2 Search Results for "Jethwani, Dhawal"

Document
DOI: 10.4230/LIPIcs.ESA.2025.73
Classical Algorithms for Constant Approximation of the Ground State Energy of Local Hamiltonians

Authors: François Le Gall

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
We construct classical algorithms computing an approximation of the ground state energy of an arbitrary k-local Hamiltonian acting on n qubits. We first consider the setting where a good "guiding state" is available, which is the main setting where quantum algorithms are expected to achieve an exponential speedup over classical methods. We show that a constant approximation (i.e., an approximation with constant relative accuracy) of the ground state energy can be computed classically in poly (1/χ,n) time and poly(n) space, where χ denotes the overlap between the guiding state and the ground state (as in prior works in dequantization, we assume sample-and-query access to the guiding state). This gives a significant improvement over the recent classical algorithm by Gharibian and Le Gall (SICOMP 2023), and matches (up to a polynomial overhead) both the time and space complexities of quantum algorithms for constant approximation of the ground state energy. We also obtain classical algorithms for higher-precision approximation. For the setting where no guided state is given (i.e., the standard version of the local Hamiltonian problem), we obtain a classical algorithm computing a constant approximation of the ground state energy in 2^O(n) time and poly(n) space. To our knowledge, before this work it was unknown how to classically achieve these bounds simultaneously, even for constant approximation. We also discuss complexity-theoretic aspects of our results.
Cite as

François Le Gall. Classical Algorithms for Constant Approximation of the Ground State Energy of Local Hamiltonians. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 73:1-73:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{legall:LIPIcs.ESA.2025.73,
  author =	{Le Gall, Fran\c{c}ois},
  title =	{{Classical Algorithms for Constant Approximation of the Ground State Energy of Local Hamiltonians}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{73:1--73:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.73},
  URN =		{urn:nbn:de:0030-drops-245419},
  doi =		{10.4230/LIPIcs.ESA.2025.73},
  annote =	{Keywords: approximation algorithms, quantum computing, dequantization}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2020.53
Quantum-Inspired Classical Algorithms for Singular Value Transformation

Authors: Dhawal Jethwani, François Le Gall, and Sanjay K. Singh

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

Abstract
A recent breakthrough by Tang (STOC 2019) showed how to "dequantize" the quantum algorithm for recommendation systems by Kerenidis and Prakash (ITCS 2017). The resulting algorithm, classical but "quantum-inspired", efficiently computes a low-rank approximation of the users' preference matrix. Subsequent works have shown how to construct efficient quantum-inspired algorithms for approximating the pseudo-inverse of a low-rank matrix as well, which can be used to (approximately) solve low-rank linear systems of equations. In the present paper, we pursue this line of research and develop quantum-inspired algorithms for a large class of matrix transformations that are defined via the singular value decomposition of the matrix. In particular, we obtain classical algorithms with complexity polynomially related (in most parameters) to the complexity of the best quantum algorithms for singular value transformation recently developed by Chakraborty, Gilyén and Jeffery (ICALP 2019) and Gilyén, Su, Low and Wiebe (STOC 2019).
Cite as

Dhawal Jethwani, François Le Gall, and Sanjay K. Singh. Quantum-Inspired Classical Algorithms for Singular Value Transformation. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 53:1-53:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{jethwani_et_al:LIPIcs.MFCS.2020.53,
  author =	{Jethwani, Dhawal and Le Gall, Fran\c{c}ois and Singh, Sanjay K.},
  title =	{{Quantum-Inspired Classical Algorithms for Singular Value Transformation}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{53:1--53:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.53},
  URN =		{urn:nbn:de:0030-drops-127193},
  doi =		{10.4230/LIPIcs.MFCS.2020.53},
  annote =	{Keywords: Sampling algorithms, quantum-inspired algorithms, linear algebra}
}
  • Refine by Type
  • 2 Document/PDF
  • 1 Document/HTML

  • Refine by Publication Year
  • 1 2025
  • 1 2020

  • Refine by Author
  • 2 Le Gall, François
  • 1 Jethwani, Dhawal
  • 1 Singh, Sanjay K.

  • Refine by Series/Journal
  • 2 LIPIcs

  • Refine by Classification
  • 1 Theory of computation → Approximation algorithms analysis
  • 1 Theory of computation → Design and analysis of algorithms
  • 1 Theory of computation → Quantum computation theory

  • Refine by Keyword
  • 1 Sampling algorithms
  • 1 approximation algorithms
  • 1 dequantization
  • 1 linear algebra
  • 1 quantum computing
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact