An Analytic Measure for Non-Gaussianity as a Quantum Resource

Abstract

As quantum computation increasingly becomes realizable physically, we must have strong theoretical foundations for the algorithms and protocols to be performed. In order to achieve speedups compared to classical computation, we would like a way to quantify the ``non-classical'' resources needed for quantum computation. Concretely classifying these resources can lead to more efficient algorithm design as high quantum resource states should be less efficient to simulate classically. In the literature, there are three known classically simulable class of states: Stabilizer states, Low-entanglement states, and Gaussian states. So in order to achieve universality, we would like to move away from these states. In this thesis we will focus on non-Gaussianity as a quantum resource, which does not currently have an accepted analytic resource measure. Analytic resource measures provide much more theoretical use than the standard distance metric for quantum resources. In this thesis, we will introduce an analytic measure for non-Gaussianity and proofs for its properties. In addition we will also provide code for simulation of bounds and calculating the non-Gaussianity of a given state. As an analytic resource, this metric for non-Gaussianity is much more theory friendly and can have applications in finding pseudo-resource states as well as understanding relationships between quantum resources.