Model Reduction for Quantum Systems: Discrete-time Quantum Walks and Open Markov Dynamics
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915498219798528 |
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| author | Grigoletto, Tommaso Ticozzi, Francesco |
| author_facet | Grigoletto, Tommaso Ticozzi, Francesco |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_06319 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Model Reduction for Quantum Systems: Discrete-time Quantum Walks and Open Markov Dynamics Grigoletto, Tommaso Ticozzi, Francesco Quantum Physics 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. |
| title | Model Reduction for Quantum Systems: Discrete-time Quantum Walks and Open Markov Dynamics |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2307.06319 |