<p>We present an advanced quantum computational framework using Gaussian spherical quantum dots (GSQDs) embedded in GaAs, integrating both theoretical and AI-driven computational methodologies. By employing Nikiforov–Uvarov Functional Analysis (NUFA) alongside machine learning-assisted modeling, we derived eigenvalues and wave functions for the GSQD system. Our study further explored the energy spectra and Rényi entanglement entropy for various quantum states, revealing a highly ordered and stable system characterized by consistently low entropy values and minimal thermal excitation of higher states. This intrinsic stability highlights the viability of GaAs and Kagome lattice materials for robust quantum computing applications. Additionally, we analyzed the quantum properties of donor impurity states within GSQDs, recalculating eigen energies in effective atomic units using donor effective Rydberg (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">${R}_{\text{D}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mtext>D</mtext> </msub> </math></EquationSource> </InlineEquation>) and donor effective Bohr radius <InlineEquation ID="IEq2"> <EquationSource Format="TEX">${a}_{\text{D}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>a</mi> <mtext>D</mtext> </msub> </math></EquationSource> </InlineEquation>. A comparative evaluation across multiple computational approaches provided a unified assessment of energy predictions and entropy calculations, reinforcing the computational accuracy and consistency of our methodology. By synthesizing results from diverse theoretical and numerical techniques, we established a robust framework for optimizing GSQD-based architectures in quantum information processing. Our findings demonstrate the efficiency of AI-driven computational techniques and NUFA in solving the Class Yukawa and Hellmann Perturbations relevant to quantum computing. Furthermore, we emphasize the significance of Rényi entropy as a key metric for analyzing quantum coherence, entanglement, and uncertainty in low-dimensional semiconductor structures. These insights contribute to the design and optimization of next-generation quantum dot architectures, reinforcing their potential for scalable quantum information technologies.</p>

Advancements in quantum computing: theoretical insights and practical applications using Gaussian spherical quantum dots

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发表日期：

2025年5月31日

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B. Yahweh,
G. J. Ibeh,
G. E. Akpojotor,
A. M. Ekanem,
N. J. George

摘要

We present an advanced quantum computational framework using Gaussian spherical quantum dots (GSQDs) embedded in GaAs, integrating both theoretical and AI-driven computational methodologies. By employing Nikiforov–Uvarov Functional Analysis (NUFA) alongside machine learning-assisted modeling, we derived eigenvalues and wave functions for the GSQD system. Our study further explored the energy spectra and Rényi entanglement entropy for various quantum states, revealing a highly ordered and stable system characterized by consistently low entropy values and minimal thermal excitation of higher states. This intrinsic stability highlights the viability of GaAs and Kagome lattice materials for robust quantum computing applications. Additionally, we analyzed the quantum properties of donor impurity states within GSQDs, recalculating eigen energies in effective atomic units using donor effective Rydberg ( ${R}_{\text{D}}$ $R_{D}$ ) and donor effective Bohr radius ${a}_{\text{D}}$ $a_{D}$ . A comparative evaluation across multiple computational approaches provided a unified assessment of energy predictions and entropy calculations, reinforcing the computational accuracy and consistency of our methodology. By synthesizing results from diverse theoretical and numerical techniques, we established a robust framework for optimizing GSQD-based architectures in quantum information processing. Our findings demonstrate the efficiency of AI-driven computational techniques and NUFA in solving the Class Yukawa and Hellmann Perturbations relevant to quantum computing. Furthermore, we emphasize the significance of Rényi entropy as a key metric for analyzing quantum coherence, entanglement, and uncertainty in low-dimensional semiconductor structures. These insights contribute to the design and optimization of next-generation quantum dot architectures, reinforcing their potential for scalable quantum information technologies.