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.2023.6
URN: urn:nbn:de:0030-drops-183163
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18316/
Hothem, Daniel ;
Parekh, Ojas ;
Thompson, Kevin
Improved Approximations for Extremal Eigenvalues of Sparse Hamiltonians
Abstract
We give a classical 1/(qk+1)-approximation for the maximum eigenvalue of a k-sparse fermionic Hamiltonian with strictly q-local terms, as well as a 1/(4k+1)-approximation when the Hamiltonian has both 2-local and 4-local terms. More generally we obtain a 1/O(qk²)-approximation for k-sparse fermionic Hamiltonians with terms of locality at most q. Our techniques also yield analogous approximations for k-sparse, q-local qubit Hamiltonians with small hidden constants and improved dependence on q.
BibTeX - Entry
@InProceedings{hothem_et_al:LIPIcs.TQC.2023.6,
author = {Hothem, Daniel and Parekh, Ojas and Thompson, Kevin},
title = {{Improved Approximations for Extremal Eigenvalues of Sparse Hamiltonians}},
booktitle = {18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)},
pages = {6:1--6:10},
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/2023/18316},
URN = {urn:nbn:de:0030-drops-183163},
doi = {10.4230/LIPIcs.TQC.2023.6},
annote = {Keywords: Approximation algorithms, Extremal eigenvalues, Sparse Hamiltonians, Fermionic Hamiltonians, Qubit Hamiltonians}
}
Keywords: |
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Approximation algorithms, Extremal eigenvalues, Sparse Hamiltonians, Fermionic Hamiltonians, Qubit Hamiltonians |
Collection: |
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18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023) |
Issue Date: |
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2023 |
Date of publication: |
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18.07.2023 |