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Phys Rev Lett. 2004 Apr 30;92(17):177906. Epub 2004 Apr 30.

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

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  • 1Institute for Quantum Computing, University of Waterloo, Ontario, Canada N2L 3G1.


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 statistics. Our result also illustrates the role of chaos in the process of decoherence.

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