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Quantum-inspired active machine learning for topological superconductors
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Perustieteiden korkeakoulu |
Bachelor's thesis
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SCI3103
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en
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18+5
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Abstract
Topological superconductors represent a fascinating area of condensed matter physics due to their potential applications in quantum computing and their rich fundamental physics. These systems exhibit exotic quantum states, such as Majorana fermions, which are of significant interest in robust quantum computation. Among the simplest models capturing the essential physics of topological superconductors is the p-wave superconductor, which provides an ideal platform to investigate the interplay between superconductivity and topology. To understand the topological properties of such systems, it is essential to characterize the multivariate dependencies of their wavefunctions, energy spectra, and topological invariants. A recently developed quantum-inspired machine learning technique known as Quantics Tensor Cross Interpolation (QTCI), is a method designed for high-resolution, parsimonious representations of multivariate functions. This thesis investigates the topological properties of the p-wave superconductor using QTCI. To determine these properties, the topological phase shift is calculated by determining the Berry curvature and the Chern number across a spectrum of chemical potentials. The QTCI algorithm obtains highly accurate and precise results, demonstrating superiority over classical methods.