Visualization of Qubits as Complex Scalars

• Grant number: 25/22638-4
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: November 01, 2025
• End date: October 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Computer Science
• Principal Investigator: João Paulo Papa
• Grantee: Fernando Ellerbrock Theodoro
• Host Institution: Faculdade de Ciências (FC). Universidade Estadual Paulista (UNESP). Campus de Bauru. Bauru , SP, Brazil
• Associated research grant: 25/12645-3 - Visualizing Qubits as Complex Scalars, AP.R

Abstract

This project investigates alternative representations of qubits (quantum bits) using complex analysis, with a focus on the parametrization z = e^(i*phi) * tan(theta), which directly relates the quantum state |psi> = alpha|0> + beta|1> and the visual representation of the state |psi> as a function of z through the projection of a colored domain onto the Bloch Sphere. The project aims to formalize and mathematically formulate the representation |psi(z)>, study quantum logic gates within this model, and develop a tool for rendering and visualizing this function. (AU)