Abstract: Analog annealing using superconducting circuits is a leading candidate to establish a quantum advantage for computing problems of application interest. This seminar will discuss some recent research thrusts in quantum annealing. The first topic will delve into new methods to extract Pauli Hamiltonians using a variant of Bravyi’s Schrieffer-Wolff technique. While this method has many compelling advantages, it also generates non-trivial holonomy of the Hilbert space over the control parameter manifold. This path dependence of the effective Hamiltonian presents both challenges and opportunities for analog control of annealing systems. The next topic builds on this framework to facilitate a direct comparison between quantum and classical models of superconducting circuits using phase space techniques which enable a clear definition of a “Quantum Advantage for Annealing.” Finally, looking to future capabilities, a definition of non-stoquasticity will be presented along with an explanation of why it is relevant for quantum annealing, why typical superconducting qubits don’t have it, and what sort of design changes are necessary to engineer qubits that are simultaneously capable of annealing and generating strong non-stoquastic interactions.