CQIS: RUI: Quantum Resources via Free Operation Symmetry

Recent and near-future quantum technologies will push the boundaries of information processing, with applications in communication, computation, and measurement. This project studies underlying problems in theoretical physics and mathematics that make “quantum advantage” possible. In addition to achieving scientific progress through new results, a major project component is scientific development of undergraduate students through participation in real research. This project will implement a resource theory framework to study classes of invertible free operations including local unitary transformations, permutations of subsystems, and matchgates (two-qubit operators arising from fermionic physics) to probe multiparticle quantum entanglement and classical simulatability, and to develop applications for quantum protocols. Methodology will utilize representation theory of Lie groups and Lie algebras, together with the PI’s past results. Achievements will contribute theoretical results and applications in mainstream Quantum Information Science. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.