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arXiv · 2307.06319

Model Reduction for Quantum Systems: Discrete-time Quantum Walks and Open Markov Dynamics

Tommaso Grigoletto·Francesco Ticozzi
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Abstract

A general approach to obtain reduced models for a wide class of discrete-time quantum systems is proposed. The obtained models not only reproduce exactly the output of a given quantum model, but are also guaranteed to satisfy physical constraints, namely complete positivity and preservation of total probability. A fundamental framework for exact model reduction of quantum systems is constructed leveraging on algebraic methods, as well as novel results on quantum conditional expectations in finite-dimensions. The proposed reduction algorithm is illustrated and tested on prototypical examples, including the quantum walk realizing Grover's algorithm.

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Tommaso Grigoletto, Francesco Ticozzi. 2023-07-12. Model Reduction for Quantum Systems: Discrete-time Quantum Walks and Open Markov Dynamics. https://doi.org/10.1109/tit.2025.3601118

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