Tomorrow at 2pm Qiushi Liu will tell us about his master's thesis, entitled "Quantum Fisher Information Dynamics in Quantum Neural Networks and Information Scrambling". See below for the abstract. Zoom link: https://ethz.zoom.us/j/362994444.

Best,

-joe 

Abstract:

Quantum Fisher information (QFI) is a central concept in the context of quantum metrology. It could be geometrically interpreted as a measure of the statistical distance between neighbouring quantum states, which makes QFI closely connected to a variety of fields in physics. In this thesis, we use QFI to characterize the flow of quantum information in quantum circuits. In particular, we consider the task of learning the optimal measurement for quantum metrology using variational quantum circuits. We empirically observe an intriguing phenomenon that the learning process is split into two stages. In the first stage the training cost undergoes a fast decrease while QFI is locally accumulated. In the second stage, the neural network slightly improves its performance with a slow decrease of local QFI, implying a global scrambling behaviour. This information-theoretic view opens a path to understanding the internal mechanism of quantum machine learning. We furthermore demonstrate that QFI is a natural quantity to detect scrambling and establish a connection between QFI and the out-of-time-order correlation (OTOC) function.