License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.TQC.2023.12
URN: urn:nbn:de:0030-drops-183222
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18322/
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Aaronson, Scott ; Grewal, Sabee

Efficient Tomography of Non-Interacting-Fermion States

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LIPIcs-TQC-2023-12.pdf (0.7 MB)

Abstract

We give an efficient algorithm that learns a non-interacting-fermion state, given copies of the state. For a system of n non-interacting fermions and m modes, we show that O(m³ n² log(1/δ) / ε⁴) copies of the input state and O(m⁴ n² log(1/δ)/ ε⁴) time are sufficient to learn the state to trace distance at most ε with probability at least 1 - δ. Our algorithm empirically estimates one-mode correlations in O(m) different measurement bases and uses them to reconstruct a succinct description of the entire state efficiently.

BibTeX - Entry

@InProceedings{aaronson_et_al:LIPIcs.TQC.2023.12,
  author =	{Aaronson, Scott and Grewal, Sabee},
  title =	{{Efficient Tomography of Non-Interacting-Fermion States}},
  booktitle =	{18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)},
  pages =	{12:1--12:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-283-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{266},
  editor =	{Fawzi, Omar and Walter, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/18322},
  URN =		{urn:nbn:de:0030-drops-183222},
  doi =		{10.4230/LIPIcs.TQC.2023.12},
  annote =	{Keywords: free-fermions, Gaussian fermions, non-interacting fermions, quantum state tomography, efficient tomography}
}

Keywords: free-fermions, Gaussian fermions, non-interacting fermions, quantum state tomography, efficient tomography
Collection: 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)
Issue Date: 2023
Date of publication: 18.07.2023

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