Investigating the complexity of error mitigation/suppression protocols on Quantum Algorithms

• Grant number: 25/11307-7
• Support Opportunities: Scholarships abroad - Research Internship - Master's degree
• Start date: September 15, 2025
• End date: March 14, 2026
• Field of knowledge: Physical Sciences and Mathematics - Physics
• Principal Investigator: Celso Jorge Villas-Bôas
• Grantee: Matheus da Silva Fonseca
• Supervisor: Marco Cerezo
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Institution abroad: Los Alamos National Laboratory, United States
• Associated to the scholarship: 23/18240-0 - Molecule Simulation in Quantum Computer, BP.MS

Abstract

This research project investigates error mitigation/suppression techniques for Variational Quantum Algorithms (VQAs), with particular focus on the Variational Quantum Eigensolver (VQE) in Noisy Intermediate-Scale Quantum(NISQ)-era and Early fault-tolerant (EFT) quantum computers. The study combines theoretical analysis of computational complexity with practical implementation on quantum hardware, examining how different error mitigation and correction protocols (including Clifford Data Regression, symmetry verification and magic state injection) affect the complexity framework of VQAs. The work builds upon the candidate's prior Master's research at UFSCar, which established foundations in Unitary Coupled Cluster Singles and Doubles (UCCSD), k-Unitary Pair Coupled Cluster Generalized Singles and Doubles (k-UpCCGSD) ansatzes, and measurement optimization techniques. Through an international internship at Los Alamos National Laboratory under Dr. Marco Cerezo's supervision, the project will analyze the scalability of error mitigation and correction techniques for molecular systems and establish complexity bounds for practical implementations. Expected outcomes include: a comprehensive comparison of error mitigation/suppression overheads, optimized protocols for quantum chemistry applications, and disseminating results through conferences and papers. The research will significantly advance the practical deployment of VQE on near-term quantum devices while strengthening Brazil-US collaborations in quantum information science.