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

Source: [Coherent chemical kinetics as quantum walks I: Reaction operators for radical pairs](<https://www.sota2.com/research/paper/68fa33301e209131ce88df6e>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T19:54:31.843Z

Authors: A. Chia, A. Gorecka, K. C. Tan, L. Pawela, P. Kurzynski, T. Paterek, D. Kaszlikowski

Published: 2015-06-13T02:59:49.000Z

## 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1506.04213>)

[PDF](<https://arxiv.org/pdf/1506.04213.pdf>)