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Quantum linear system algorithms (QLSA) have the potential to speed up Interior Point Methods (IPM).
Quantum algorithm for systems of linear equations with exponentially improved dependence on precision
Andrew M Childs, Robin Kothari, and Rolando D Somma. 2017 · 1950
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An O ( n L ) O(\sqrt{nL}) -iteration homogeneous and self-dual linear programming algorithm
Yinyu Ye, Michael J. Todd, and Shinji Mizuno. 1994 · 1994
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Primal-Dual Interior-Point Methods
Stephen J Wright. 1997 · 1997
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Convergence analysis of a long-step primal-dual infeasible interior-point LP algorithm based on iterative linear solvers
Renato DC Monteiro and Jerome W O’Neal. 2003 · 2003
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Uniform boundedness of a preconditioned normal matrix used in interior-point methods
Renato DC Monteiro, Jerome W O’Neal, and Takashi Tsuchiya. 2004 · 2004
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Polynomiality of an inexact infeasible interior point algorithm for semidefinite programming
Guanglu Zhou and Kim-Chuan Toh. 2004 · 2004
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Interior Point Methods for Linear Optimization
Cornelis Roos, Tamás Terlaky, and J-Ph Vial. 2005 · 2005
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The use of preconditioned iterative linear solvers in interior-point methods and related topics
Jerome W O’Neal. 2006 · 2006
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Convergence analysis of the inexact infeasible interior-point method for linear optimization
Ghussoun Al-Jeiroudi and Jacek Gondzio. 2009 · 2009
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Quantum algorithm for linear systems of equations
Aram W. Harrow, Avinatan Hassidim, and Seth Lloyd. 2009 · 2009
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Variable time amplitude amplification and quantum algorithms for linear algebra problems. In STACS’12 (29th Symposium on Theoretical Aspects of Computer Science) , Vol. 14. LIPIcs, 636–647
Andris Ambainis. 2012 · 2012
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A quantum approximate optimization algorithm
Edward Farhi, Jeffrey Goldstone, and Sam Gutmann. 2014 · 2014
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Iterative refinement for linear programming
Ambros M Gleixner, Daniel E Steffy, and Kati Wolter. 2016 · 2016
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Shantanav Chakraborty, András Gilyén, and Stacey Jeffery. 2018 · 2018
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Quantum linear system algorithm for dense matrices
Leonard Wossnig, Zhikuan Zhao, and Anupam Prakash. 2018 · 2018
An inexact-feasible quantum interior point method for second-order cone optimization
Brandon Augustino, Tamás Terlaky, Mohammadhossein Mohammadisiahroudi, and Luis F Zuluaga. 2021 · 2021
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Efficient use of quantum linear system algorithms in interior point methods for linear optimization
Mohammadhossein Mohammadisiahroudi, Ramin Fakhimi, and Tamás Terlaky. 2022 · 2022
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Fast quantum subroutines for the simplex method
Giacomo Nannicini. 2022 · 2022
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Enhancing the quantum linear systems algorithm using Richardson extrapolation
Almudena Carrera Vazquez, Ralf Hiptmair, and Stefan Woerner. 2022 · 2022
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A Quantum Interior Point Method for Semidefinite Optimization Problems
Brandon Augustino, Giacomo Nannicini, Tamás Terlaky, and Luis F. Zuluaga. 2023 · 2023
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Cited alongside, same era.
Quantum singular value transformation & its algorithmic applications
András Gilyén. 2019 · 2019
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Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics. In Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing , Moses Charikar and Edith Cohen (Eds.). 193–204
András Gilyén, Yuan Su, Guang Hao Low, and Nathan Wiebe. 2019 · 2019
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Hamiltonian simulation by qubitization
Guang Hao Low and Isaac L Chuang. 2019 · 2019
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A quantum interior-point predictor–corrector algorithm for linear programming
PAM Casares and MA Martin-Delgado. 2020 · 2020
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A quantum interior point method for LPs and SDPs
Iordanis Kerenidis and Anupam Prakash. 2020 · 2020
Cited alongside, same era.
Accurately Solving Linear Systems with Quantum Oracles
Mohammadhossein Mohammadisiahroudi, Brandon Augustino, Ramin Fakhimi, Giacomo Nannicini, and Tamás Terlaky. 2023a · 2023
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Mohammadhossein Mohammadisiahroudi, Ramin Fakhimi, Brandon Augustino, and Tamás Terlaky. 2023b · 2023
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Mohammadhossein Mohammadisiahroudi, Ramin Fakhimi, Zeguan Wu, and Tamás Terlaky. 2023c · 2023
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Quantum tomography using state-preparation unitaries. In Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) . SIAM, 1265–1318
Joran van Apeldoorn, Arjan Cornelissen, András Gilyén, and Giacomo Nannicini. 2023 · 2023
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An inexact feasible quantum interior point method for linearly constrained quadratic optimization
Zeguan Wu, Mohammadhossein Mohammadisiahroudi, Brandon Augustino, Xiu Yang, and Tamás Terlaky. 2023 · 2023
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