Towards a quantum advantage in machine learning

Abstract: Arguably one of the central challenges in the field of quantum computing is to demonstrate a quantum advantage. This means solving a practically relevant problem faster or better on a current quantum computer than on any classical supercomputer. Machine learning problems may be good candidates for achieving this ambitious goal in the close future.

In this talk I will explain why we think this is the case and which difficulties need to be circumvented to demonstrate a quantum advantage. In particular, we need mathematical tools that allow us to quantify the power of quantum models. I will discuss a recently introduced capacity measure called “effective dimension” and illustrate what it tells us about the power of quantum neural networks. [Based on joint work with Amira Abbas, Alessio Figalli and Stefan Woerner [See https://arxiv.org/abs/2011.00027 and https://arxiv.org/abs/2112.04807].