Dominic Berry, Macquarie University
Abstract
This is a talk in two parts. The first is on quantum simulation of quantum systems. This is one of the most important applications where a quantum computer could give an exponential speedup, but a drawback to many current algorithms is that they scale poorly with the allowable error. Here I present a new algorithm that provides polylog scaling in the error, thereby providing far more efficient simulations when high accuracy is required. The second part is on phase measurement. For a constant phase, the Heisenberg limit provides the ultimate bound to the accuracy of measurement, and corresponds to accuracy far greater than can normally be achieved. However, there is the open question of what the limit is when the phase is varying. Here I provide a partial answer, giving the ultimate limit if one restricts to Gaussian states and phase variation with a power-law spectrum.