Exponential speedup with a single bit of quantum information: measuring the average fidelity decay.

@article{Poulin2003ExponentialSW,
  title={Exponential speedup with a single bit of quantum information: measuring the average fidelity decay.},
  author={David Poulin and Robin Blume-Kohout and Raymond Laflamme and Harold Ollivier},
  journal={Physical review letters},
  year={2003},
  volume={92 17},
  pages={
          177906
        }
}
We present an efficient quantum algorithm to measure the average fidelity decay of a quantum map under perturbation using a single bit of quantum information. Our algorithm scales only as the complexity of the map under investigation. Thus for those maps admitting an efficient gate decomposition, it provides an exponential speedup over known classical procedures. Fidelity decay is important in the study of complex dynamical systems, where it is conjectured to be a signature of eigenvector… 

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