Abstract:

This is a talk in two parts.  In the first part I discuss recent work challenging the Heisenberg limit, and present our results showing that the Heisenberg limit is universal, provided one takes into account lack of initial knowledge of the phase.  In the second part I present an approach to simulate Hamiltonian evolution by using a Szegedy quantum walk.  This provides an improvement in efficiency that seems to be impossible using a standard Trotter-Suzuki approach.