Abstract

Nonstabilizerness, or ?magic,? quantifies the non-Clifford resources underlying quantum computation and provides a useful lens for understanding quantum computational complexity. Despite its fundamental importance, characterizing magic has traditionally been limited to relatively small systems. In this seminar, I will present efficient methods for studying magic in quantum circuits and many-body systems, revealing connections between magic, entanglement, and computational complexity. I will also discuss how magic behaves in critical quantum systems and how universal structures emerge in nonequilibrium quantum dynamics. Finally, I will describe an approach that combines Clifford circuits with matrix product states, enabling efficient simulation of quantum states that can simultaneously exhibit strong nonstabilizerness and volume-law entanglement. Together, these results illustrate how magic can serve not only as a computational resource, but also as a framework for probing the complexity of quantum many-body systems.