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.
@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/entities/document/10.4230/LIPIcs.TQC.2023.12}, 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} }
Feedback for Dagstuhl Publishing