PIRSA:12030117

Negative Quasi-Probability Representation is a Necessary Resource for Quantum Computation

Veitch, V. (2012). Negative Quasi-Probability Representation is a Necessary Resource for Quantum Computation. Perimeter Institute. https://pirsa.org/12030117

Veitch, Victor. Negative Quasi-Probability Representation is a Necessary Resource for Quantum Computation. Perimeter Institute, Mar. 21, 2012, https://pirsa.org/12030117 

          @misc{ pirsa_PIRSA:12030117,
            doi = {10.48660/12030117},
            url = {https://pirsa.org/12030117},
            author = {Veitch, Victor},
            keywords = {Quantum Information},
            language = {en},
            title = {Negative Quasi-Probability Representation is a Necessary Resource for Quantum Computation},
            publisher = {Perimeter Institute},
            year = {2012},
            month = {mar},
            note = {PIRSA:12030117 see, \url{https://pirsa.org}}
          }

Victor Veitch Institute for Quantum Computing (IQC)

DOI 10.48660/12030117
Collection
Talk Type Scientific Series
Subject

Abstract

Abstract The magic state model of quantum computation gives a recipe for universal quantum computation using perfect Clifford operations and repeat preparations of a noisy ancilla state. It is an open problem to determine which ancilla states enable universal quantum computation in this model. Here we show that for systems of odd dimension a necessary condition for a state to enable universal quantum computation is that it have negative representation in a particular quasi-probability representation which is a discrete analogue to the Wigner function. This condition implies the existence of a large class of bound states for magic state distillation: states which cannot be prepared using Clifford operations but do not enable universal quantum computation.