Quantum Resources in Strongly Interacting Fermion Systems

• Grant number: 25/05607-8
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• Start date: July 01, 2025
• End date: February 28, 2026
• Field of knowledge: Physical Sciences and Mathematics - Chemistry
• Principal Investigator: Vivian Vanessa França Henn
• Grantee: Isaac Martins Carvalho
• Supervisor: Marcello Dalmonte
• Host Institution: Instituto de Química (IQ). Universidade Estadual Paulista (UNESP). Campus de Araraquara. Araraquara , SP, Brazil
• Institution abroad: Abdus Salam International Centre for Theoretical Physics (ICTP), Italy
• Associated to the scholarship: 23/00510-0 - Quantum Phase Transitions in inhomogeneous nanomaterials, BP.PD

Abstract

Simulating many-body quantum systems on classical computers is a fundamental challenge in theoretical materials science, particularly in the study of quantum materials with potential applications in emerging technologies. This is due to the exponential growth of the Hilbert space, which encodes complex quantum correlations into the wavefunction - making classical simulations intractable for large systems. In the context of quantum machines with error correction, the dominant source of computational cost is a quantum resource called nonstabilizerness, or magic. In this context, certain quantum states, generated by stabilizer states from Clifford operations, allow efficient classical simulation. Quantum advantage emerges from non-Clifford resources required to prepare a state, quantified by nonstabilizerness. Recent advances in measuring nonstabilizerness, such as the stabilizer Rényi entropies (SREs), have been successfully benchmarked in systems with a local binary basis (e.g., spin models), focusing on criticality. Yet, it remains unclear how these methods generalize to strongly correlated fermionic materials, where interactions play a pivotal role in shaping quantum correlations.This project investigates how fermionic interactions drive the connection between nonstabilizerness and quantum criticality in quasi-1D nanomaterials modeled by the extended Hubbard model. Using tensor network methods - Matrix Product States (MPS) and Density Matrix Renormalization Group (DMRG) - we quantify nonstabilizerness, applying Jordan-Wigner transformations and optimizing tensor contractions for SRE calculations.Expected outcomes include: (1) understanding how electron interactions drive magic-criticality scaling, (2) rigorous benchmarks for fermionic magic measures, and (3) universal scaling laws near quantum phase transitions. These results will represent a key stepping stone in our understanding of magic in the context of fermionic matter, serving as a fundamental step towards more advanced applications in chemistry and quantum materials.