A key objective behind the inception of Google’s Quantum Artificial Intelligence Lab was to accelerate the approximate solution of hard combinatorial optimization problems with quantum enhanced optimization. We have developed a sequence of algorithms that aim at accomplishing this task in a manner that is forgiving to the noise present in near-term quantum processors. I will describe the latest incarnation of our method which is based on multi-spin updates generated by non-ergodic many body delocalized states. We recently showed that this approach can recover the Grover speedup for unstructured search problems and I will describe numerical experiments that illustrate how this method behaves when applied to structured optimization problems. I will conclude my talk with updates on other activities going on in Google’s Quantum AI lab: I will describe the properties of our latest chip, the 72 qubit Bristlecone processor; a formulation of quantum neural networks which lends itself to implementation on shallow quantum circuits; and if time permits I will sketch where we stand in attempting to perform electronic structure calculations, again using low resource count quantum circuits.