Grant: Discovery Grants Program - Individual

Recently, quantum information theory has produced significant scientific achievements, such as the complexity theory result MIP* = RE, the establishment of quantum advantage, and protocols for delegating quantum computation. Central to these breakthroughs is a delicate interplay between the relatively young field of quantum complexity theory, and various disciplines. For example, techniques in operator algebras have facilitated breakthroughs in non-locality/self-testing, a key ingredient in both delegated quantum computation and the MIP* = RE result. Conversely, techniques in complexity theory can help make progress in operator algebras, as illustrated by the resolution of Connes Embedding problem via the MIP* = RE result. Similarly, complexity theory tells us which physical systems we cannot efficiently simulate, and thus informs demonstrations of quantum advantage. Navigating this interdisciplinary landscape requires collaboration between experts who can differ significantly in their techniques, and intuitions. This proposal aims to build bridges across these disciplines in order to obtain highly impactful results on topics such as: Complexity in games, Complexity in quantum graphs, Applications/ Advances in quantum proof protocols, and Applications of quantum advantage. These results are poised to make pivotal contributions to this rapidly evolving field and further reinforce Canada's reputation as a global frontrunner in quantum computing and quantum information theory.