Exponential quantum speed-ups are generic

  title={Exponential quantum speed-ups are generic},
  author={Fernando G. S. L. Brand{\~a}o and Michal Horodecki},
  journal={Quantum Information & Computation},
A central problem in quantum computation is to understand which quantum circuits are useful for exponential speed-ups over classical computation. We address this question in the setting of query complexity and show that for almost any sufficiently long quantum circuit one can construct a black-box problem which is solved by the circuit with a constant number of quantum queries, but which requires exponentially many classical queries, even if the classical machine has the ability to postselect. 

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