Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)when quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2019.31
URN: urn:nbn:de:0030-drops-112463
URL: https://drops.dagstuhl.de/opus/volltexte/2019/11246/
Gharibian, Sevag ; Parekh, Ojas
Almost Optimal Classical Approximation Algorithms for a Quantum Generalization of Max-Cut
| pdf-format: |
|
Abstract
Approximation algorithms for constraint satisfaction problems (CSPs) are a central direction of study in theoretical computer science. In this work, we study classical product state approximation algorithms for a physically motivated quantum generalization of Max-Cut, known as the quantum Heisenberg model. This model is notoriously difficult to solve exactly, even on bipartite graphs, in stark contrast to the classical setting of Max-Cut. Here we show, for any interaction graph, how to classically and efficiently obtain approximation ratios 0.649 (anti-feromagnetic XY model) and 0.498 (anti-ferromagnetic Heisenberg XYZ model). These are almost optimal; we show that the best possible ratios achievable by a product state for these models is 2/3 and 1/2, respectively.
BibTeX - Entry
@InProceedings{gharibian_et_al:LIPIcs:2019:11246,
author = {Sevag Gharibian and Ojas Parekh},
title = {{Almost Optimal Classical Approximation Algorithms for a Quantum Generalization of Max-Cut}},
booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)},
pages = {31:1--31:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-125-2},
ISSN = {1868-8969},
year = {2019},
volume = {145},
editor = {Dimitris Achlioptas and L{\'a}szl{\'o} A. V{\'e}gh},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2019/11246},
URN = {urn:nbn:de:0030-drops-112463},
doi = {10.4230/LIPIcs.APPROX-RANDOM.2019.31},
annote = {Keywords: Approximation algorithm, Max-Cut, local Hamiltonian, QMA-hard, Heisenberg model, product state}
}
| Keywords: | Approximation algorithm, Max-Cut, local Hamiltonian, QMA-hard, Heisenberg model, product state | |
| Seminar: | Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019) | |
| Issue date: | 2019 | |
| Date of publication: | 17.09.2019 |
