Beecroft Building, Department of Physics, University of Oxford, Parks Road, Oxford, OX1 3PU
Complexity of quantum matter
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.