Extremal eigenvalues of local Hamiltonians

Aram W. Harrow; Ashley Montanaro

doi:10.22331/q-2017-04-25-6

Extremal eigenvalues of local Hamiltonians

Aram W. Harrow¹ and Ashley Montanaro²

¹Center for Theoretical Physics, Department of Physics, MIT
²School of Mathematics, University of Bristol, UK

Published:	2017-04-25, volume 1, page 6
Eprint:	arXiv:1507.00739v4
Doi:	https://doi.org/10.22331/q-2017-04-25-6
Citation:	Quantum 1, 6 (2017).

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Abstract

We apply classical algorithms for approximately solving constraint satisfaction problems to find bounds on extremal eigenvalues of local Hamiltonians. We consider spin Hamiltonians for which we have an upper bound on the number of terms in which each spin participates, and find extensive bounds for the operator norm and ground-state energy of such Hamiltonians under this constraint. In each case the bound is achieved by a product state which can be found efficiently using a classical algorithm.

► BibTeX data

@article{Harrow2017extremaleigenvalues,
  doi = {10.22331/q-2017-04-25-6},
  url = {https://doi.org/10.22331/q-2017-04-25-6},
  title = {Extremal eigenvalues of local {H}amiltonians},
  author = {Harrow, Aram W. and Montanaro, Ashley},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {1},
  pages = {6},
  month = apr,
  year = {2017}
}

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Cited by

[1] Sergey Bravyi, David Gosset, Robert König, and Kristan Temme, "Approximation algorithms for quantum many-body problems", Journal of Mathematical Physics 60 3, 032203 (2019).

[2] Anurag Anshu, David Gosset, Karen J. Morenz Korol, and Mehdi Soleimanifar, "Improved Approximation Algorithms for Bounded-Degree Local Hamiltonians", Physical Review Letters 127 25, 250502 (2021).

[3] A. Roggero and A. Baroni, "Short-depth circuits for efficient expectation-value estimation", Physical Review A 101 2, 022328 (2020).

[4] Cedric Yen-Yu Lin and Yechao Zhu, "Performance of QAOA on Typical Instances of Constraint Satisfaction Problems with Bounded Degree", arXiv:1601.01744, (2016).

[5] Thiago Bergamaschi, "Improved Product-state Approximation Algorithms for Quantum Local Hamiltonians", arXiv:2210.08680, (2022).

The above citations are from Crossref's cited-by service (last updated successfully 2023-06-08 08:34:15) and SAO/NASA ADS (last updated successfully 2023-06-08 08:34:15). The list may be incomplete as not all publishers provide suitable and complete citation data.

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