Quantum model reduction based on Oja's flow
arXiv:2607.26669
The paper introduces two non‑perturbative algorithms based on Oja's continuous‑time principal component flow to obtain reduced dynamical models for Markovian open quantum systems, offering an alternative to adiabatic elimination and enabling the identification of noise‑protected subspace codes.
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.