Hamiltonian simulation of quantum beats in radical pairs undergoing thermal relaxation on near-term quantum computers

Quantum dynamics of the radical pair mechanism is a major driving force in quantum biology, materials science, and spin chemistry. The rich quantum physical underpinnings of the mechanism are determined by a coherent oscillation (quantum beats) between the singlet and triplet spin states and their interactions with the environment, which is challenging to experimentally explore and computationally simulate. In this work, we take advantage of quantum computers to simulate the Hamiltonian evolution and thermal relaxation of two radical pair systems undergoing the quantum beats phenomenon. We study radical pair systems with nontrivial hyperfine coupling interactions, namely, 9,10-octalin⁺/p-terphenyl-d₁₄ (PTP)^- and 2,3-dimethylbutane (DMB)⁺/p-terphenyl-d₁₄ (PTP)^- with one and two groups of magnetically equivalent nuclei, respectively. Thermal relaxation dynamics in these systems are simulated using three methods: Kraus channel representations, noise models on Qiskit Aer and the inherent qubit noise present on the near-term quantum hardware. By leveraging the inherent qubit noise, we are able to simulate the noisy quantum beats in the two radical pair systems better than with any classical approximation or quantum simulator. While classical simulations of paramagnetic relaxation grow errors and uncertainties as a function of time, near-term quantum computers can match the experimental data throughout its time evolution, showcasing their unique suitability and future promise in simulating open quantum systems in chemistry.