PIRSA:17100062

The sum-over-paths technique for Clifford circuits

Penney, M. (2017). The sum-over-paths technique for Clifford circuits. Perimeter Institute. https://pirsa.org/17100062

Penney, Mark. The sum-over-paths technique for Clifford circuits. Perimeter Institute, Oct. 17, 2017, https://pirsa.org/17100062 

          @misc{ pirsa_PIRSA:17100062,
            doi = {10.48660/17100062},
            url = {https://pirsa.org/17100062},
            author = {Penney, Mark},
            keywords = {Quantum Foundations},
            language = {en},
            title = {The sum-over-paths technique for Clifford circuits},
            publisher = {Perimeter Institute},
            year = {2017},
            month = {oct},
            note = {PIRSA:17100062 see, \url{https://pirsa.org}}
          }

Mark Penney

Scotiabank

Talk number
PIRSA:17100062
Collection
Talk Type
Subject
Abstract

The path integral formulation of quantum mechanics has been immensely influential, particularly in high energy physics. However, its applications to quantum circuits has so far been more limited. In this talk I will discuss the sum-over-paths approach to computing transition amplitudes in Clifford circuits. In such a formulation, the relative phases of different discrete-time paths through the configuration space can be defined in terms of a classical action which is provided by the discrete Wigner representation. As an application of the sum-over-paths technique I will show how to recover a version of the Gottesman-Knill theorem, namely that the transition amplitudes in Clifford circuits can be computed efficiently.