Quantum Information and Network Science
This event is part of the PhD Final Oral Exams.
It is key to understand how quantum information theory works at the large scale---especially, on or within the statistical theory of graphs/networks. New concepts and methods are awaiting ahead to promote the development of both communities. This presentation consists of three parts to explore this potential direction: Our first work is to understand how to establish long-distance entanglement transmission in a quantum network where each link has non-zero concurrence---a measure of bipartite entanglement. We introduce a fundamental statistical theory, concurrence percolation theory (ConPT), and find the existence of an entanglement transmission threshold predicted by ConPT which is lower than the known classical-percolation-based results---a “quantum advantage” that is more general and efficient than expected. ConPT also shows a percolation-like universal critical behavior derived by finite-size analysis. Our second work is to study continuous-time quantum walk as an open system that strongly interacts with the environment where non-Markovianity may significantly speed up the dynamics. We confirm this speed-up by first introducing a general multi-scale perturbation method that works on integro-differential equations and then building the Hamiltonian on regular networks, e.g., star or complete graphs, which can be mapped to an error correction algorithm scheme of practical significance. Our third work explores the possible use of entanglement entropy (EE) in machine-learning fields. We introduce a new long-short-term-memory-based recurrent neural network architecture using tensorization techniques to forecast chaotic time series, the learnability of which is determined not only by the number of free parameters but also the tensorization complexity---recognized as how EE scales.
Join Zoom Meeting https://bostonu.zoom.us/j/95158303290?pwd=Y0c2QU9sZmh1WDdRSWJ5bDhBOVFXdz09
Meeting ID: 951 5830 3290 Passcode: 873607