Exploring Complex Superconducting Nanohybrids with Neural Network Quantum States

Lukáš Frk

Published Jan 1, 2026• 0 citations

Abstract

Systems of quantum dots coupled to superconducting (SC) leads designed for practical applications are becoming increasingly complicated, ren- dering traditional analytical and numerical methods insufficient. Therefore, we tested new Neural Network Quantum States (NNQS) methods based on various network architectures and on variational Monte Carlo. To simplify their appli- cation, a new Chain Expansion method developed in our research group, which constructs effective models, was used. We applied these methods to systems of one to three quantum dots coupled to one to three SC leads, benchmarking them against conventional techniques and analyzing their phase diagrams. While at least one NNQS variant typically yielded correct predictions, no single method performed consistently well across all studied configurations. Thus, we conclude that current NNQS methods still face significant limitations when systematically studying complex hybrid su- perconducting nanostructures. This thesis also introduces a focused analytical study of effective models for fundamental quantum dot configurations. 1

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