Mitchell Institute for Fundamental Physics & Astronomy
College Station, Texas 77843
Computing the spectral gap of a local Hamiltonian is a notoriously hard problem, but if the Hamiltonian is frustration-free, the problem becomes far more tractable. We’ll write down some general criteria for lower-bounding the spectral gap of frustration-free Hamiltonians. We’ll then discuss some applications, including relating the gap of a specific Hamiltonian to the mixing time of random quantum circuits (which is closely related to recent claims of quantum advantage).