The Governors of the University of Calgary

Purpose

Develop a novel representation-theoretic framework for quantum algorithms and quantum compilation using recently developed connections between adelic methods and the Langlands program to quantum computing. Golden gates, optimal gate sets generalizing Clifford+T, are known to exist for all practical application via arithmetic constructions exploiting adelic analysis and recent developments in the Langlands Program. Precisely, these methods produce a number-theoretic shadow of any quantum gate, the “arithmetic avatar”, that allows for the translation of complex structures in quantum computing to a straight-forward combinatorial setting. The project will produce the first practical implementation of this construction in a quantum SDK (Qiskit), as well a rigorous study of a novel approach to quantum algorithm development that arises from this application of adelic methods.