For more information about Prof. Sevag Gharibian please see the following link:
A central direction of research in condensed matter physics is the determination of properties of local Hamiltonian systems. Unfortunately, computing such properties is often intractable, in that the complex matrices involved are typically of exponential size. Over the last 15 years, a burgeoning area of research at the intersection of condensed matter physics and computational complexity theory, known as Quantum Hamiltonian Complexity, has made significant strides in characterizing the complexity of such computational tasks. In this talk, we begin with a gentle introduction to the field of Quantum Hamiltonian Complexity. We then show that a central and basic task in condensed matter physics, computing the expected value of a local observable against the ground state of a local Hamiltonian, is an intractable task in the worst case (assuming standard complexity theoretic conjectures), even if the observable acts on just a single qubit.
This talk is based on joint work with Xiaodi Wu (U Oregon) and Justin Yirka (VCU).