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Riofrío, C A; Gross, D; Flammia, S T; Monz, T; Nigg, D; Blatt, R; Eisert, J
Nature communications, 05/2017, Volume: 8, Issue: 1Journal Article
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.
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