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Efficient tomography of a quantum many-body system

Nature Physics volume 13, pages 1158–1162 (2017)Cite this article

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Abstract

Quantum state tomography is the standard technique for estimating the quantum state of small systems1. But its application to larger systems soon becomes impractical as the required resources scale exponentially with the size. Therefore, considerable effort is dedicated to the development of new characterization tools for quantum many-body states2,3,4,5,6,7,8,9,10,11. Here we demonstrate matrix product state tomography2, which is theoretically proven to allow for the efficient and accurate estimation of a broad class of quantum states. We use this technique to reconstruct the dynamical state of a trapped-ion quantum simulator comprising up to 14 entangled and individually controlled spins: a size far beyond the practical limits of quantum state tomography. Our results reveal the dynamical growth of entanglement and describe its complexity as correlations spread out during a quench: a necessary condition for future demonstrations of better-than-classical performance. Matrix product state tomography should therefore find widespread use in the study of large quantum many-body systems and the benchmarking and verification of quantum simulators and computers.

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Figure 1: Generation and efficient characterization of locally correlated quantum states.
Figure 2: Local measurement results for an 8-spin system quench.
Figure 3: MPS tomography results for an 8-spin quench.
Figure 4: MPS tomography results for a 14-spin quench.

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Acknowledgements

Work in Innsbruck was supported by the Austrian Science Fund (FWF) under the grant number P25354-N20, by the European Commission via the integrated project SIQS, by the Institut für Quanteninformation GmbH and by the US Army Research Office through grant W911NF-14-1-0103. All statements of fact, opinion or conclusions contained herein are those of the authors and should not be construed as representing the official views or policies of ARO, the ODNI, or the US Government. We thank H. Shen and T. Brydges for experimental support in the final stage of the experiment. Work in Ulm was supported by an Alexander von Humboldt Professorship, the ERC Synergy grant BioQ, the EU projects QUCHIP and EQUAM, the US Army Research Office Grant No. W91-1NF-14-1-0133 and the BMBF Verbundproject QuOReP. Numerical computations have been supported by the state of Baden-Württemberg through bwHPC and the German Research Foundation (DFG) through grant no INST 40/467-1 FUGG. I.D. acknowledges support from the Alexander von Humboldt Foundation. M.H. acknowledges contributions from D. Suess to jointly developed code used for data analysis. Work at Strathclyde is supported by the European Union Horizon 2020 collaborative project QuProCS (grant agreement 641277), and by AFOSR grant FA9550-12-1-0057. M.C. acknowledges the ERC grant QFTCMPS and SIQS, the cluster of excellence EXC201 Quantum Engineering and Space-Time Research, and the DFG SFB 1227 (DQ-mat). T.B. acknowledges EPSRC (EP/K04057X/2) and the UK National Quantum Technologies Programme (EP/M01326X/1). B.P.L. acknowledges support by the START prize of the Austrian FWF project Y 849-N20.

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Author notes

  1. B. P. Lanyon and C. Maier: These authors contributed equally to this work.

Authors and Affiliations

  1. Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Technikerstr. 21A, 6020 Innsbruck, Austria

    B. P. Lanyon, C. Maier, P. Jurcevic, R. Blatt & C. F. Roos

  2. Institut für Experimentalphysik, Universität Innsbruck, Technikerstr. 25, 6020 Innsbruck, Austria

    B. P. Lanyon, C. Maier, C. Hempel, P. Jurcevic, R. Blatt & C. F. Roos

  3. Institut für Theoretische Physik and IQST, Albert-Einstein-Allee 11, Universität Ulm, 89069 Ulm, Germany

    M. Holzäpfel, T. Baumgratz, I. Dhand, M. Cramer & M. B. Plenio

  4. Department of Physics, Clarendon Laboratory, University of Oxford, Oxford OX1 3PU, UK

    T. Baumgratz

  5. Department of Physics, University of Warwick, Coventry CV4 7AL, UK

    T. Baumgratz

  6. ARC Centre for Engineered Quantum Systems, School of Physics, The University of Sydney, Sydney, New South Wales, 2006, Australia

    C. Hempel

  7. Department of Physics and SUPA, University of Strathclyde, Glasgow G4 0NG, UK

    A. S. Buyskikh & A. J. Daley

  8. Institut für Theoretische Physik, Leibniz Universität Hannover, 30167 Hannover, Germany

    M. Cramer

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Contributions

B.P.L., C.F.R., M.B.P. and M.C. developed and supervised the project; C.M., C.H., B.P.L., P.J., R.B. and C.F.R. performed and contributed to the experiments; B.P.L., M.H., T.B., C.M., C.F.R., I.D., A.S.B. and A.J.D. performed data analysis and modelling; B.P.L. wrote the manuscript, with contributions from all authors.

Corresponding authors

Correspondence to B. P. Lanyon, M. B. Plenio or C. F. Roos.

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The authors declare no competing financial interests.

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Lanyon, B., Maier, C., Holzäpfel, M. et al. Efficient tomography of a quantum many-body system. Nature Phys 13, 1158–1162 (2017). https://doi.org/10.1038/nphys4244

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