Statistical properties of dynamical systems & A gentle introduction to quantum optimisation

Speaker: Dr Sakshi Jain
Affiliation: University of Queensland

Abstract: 

A deterministic dynamical system is, in principle, completely predictable once its initial condition is known. Yet in many systems of interest, predicting individual trajectories over long times is impossible or uninformative. Instead, we ask statistical questions: How are states distributed in the long run? How quickly does the system forget its initial condition? How do long-time averages behave?

In this talk I will introduce the statistical viewpoint of dynamical systems. I will then discuss a natural question: how do these statistical properties change when the dynamics is perturbed? 

Speaker: Dr John Tanner
Affiliation: University of Queensland

Abstract: 

In this talk, we will take a short journey from the Schrödinger equation to the basic ingredients of a quantum computing and quantum algorithms. Starting with the familiar picture of quantum states evolving according to a differential equation, we will see how this continuous-time description leads naturally to unitary transformations, qubits and quantum gates. We will then discuss how these ingredients can be assembled into a simple quantum algorithm, and why superposition and interference may provide computational advantages that have no classical analogue.

Finally, we will sketch a more recent idea underlying an algorithm known as Decoded Quantum Interferometry, in which a polynomial is applied to the objective function of an optimisation problem whose values are encoded in quantum superposition. This provides a glimpse of how the mathematical structure of polynomials, quantum dynamics and optimisation can come together to approach optimisation problems with a quantum computer. The aim is not to assume a background in quantum computing, but to use familiar ideas from mathematics and physics to build an intuitive picture of how quantum algorithms arise.