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Fast and Robust Quantum State Tomography from Few Basis Measurements

Authors Daniel Stilck França , Fernando G.S L. Brandão , Richard Kueng

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Author Details

Daniel Stilck França
  • QMATH, Department of Mathematical Sciences, University of Copenhagen, Denmark
Fernando G.S L. Brandão
  • AWS Center for Quantum Computing, Pasadena, CA, USA
  • Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, USA
Richard Kueng
  • Institute for Integrated Circuits, Johannes Kepler University Linz, Austria


We thank Chris Ferrie, David Gross, Thomas Grurl, Cécilia Lancien, Robert König, Oliver H. Schwarze and Joel Tropp for valuable input and helpful discussions.

Cite AsGet BibTex

Daniel Stilck França, Fernando G.S L. Brandão, and Richard Kueng. Fast and Robust Quantum State Tomography from Few Basis Measurements. In 16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 197, pp. 7:1-7:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


Quantum state tomography is a powerful but resource-intensive, general solution for numerous quantum information processing tasks. This motivates the design of robust tomography procedures that use relevant resources as sparingly as possible. Important cost factors include the number of state copies and measurement settings, as well as classical postprocessing time and memory. In this work, we present and analyze an online tomography algorithm designed to optimize all the aforementioned resources at the cost of a worse dependence on accuracy. The protocol is the first to give provably optimal performance in terms of rank and dimension for state copies, measurement settings and memory. Classical runtime is also reduced substantially and numerical experiments demonstrate a favorable comparison with other state-of-the-art techniques. Further improvements are possible by executing the algorithm on a quantum computer, giving a quantum speedup for quantum state tomography.

Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum computation theory
  • Hardware → Quantum technologies
  • Theory of computation → Quantum information theory
  • Mathematics of computing → Probabilistic inference problems
  • quantum tomography
  • low-rank tomography
  • Gibbs states
  • random measurements


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