### Abstract

Quantum state tomography (QST) is the gold standard technique for obtaining an estimate for the state of small quantum systems in the laboratory [1]. Its application to systems with more than a few constituents (e.g. particles) soon becomes impractical as the e ff ort required grows exponentially with the number of constituents. Developing more e ffi cient techniques is particularly pressing as precisely-controllable quantum systems that are well beyond the reach of QST are emerging in laboratories. Motivated by this, there is a considerable ongoing e ff ort to develop new state characterisation tools for quantum many-body systems [2–11]. Here we demonstrate Matrix Product State (MPS) tomography [2], which is theoretically proven to allow the states of a broad class of quantum systems to be accurately estimated with an e ff ort that increases e ffi ciently with constituent number. We use the technique to reconstruct the dynamical state of a trapped-ion quantum simulator comprising up to 14 entangled and individually-controlled spins (qubits): a size far beyond the practical limits of QST. Our results reveal the dynamical growth of entanglement and description complexity as correlations spread out during a quench: a necessary condition for future beyond-classical performance. MPS tomography should therefore find widespread use to study large quantum many-body systems and to benchmark and verify quantum simulators and computers.

Original language | English |
---|---|

Pages (from-to) | 1158–1162 |

Number of pages | 23 |

Journal | Nature Physics |

Volume | 13 |

Early online date | 4 Sep 2017 |

DOIs | |

Publication status | E-pub ahead of print - 4 Sep 2017 |

### Keywords

- quantum state tomography
- small quantum systems
- matrix product state (MPS) tomography

## Profiles

## Cite this

Lanyon, B. P., Maier, C., Holzäpfel, M., Baumgratz, T., Hempel, C., Jurcevic, P., Dhand, I., Buyskikh, A. S., Daley, A. J., Cramer, M., Plenio, M. B., Blatt, R., & Roos, C. F. (2017). Efficient tomography of a quantum many-body system.

*Nature Physics*,*13*, 1158–1162. https://doi.org/10.1038/nphys4244