Coherent chemical kinetics as quantum walks I: Reaction operators for radical pairs

TL;DR

This paper introduces a quantum walk framework to model coherent chemical kinetics, specifically applying it to radical-pair reactions, resulting in a reaction operator that aligns with experimental data and offers new insights into reaction dynamics.

Contribution

It develops a quantum walk-based method to derive reaction operators for radical-pair reactions, improving upon previous models and matching experimental results.

Findings

Reaction operator predicts dephasing rates consistent with experiments

Quantum walk formalism provides a natural framework for multisite reactions

Demonstrates a normalized density operator for radical-pair states

Abstract

Classical chemical kinetics use rate-equation models to describe how a reaction proceeds in time. Such models are sufficient for describing state transitions in a reaction where coherences between different states do not arise, or in other words, a reaction which contain only incoherent transitions. A prominent example reaction containing coherent transitions is the radical-pair model. The kinetics of such reactions is defined by the so-called reaction operator which determines the radical-pair state as a function of intermediate transition rates. We argue that the well-known concept of quantum walks from quantum information theory is a natural and apt framework for describing multisite chemical reactions. By composing Kraus maps that act only on two sites at a time, we show how the quantum-walk formalism can be applied to derive a reaction operator for the standard avian radical-pair reaction. Our reaction operator predicts a recombination dephasing rate consistent with recent experiments [J. Chem. Phys. {\bf 139}, 234309 (2013)], in contrast to previous work by Jones and Hore [Chem. Phys. Lett. {\bf 488}, 90 (2010)]. The standard radical-pair reaction has conventionally been described by either a normalised density operator incorporating both the radical pair and reaction products, or by a trace-decreasing density operator that considers only the radical pair. We demonstrate a density operator that is both normalised and refers only to radical-pair states. Generalisations to include additional dephasing processes and an arbitrary number of sites are also discussed.