PIRSA:24050006 Conference Quantum Information

DOI10.48660/24050006

Conference/School: Foundations of Quantum Computational Advantage

Paykin, J. (2024). Programming Clifford Unitaries with Symplectic Types. Perimeter Institute. https://pirsa.org/24050006

Paykin, Jennifer. Programming Clifford Unitaries with Symplectic Types. Perimeter Institute, May. 01, 2024, https://pirsa.org/24050006 

@misc{ pirsa_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},
  year = {2024},
  month = {may},
  note = {PIRSA:24050006 see, \url{https://pirsa.org}}
}

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.

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