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

• URL: http://arxiv.org/abs/2307.06319v1
• Date: Wed, 12 Jul 2023 17:30:12 GMT
• Title: Model Reduction for Quantum Systems: Discrete-time Quantum Walks and Open Markov Dynamics
• Authors: Tommaso Grigoletto and Francesco Ticozzi
• Abstract summary: A framework for exact model reduction of quantum systems is constructed leveraging on algebraic methods. The proposed reduction algorithm is illustrated and tested on prototypical examples, including the quantum walk realizing Grover's algorithm.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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