Experimental quantum compressed sensing for a seven-qubit system

C. A. Riofrío (), D. Gross, S. T. Flammia, T. Monz, D. Nigg, R. Blatt and J. Eisert ()
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C. A. Riofrío: Dahlem Center for Complex Quantum Systems, Freie Universität Berlin
D. Gross: Institute for Theoretical Physics, University of Cologne
S. T. Flammia: Centre for Engineered Quantum Systems, School of Physics, The University of Sydney
T. Monz: Institut für Experimentalphysik, Universität Innsbruck
D. Nigg: Institut für Experimentalphysik, Universität Innsbruck
R. Blatt: Institut für Experimentalphysik, Universität Innsbruck
J. Eisert: Dahlem Center for Complex Quantum Systems, Freie Universität Berlin

Nature Communications, 2017, vol. 8, issue 1, 1-8

Abstract: Abstract Well-controlled quantum devices with their increasing system size face a new roadblock hindering further development of quantum technologies. The effort of quantum tomography—the reconstruction of states and processes of a quantum device—scales unfavourably: state-of-the-art systems can no longer be characterized. Quantum compressed sensing mitigates this problem by reconstructing states from incomplete data. Here we present an experimental implementation of compressed tomography of a seven-qubit system—a topological colour code prepared in a trapped ion architecture. We are in the highly incomplete—127 Pauli basis measurement settings—and highly noisy—100 repetitions each—regime. Originally, compressed sensing was advocated for states with few non-zero eigenvalues. We argue that low-rank estimates are appropriate in general since statistical noise enables reliable reconstruction of only the leading eigenvectors. The remaining eigenvectors behave consistently with a random-matrix model that carries no information about the true state.

Date: 2017
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DOI: 10.1038/ncomms15305

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