Quantum Optimal Control for Coherent Spin Dynamics of Radical Pairs via Pontryagin Maximum Principle

Ugur G. Abdulla; Jose H. Rodrigues; Jean-Jacques Slotine

doi:10.22331/q-2026-05-06-2096

Quantum Optimal Control for Coherent Spin Dynamics of Radical Pairs via Pontryagin Maximum Principle

Ugur G. Abdulla¹, Jose H. Rodrigues¹, and Jean-Jacques Slotine²

¹Okinawa Institute of Science and Technology 1919-1 Tancha, Onna-son, Kunigami-gun, Okinawa, Japan 904-0495
²Nonlinear Systems Laboratory, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA

Published:	2026-05-06, volume 10, page 2096
Editor:	Alessio Benavoli
Eprint:	arXiv:2508.01806v2
Doi:	https://doi.org/10.22331/q-2026-05-06-2096
Citation:	Quantum 10, 2096 (2026).

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Abstract

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 ($\textit{Abdulla et al, Quantum Sci. Technol., $\bf{9}$, 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.

Popular summary

We solve the quantum optimal control problem to find an external electromagnetic field that drives the spin dynamics of radical pairs to a quantum coherent state. In this context, the quantum coherence refers to the phase-coherent superposition of singlet and triplet states in a pair of free radicals, allowing them to exist simultaneously in both states in biochemical reactions. It is demonstrated that the Pontryagin Maximum Principle – a fundamental mathematical principle for the optimality of complex dynamical systems – turns out to be a fundamental principle for quantum coherence. We introduce a model of a filtered Schrödinger system, and demonstrate that trading off between the original non-filtered model with a bang-bang optimal magnetic field and the filtered model with a continuous in-time optimal magnetic field preserves quantum coherence. We develop a novel iterative regularization method for the identification of the bang-bang optimal control, and an associated simple continuous-in-time optimal magnetic field input. The method has some similarity with the gradient ascent method, with the difference being that instead of moving in the gradient direction in the full control space, it generates the movement in the manifold of bang-bang control vectors guided by the Pontryagin Maximum Principle.

► BibTeX data

@article{Abdulla2026quantumoptimal,
  doi = {10.22331/q-2026-05-06-2096},
  url = {https://doi.org/10.22331/q-2026-05-06-2096},
  title = {Quantum {O}ptimal {C}ontrol for {C}oherent {S}pin {D}ynamics of {R}adical {P}airs via {P}ontryagin {M}aximum {P}rinciple},
  author = {Abdulla, Ugur G. and Rodrigues, Jose H. and Slotine, Jean-Jacques},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {10},
  pages = {2096},
  month = may,
  year = {2026}
}

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Cited by

[1] Farhan T. Chowdhury, Luke D. Smith, and Daniel R. Kattnig, "Engineering the uncontrollable: Steering noisy spin-correlated radical-pairs with coherent and incoherent control", Journal of Chemical Physics 164 3, 031102 (2026).

[2] Luke D. Smith, Farhan T. Chowdhury, Jonas Glatthard, and Daniel R. Kattnig, "Interradical motion can push magnetosensing precision toward quantum limits", Physical Review Applied 25 2, 024074 (2026).

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