Speaker: Mark Adcock Quantum speed-up for sampling functions: a Deutsch-Jozsa algorithm for Gaussian states In classical information systems, there are both discrete and analogue computation models. Quantum information systems also employ both models, but discrete quantum computation has been the subject of most of the research primarily for reasons of error correction. Discrete quantum algorithms for database search and for factoring integers have significantly improved performance over their classical counterparts. A quantum algorithm of historical importance is the Deutsch-Jozsa (DJ) algorithm, which has been shown to determine global properties of an unknown function with exponentially fewer queries than its deterministic classical counterpart. The DJ algorithm was one of the earliest discrete quantum algorithms studied, and it is also easy to understand in its ideal operational context. For these reasons, we select the DJ algorithm as the starting point of a Continuous Variable (CV) quantum algorithm. Inspired by work done by Braunstein and Pati, we study the CVDJ problem with Gaussian states. We calculate the Wigner functions of the algorithmic evolution of the control and target states and use these to generate probability distributions, which we employ to calculate the probability of successful output of the algorithm. We show that the CVDJ algorithm can be viewed as solving a sampling problem of a continuous function. Using the Nyquist criterion to set the sampling frequency, we quantify the speedup over a classical analog computation process. We also use interpretations of this work to elucidate the DJ Quantum Algorithm for the discrete case when imperfect input states are provided.