Higher-level mathematical language for verifiable quantum information processing
Abstract
The standard formulation of quantum mechanics is not sufficient for an understanding of the interplay of classical and quantum information processing (QIP). This is evident in the plethora of models of quantum computation corresponding to different physical platforms (circuit-based (IBM, Rigetti, IonQ), quantum annealing (D-wave), etc.). A higher-level language is needed. This four-year project will seek to elucidate QIP, which is of great practical importance, by developing tools based on recent mathematical advances, such as categorical quantum mechanics, topological quantum field theories, homotopy type theory, and the Quon picture-language. The project will explore synergies between higher category theory, topological quantum field theories, and quantum information processing. The project will investigate questions such as: how to apply (topological) quantum field theory to quantum information processing in the context of higher category theory; how to draw inspirations from classical information processing in applying category theories; how to frame theorem proving in the context of quantum computation; how to connect homotopy type theory to quantum physics; the relationship between path-integral quantization and higher categories. The project will build on two main approaches: categorical quantum mechanics pioneered by Abramsky and Coecke, and the recent Quon topological picture-language for quantum information developed by Jaffe and collaborators. The results will provide insights in quantum information processing and in areas of pure mathematics and logic, such as quantum probability theory, topological quantum field theories, and homotopy type theory.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jul 02, 2019
- Source ID
- W911NF1910397
Entities
People
- George Siopsis
Organizations
- Army Contracting Command
- United States Army
- University of Tennessee