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Science 28 September 2007:
Vol. 317. no. 5846, pp. 1893 - 1896
DOI: 10.1126/science.1145699
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Reports

Symmetrized Characterization of Noisy Quantum Processes

Joseph Emerson1,2, Marcus Silva2,3, Osama Moussa2,3, Colm Ryan2,3, Martin Laforest2,3, Jonathan Baugh2, David G. Cory4 and Raymond Laflamme2,3,5

1 Department of Applied Math, University of Waterloo, Waterloo, ON N2L 3G1, Canada.
2 Institute for Quantum Computing, University of Waterloo, Waterloo, ON N2L 3G1, Canada.
3 Department of Physics and Astronomy, University of Waterloo, Waterloo, ON N2L 3G1, Canada.
4 Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
5 Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5, Canada.


Figure 1 Fig. 1. Schematic of coarse-graining by symmetrization. Averaging the noise {Lambda} by twirling under a symmetry group yields an effective noise process that has a reduced number of independent parameters. Distinct symmetrization groups [represented by (a) red and (b) blue] uniformize different subsets of parameters. [View Larger Version of this Image (33K GIF file)]
 

Figure 2 Fig. 2. Quantum circuit. One experimental run consists of a conjugation of the noise process {Lambda}. The standard protocol requires conjugation only by an element Ci, whereas the ensemble protocol requires conjugating {Lambda} also by a permutation {pi}s of the qubits. The standard protocol requires only one input state Formula, whereas the ensemble protocol requires n distinct input operators {rho}w. [View Larger Version of this Image (7K GIF file)]
 

Figure 3 Fig. 3. Results for pw from experiments 5 and 6 in Table 1. Shown are projections of the four-dimensional likelihood function onto various probability planes. The asymmetry seen in some of the confidence areas is a result of this projection. The results for one cycle with 10 µs pulse spacing (experiment 5) are in red, and the results for two cycles with 5 µs spacing (experiment 6) are in blue. [View Larger Version of this Image (29K GIF file)]
 

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