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Updated: Jun 4, 2025

Measuring Statistical Learning Across Modalities and Domains in School-Aged Children Via an Online Platform and Neuroimaging Techniques
Published on: June 30, 2020
Partially unitary learning
Mikhail Gennadievich Belov1, Vladislav Gennadievich Malyshkin2
1Faculty of Mechanics and Mathematics, <a href="https://ror.org/010pmpe69">Lomonosov Moscow State University</a>, GSP-1, Moscow, Vorob'evy Gory 119991, Russia.
Abstract:
The problem of an optimal mapping between Hilbert spaces IN of |ψ〉 and OUT of |ϕ〉 based on a set of wavefunction measurements (within a phase) ψ_{l}→ϕ_{l}, l=1,⋯,M, is formulated as an optimization problem maximizing the total fidelity ∑_{l=1}^{M}ω^{(l)}|〈ϕ_{l}|U|ψ_{l}〉|^{2} subject to probability preservation constraints on U (partial unitarity). The constructed operator U can be considered as an IN to OUT quantum channel; it is a partially unitary rectangular matrix (an isometry) of dimension dim(OUT)×dim(IN) transforming operators as A^{OUT}=UA^{IN}U^{†}. An iterative algorithm for finding the global maximum of this optimization problem is developed, and its application to a number of problems is demonstrated. A software product implementing the algorithm is available from the authors.
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