2023/07/12 by Tommaso Grigoletto, Francesco Ticozzi, Grigoletto, Tommaso +1 · 4 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Neural Networks and Reservoir Computing #Model Reduction and Neural Networks
paper · pdf · doi:10.48550/arxiv.2307.06319
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.