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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.2022.7
URN: urn:nbn:de:0030-drops-165144
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16514/
Basso, Joao ;
Farhi, Edward ;
Marwaha, Kunal ;
Villalonga, Benjamin ;
Zhou, Leo
The Quantum Approximate Optimization Algorithm at High Depth for MaxCut on Large-Girth Regular Graphs and the Sherrington-Kirkpatrick Model
Abstract
The Quantum Approximate Optimization Algorithm (QAOA) finds approximate solutions to combinatorial optimization problems. Its performance monotonically improves with its depth p. We apply the QAOA to MaxCut on large-girth D-regular graphs. We give an iterative formula to evaluate performance for any D at any depth p. Looking at random D-regular graphs, at optimal parameters and as D goes to infinity, we find that the p = 11 QAOA beats all classical algorithms (known to the authors) that are free of unproven conjectures. While the iterative formula for these D-regular graphs is derived by looking at a single tree subgraph, we prove that it also gives the ensemble-averaged performance of the QAOA on the Sherrington-Kirkpatrick (SK) model defined on the complete graph. We also generalize our formula to Max-q-XORSAT on large-girth regular hypergraphs. Our iteration is a compact procedure, but its computational complexity grows as O(p² 4^p). This iteration is more efficient than the previous procedure for analyzing QAOA performance on the SK model, and we are able to numerically go to p = 20. Encouraged by our findings, we make the optimistic conjecture that the QAOA, as p goes to infinity, will achieve the Parisi value. We analyze the performance of the quantum algorithm, but one needs to run it on a quantum computer to produce a string with the guaranteed performance.
BibTeX - Entry
@InProceedings{basso_et_al:LIPIcs.TQC.2022.7,
author = {Basso, Joao and Farhi, Edward and Marwaha, Kunal and Villalonga, Benjamin and Zhou, Leo},
title = {{The Quantum Approximate Optimization Algorithm at High Depth for MaxCut on Large-Girth Regular Graphs and the Sherrington-Kirkpatrick Model}},
booktitle = {17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)},
pages = {7:1--7:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-237-2},
ISSN = {1868-8969},
year = {2022},
volume = {232},
editor = {Le Gall, Fran\c{c}ois and Morimae, Tomoyuki},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/16514},
URN = {urn:nbn:de:0030-drops-165144},
doi = {10.4230/LIPIcs.TQC.2022.7},
annote = {Keywords: Quantum algorithm, Max-Cut, spin glass, approximation algorithm}
}
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Keywords: |
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Quantum algorithm, Max-Cut, spin glass, approximation algorithm |
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Collection: |
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17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022) |
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Issue Date: |
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2022 |
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Date of publication: |
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04.07.2022 |
