM quantum simulator. The results confirmed that the SVD algorithm very accurately captures and reproduces the environment-driven dynamical processes appearing in both biological systems across both short- and long-time quantum dynamics, regardless of the time duration. This study holds great significance in that it demonstrated the potential of the SVD quantum algorithm to become a powerful and effective tool for simulating complex in vivo quantum mechanics as quantum computing advances, even though such complex biological systems face physical limitations for perfect implementation at the current level of noisy intermediate-scale quantum (NISQ) hardware. Experts anticipate that this algorithm will accelerate quantum biology research and play a key role in designing biomimetic quantum technologies and new drug discovery platforms.
The radical-pair mechanism is one of two distinct mechanisms used to explain the navigation of birds in geomagnetic fields, however little research has been done to explore the role of quantum entanglement in this mechanism. In this paper we study the lifetime of radical-pair entanglement corresponding to the magnitude and direction of magnetic fields to show that the entanglement lasts long enough in birds to be used for navigation. We also find that the birds appear to not be able to orient themselves directly based on radical-pair entanglement due to a lack of orientation sensitivity of the entanglement in the geomagnetic field. To explore the entanglement mechanism further, we propose a model in which the hyperfine interactions are replaced by local magnetic fields of similar strength. The entanglement of the radical pair in this model lasts longer and displays an angular sensitivity in weak magnetic fields, both of which are not present in previous models.