Programming Clifford Unitaries with Symplectic Types

          @misc{ scivideos_PIRSA:24050006,
            doi = {10.48660/24050006},
            url = {https://pirsa.org/24050006},
            author = {Paykin, Jennifer},
            keywords = {Quantum Information},
            language = {en},
            title = {Programming Clifford Unitaries with Symplectic Types},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2024},
            month = {may},
            note = {PIRSA:24050006 see, \url{https://scivideos.org/index.php/pirsa/24050006}}
          }
          

Abstract

This talk will present work-in-progress towards a new programming methodology for Cliffords, where n-ary Clifford unitaries over qudits can be expressed as functions on compact Pauli. Inspired by the fact that projective Cliffords correspond to center-fixing automorphisms on the Pauli group, we develop a type system where well-typed expressions correspond to symplectic morphisms---that is, linear transformations that respect the symplectic form. This language is backed up by a robust categorical and operational semantics, and well-typed functions can be efficiently simulated and synthesized into circuits via Pauli tableaus.