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Improved Approximations for Extremal Eigenvalues of Sparse Hamiltonians

Authors: Daniel Hothem, Ojas Parekh, and Kevin Thompson

Published in: LIPIcs, Volume 266, 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)


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.

Cite as

Daniel Hothem, Ojas Parekh, and Kevin Thompson. Improved Approximations for Extremal Eigenvalues of Sparse Hamiltonians. In 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 266, pp. 6:1-6:10, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@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/entities/document/10.4230/LIPIcs.TQC.2023.6},
  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}
}
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