PIRSA:12030117 Scientific Series Quantum Information

DOI10.48660/12030117

Series: Perimeter Institute Quantum Discussions

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}}
}

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.

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