Have we seen a demonstration of experimental quantum advantage?

In this talk we'll discuss the status quo regarding the latest experimental quantum advantage claims and the evidence for their classical hardness. In particular, we'll talk about the latest complexity theoretic results for believing that near-term, random quantum circuit experiments give rise to a provable quantum advantage over any efficient classical algorithm. We'll then talk about the current gaps between theory and experiment. A particular focus will be on understanding if uncorrected noise, which is a defining characteristic of any near-term quantum experiment, can be exploited by fast classical simulation algorithms.

This will be a survey talk that will discuss the latest results in the area including arXiv:2411.04566, 2306.16659 and 2306.03709.