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Quantum process tomography of the quantum Fourier transform

J. Chem. Phys. 121, 6117 (2004); doi:10.1063/1.1785151

Issue Date: 1 October 2004

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Yaakov S. Weinstein, Timothy F. Havel, Joseph Emerson, and Nicolas Boulant
Department of Nuclear Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

Marcos Saraceno
Unidad de Actividad Fisica, Comisión Nacional de Energia Atómica, Tandar, 1429 Buenos Aires, Argentina

Seth Lloyd
d'Arbeloff Laboratory for Information Systems and Technology, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

David G. Cory
Department of Nuclear Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
The results of quantum process tomography on a three-qubit nuclear magnetic resonance quantum information processor are presented and shown to be consistent with a detailed model of the system-plus-apparatus used for the experiments. The quantum operation studied was the quantum Fourier transform, which is important in several quantum algorithms and poses a rigorous test for the precision of our recently developed strongly modulating control fields. The results were analyzed in an attempt to decompose the implementation errors into coherent (overall systematic), incoherent (microscopically deterministic), and decoherent (microscopically random) components. This analysis yielded a superoperator consisting of a unitary part that was strongly correlated with the theoretically expected unitary superoperator of the quantum Fourier transform, an overall attenuation consistent with decoherence, and a residual portion that was not completely positive—although complete positivity is required for any quantum operation. By comparison with the results of computer simulations, the lack of complete positivity was shown to be largely a consequence of the incoherent errors which occurred over the full quantum process tomography procedure. These simulations further showed that coherent, incoherent, and decoherent errors can often be identified by their distinctive effects on the spectrum of the overall superoperator. The gate fidelity of the experimentally determined superoperator was 0.64, while the correlation coefficient between experimentally determined superoperator and the simulated superoperator was 0.79; most of the discrepancies with the simulations could be explained by the cummulative effect of small errors in the single qubit gates. ©2004 American Institute of Physics.
History: Received 1 April 2004; accepted 30 June 2004
Permalink: http://link.aip.org/link/?JCPSA6/121/6117/1
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KEYWORDS and PACS

Keywords
PACS
  • 03.65.Wj
    State reconstruction, quantum tomography
  • 03.65.Yz
    Decoherence; open systems; quantum statistical methods
  • 03.67.Pp
    Quantum error correction and other methods for protection against decoherence
  • 02.30.Nw
    Fourier analysis
  • YEAR: 2004

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PUBLICATION DATA

ISSN:
0021-9606 (print)   1089-7690 (online)
Publisher:
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