Research Seminars @ Illinois

"Complexity of quantum matter"

Abstract: Quantum information theory has provided a connection between physical properties of many-body quantum ground states and the resources required to describe them on classical computers. I will present two new connections between computational complexity and the physics of quantum matter. First, I will construct rigorous upper bounds on the entanglement entropies of quantum states that have fixed energy expectation values with respect to local Hamiltonians. Using these bounds, I will show how volume-law entanglement emerges as the energy is increased, and how the crossover from ground-state behavior is encoded in the system’s heat capacity. Then, I will prove area-law entanglement for the ground states of wide varieties of frustration-free systems in general spatial dimensions. In the second part of the talk I will show how a foundational idea in quantum cryptography can be developed into a probe of the resources required to prepare mixed states on quantum computers. For thermal states, this result relates quantum state complexity to standard probes of linear response. 

Bio: Sam has been an Associate Research Scholar at Princeton University since 2025. Prior to that, from 2021-25, he held a Gordon & Betty Moore Postdoctoral Fellowship at the University of California, Berkeley. He obtained his doctorate in Theoretical Physics from the University of Oxford in 2021 and his BA and MSci from the University of Cambridge in 2017.