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Title:
Exponential Speedup with a Single Bit of Quantum Information: Measuring the Average Fidelity Decay
Authors:
Poulin, David; Blume-Kohout, Robin; Laflamme, Raymond; Ollivier, Harold
Affiliation:
AA(Institute for Quantum Computing, University of Waterloo, Ontario, Canada N2L 3G1 and Perimeter Institute for Theoretical Physics, 35 King Street N., Waterloo, Ontario, Canada N2J 2W9), AB(Institute for Quantum Computing, University of Waterloo, Ontario, Canada N2L 3G1 and Perimeter Institute for Theoretical Physics, 35 King Street N., Waterloo, Ontario, Canada N2J 2W9), AC(Institute for Quantum Computing, University of Waterloo, Ontario, Canada N2L 3G1 and Perimeter Institute for Theoretical Physics, 35 King Street N., Waterloo, Ontario, Canada N2J 2W9), AD(Institute for Quantum Computing, University of Waterloo, Ontario, Canada N2L 3G1 and Perimeter Institute for Theoretical Physics, 35 King Street N., Waterloo, Ontario, Canada N2J 2W9)
Publication:
Physical Review Letters, vol. 92, Issue 17, id. 177906 (PhRvL Homepage)
Publication Date:
04/2004
Origin:
APS
PACS Keywords:
Quantum computation, Decoherence, open systems, quantum statistical methods, Quantum chaos, semiclassical methods
DOI:
10.1103/PhysRevLett.92.177906
Bibliographic Code:
2004PhRvL..92q7906P

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.
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