Quantum boolean functions

          @misc{ scivideos_PIRSA:08120019,
            doi = {10.48660/08120019},
            url = {https://pirsa.org/08120019},
            author = {Montanaro, Ashley},
            keywords = {Quantum Information},
            language = {en},
            title = {Quantum boolean functions},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2008},
            month = {dec},
            note = {PIRSA:08120019 see, \url{https://scivideos.org/pirsa/08120019}}
          }
          

Abstract

In recent years, the analysis of boolean functions has arisen as an important theme in theoretical computer science. In this talk I will discuss an extension of the concept of a boolean function to quantum computation. It turns out that many important classical results in the theory of boolean functions have natural quantum analogues. These include property testing of boolean functions; the Goldreich-Levin algorithm for approximately learning boolean functions; and a theorem of Friedgut, Kalai and Naor on the Fourier spectra of boolean functions. The quantum generalisation of this theorem uses a quantum extension of the hypercontractive inequality of Bonami, Gross and Beckner. This talk is based on joint work with Tobias Osborne.