Classical verification of quantum circuits containing few basis changes

  title={Classical verification of quantum circuits containing few basis changes},
  author={Tommaso F. Demarie and Yingkai Ouyang and Joseph Fitzsimons},
We consider the task of verifying the correctness of quantum computation for a restricted class of circuits which contain at most two basis changes. This contains circuits giving rise to the second level of the Fourier Hierarchy, the lowest level for which there is an established quantum advantage. We show that, when the circuit has an outcome with probability at least the inverse of some polynomial in the circuit size, the outcome can be checked in polynomial time with bounded error by a… 
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