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This research introduces non-perturbative algorithms using Oja's continuous-time principal component flow to derive reduced dynamical models for Markovian quantum open systems, offering a robust alternative to standard Adiabatic Elimination methods. The approach effectively projects evolution onto slowest degrees of freedom and can identify noise-protected subspaces critical for future quantum information processing tasks.
Quantum model reduction based on Oja's flow
arXiv:2607.26669v1 Announce Type: new Abstract: We propose a novel approach to numerically derive approximate reduced dynamical models for Markovian quantum open systems without perturbative iterations, projecting the evolution to the subspace associated to their slowest degrees of freedom. The two algorithms we develop are based on Oja's continuous-time principal component flow: the first returns the optimal reduction to the slowest decaying operator-subspace, and is extended to time-dependent dynamics, while the second one is designed to reduce the dynamics on a subspace of the system's Hilbert space, and thus preserve conditional complete positivity. The methods represent a non-perturbative alternative to well-established Adiabatic Elimination (AE) methods, and the second can be used to find noise-protected subspace codes for quantum information processing. Both are tested on a paradigmatic central spin model.
Abstract:We propose a novel approach to numerically derive approximate reduced dynamical models for Markovian quantum open systems without perturbative iterations, projecting the evolution to the subspace associated to their slowest degrees of freedom. The two algorithms we develop are based on Oja's continuous-time principal component flow: the first returns the optimal reduction to the slowest decaying operator-subspace, and is extended to time-dependent dynamics, while the second one is designed to reduce the dynamics on a subspace of the system's Hilbert space, and thus preserve conditional complete positivity. The methods represent a non-perturbative alternative to well-established Adiabatic Elimination (AE) methods, and the second can be used to find noise-protected subspace codes for quantum information processing. Both are tested on a paradigmatic central spin model.
arXiv:2607.26669 [quant-ph]
(or arXiv:2607.26669v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2607.26669 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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