Browsing by Author "Rowell, Eric"

Now showing 1 - 2 of 2

Conference: ICMS: Topological Quantum Computing
Mathematics; https://hdl.handle.net/20.500.14641/1100; National Science Foundation
Quantum computation has been a major area of research for several decades now, with researchers from many scientific fields across academia, industry and government working together towards the development of quantum technologies. If a powerful quantum computer can be built it will fundamentally transform the landscape of information science and technology. While errors due to the delicate nature of typical quantum states have mitigated progress, topological quantum computation (TQC) is an approach that could overcome this issue. This is by utilizing materials in which information can be "knotted," like a quantum quipu, making them naturally robust against the most common errors. After several years of the relevant research groups working separately, the time is right to bring together a diverse group of physicists and mathematicians with the goal of re-examining the field and exploring new platforms for topological quantum computation. This grant supports the participation of US-based researchers in a workshop to be held in the UK to achieve this goal, foster new collaborations between researchers in the US, the UK, and the rest of the world, and broaden the participation of junior researchers and members of groups historically under-represented in this area. This workshop will bring together researchers in a diversity of fields in and around TQC for the purpose of broadening and deepening the subject, with an eye towards accelerating the realization of scalable technology. The hurdle of scalable fault-tolerance is insurmountable with the current incremental progress -- while it is possible to engineer systems supporting hundreds of physical qubits, applications beyond mere proof of principle require millions of qubits to implement robust error correction. Topological quantum computation relies upon the preparation of topological phases of matter supporting non-abelian anyons to perform inherently fault-tolerant operations. As errors are corrected at the hardware level through the topological nature of anyons, the problem of scalability is simultaneously overcome. On the other hand, despite years of effort we still do not have unassailable confirmation that non-abelian anyons exist. We will explore new directions beyond the traditional anyon community, embracing relevant topics such as quantum cellular automata, fractons, categorical symmetries and motion groups in 3-dimensions. A website for this event is available at: https://www.icms.org.uk/TopologicalQuantumComputation.
FRG: cQIS: Collaborative Research: Mathematical Foundations of Topological Quantum Computation and Its Applications
Mathematics; TAMU; https://hdl.handle.net/20.500.14641/524; National Science Foundation
A second quantum revolution in and around the construction of a useful quantum computer has been advancing dramatically in the last few years. Topological phases of matter, the importance of which has been recognized by scientific awards that include the 2016 Nobel prize in physics, exhibit many-body quantum entanglement. This makes such materials prime candidates for use in a quantum computer. Topological quantum computation is maturing at the forefront of the second quantum revolution as a primary application of topological phases of matter. The theoretical foundation for the second quantum revolution remains under development, but it appears clear that algebras and their representations will play a role analogous to that played by group theory in the first quantum revolution. This focused research group aims to formulate the theoretical foundations of topological quantum computation, leading to an eventual theoretical foundation for the second quantum revolution. It is anticipated that the results of the research will guide and accelerate the construction of a topological quantum computer. A working topological quantum computer will fundamentally transform the landscape of information science and technology. The project includes participation by graduate students and postdoctoral associates in the interdisciplinary research. The goal of topological quantum computation is the construction of a useful quantum computer based on braiding anyons. The hardware of an anyonic quantum computer will be a topological phase of matter that harbors non-abelian anyons. A physical system is in a topological phase if at low energies some physical quantities are topologically invariant. Topological properties are non-local, yet can manifest themselves through local geometric properties. The success of topological quantum computation hinges on controlling topological phases and understanding their computational power. This research addresses the mathematical, physical, and computational aspects of topological quantum computation. The projects include classification of super-modular categories, vector-valued modular forms for modular categories, extension of modular categories to three dimensions, simulation of conformal field theories, topological quantum computation with gapped boundaries and symmetry defects, and universality of topological computing models. The research has potential impacts ranging from new understanding of vertex operator algebras to the development of useful quantum computers. One specific goal is a structure theory of modular categories analogous to that of finite groups. Such a theory would lead to a structure theory of two-dimensional topological phases of matter.