Artificial Intelligence and Electrical & Electronics Engineering: AIEEE Open Access
From 1D Proof-of-Concept to 2D Simulation and Prototype Fabrication Design: Qubit Dynamics in GrapheneâhBN Heterostructures via Python Numerical Analysis
Abstract
Chur Chin
Topological quantum devices based on Graphene–hexagonal Boron Nitride (hBN) heterostructures represent a promising platform for next-generation qubit architectures. This study presents a progressive numerical simulation framework — advancing from a one-dimensional (1D) proof-of-concept (PoC) to a full two-dimensional (2D) spatial model — implemented entirely in Python without reliance on commercial finite-element solvers. The 1D model validates fundamental physical quantities including Zeeman splitting (ΔE = 4.63 × 10−5 eV), resonance frequency (f = 11.20 GHz), and ground state energy (E0 = 4.587 × 10−5 eV) to greater than 99% accuracy against theoretical guidebook targets. Extension to 2D via sparse-matrix eigenvalue analysis yields a validated 2D ground state energy of E0 = 1.353 × 10−4 eV — a ~2.93-fold increase consistent with the additional zero-point energy contribution from the second spatial degree of freedom. Giant magnetoresistance (GMR) stack simulations confirm stable resistance switching between R_P ≈ 226 Ω and R_AP ≈ 260 Ω at B = 0.4 T across the full 2D device plane. Based on these results, a complete prototype fabrication layout is proposed, including a GDSII layer stack, top-view coordinate map, and process tolerance analysis. The framework provides physical grounds for the Prajna-Transformer — an AI architecture integrating topological information preservation with Buddhist epistemological principles.