Exponential Speedup with a Single Bit of Quantum Information: Measuring the Average Fidelity Decay
Abstract
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.
 Publication:

Physical Review Letters
 Pub Date:
 April 2004
 DOI:
 10.1103/PhysRevLett.92.177906
 arXiv:
 arXiv:quantph/0310038
 Bibcode:
 2004PhRvL..92q7906P
 Keywords:

 03.67.Lx;
 03.65.Yz;
 05.45.Mt;
 Quantum computation;
 Decoherence;
 open systems;
 quantum statistical methods;
 Quantum chaos;
 semiclassical methods;
 Quantum Physics
 EPrint:
 4 pages, 2 eps figures