Experimental quantum compressed sensing for a seven-qubit system

Nature Communications
C A RiofríoJens Eisert

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.

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Citations

Mar 10, 2018·Science·Jianwei WangMark G Thompson
Jul 7, 2017·Reports on Progress in Physics·G Wendin
Jun 30, 2019·Optics Express·Frédéric BouchardEbrahim Karimi
Aug 7, 2019·Physical Review Letters·Timothy J ProctorKevin Young
Jan 25, 2020·Physical Review Letters·Pengcheng YangJianming Cai
May 26, 2018·Physical Review Letters·M GluzaL Aolita
Nov 10, 2018·Physical Review Letters·I RothM Kliesch
Jun 27, 2019·Nature Communications·James SchneelochGregory A Howland
Jan 25, 2020·Physical Review Letters·Andreas ElbenPeter Zoller
Apr 2, 2019·Physical Review Letters·D AhnL L Sánchez-Soto
Dec 24, 2019·Physical Review Letters·Giacomo TorlaiManuel Endres
Oct 28, 2017·Physical Review Letters·H Sosa-MartinezP S Jessen
Jan 16, 2019·Optics Express·Radim HošákMiroslav Ježek
Jun 13, 2020·Physical Review Letters·Yosep KimYoon-Ho Kim
Sep 7, 2019·Physical Review Letters·V MétillonI Dotsenko

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