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We propose quantum subroutines for the simplex method that avoid classical computation of the basis inverse.
Quantum algorithms for zero-sum games
van Apeldoorn, J. and Gilyén, A. (2019b) · 1904
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Quantum algorithm for systems of linear equations with exponentially improved dependence on precision
Childs, A. M., Kothari, R., and Somma, R. D. (2017) · 1950
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How good is the simplex algorithm
Klee, V. and Minty, G. J. (1972) · 1972
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The average number of pivot steps required by the simplex-method is polynomial
Borgwardt, K.-H. (1982) · 1982
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Linear programming
Chvátal, V. (1983) · 1983
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A practical anti-cycling procedure for linearly constrained optimization
Gill, P. E., Murray, W., Saunders, M. A., and Wright, M. H. (1989) · 1989
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Steepest-edge simplex algorithms for linear programming
Forrest, J. J. and Goldfarb, D. (1992) · 1992
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A subexponential randomized simplex algorithm
Kalai, G. (1992) · 1992
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Estimating the largest eigenvalue by the power and Lanczos algorithms with a random start
Kuczyński, J. and Woźniakowski, H. (1992) · 1992
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A sublinear-time randomized approximation algorithm for matrix games
Grigoriadis, M. D. and Khachiyan, L. G. (1995) · 1995
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A quantum algorithm for finding the minimum
Durr, C. and Hoyer, P. (1996) · 1996
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A fast quantum mechanical algorithm for database search
Grover, L. K. (1996) · 1996
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A subexponential bound for linear programming
Matoušek, J., Sharir, M., and Welzl, E. (1996) · 1996
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Strengths and weaknesses of quantum computing
Bennett, C. H., Bernstein, E., Brassard, G., and Vazirani, U. (1997) · 1997
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Introduction to Linear Optimization
Bertsimas, D. and Tsitsiklis, J. (1997) · 1997
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Quantum amplitude amplification and estimation
Brassard, G., Hoyer, P., Mosca, M., and Tapp, A. (2002) · 2002
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Creating superpositions that correspond to efficiently integrable probability distributions
Grover, L. and Rudolph, T. (2002) · 2002
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Quantum computation and quantum information
Nielsen, M. A. and Chuang, I. (2002) · 2002
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Quantum search on bounded-error inputs
Høyer, P., Mosca, M., and De Wolf, R. (2003) · 2003
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Quantum search algorithms
Ambainis, A. (2004) · 2004
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Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time
Spielman, D. A. and Teng, S.-H. (2004) · 2004
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Quantum speed-ups for solving semidefinite programs
Brandao, F. G. and Svore, K. M. (2017) · 2017
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An introduction to quantum computing, without the physics
Nannicini, G. (2017) · 2017
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Quantum SDP-solvers: Better upper and lower bounds
van Apeldoorn, J., Gilyén, A., Gribling, S., and de Wolf, R. (2017) · 2017
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Chakraborty, S., Gilyén, A., and Jeffery, S. (2018) · 2018
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A friendly smoothed analysis of the simplex method
Dadush, D. and Huiberts, S. (2018) · 2018
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Selected topics in column generation
Lübbecke, M. E. and Desrosiers, J. (2005) · 2005
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Fast sparse matrix multiplication
Yuster, R. and Zwick, U. (2005) · 2005
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Two new bounds for the random-edge simplex-algorithm
Gärtner, B. and Kaibel, V. (2007) · 2007
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Quantum random access memory
Giovannetti, V., Lloyd, S., and Maccone, L. (2008) · 2008
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Quantum Algorithm for Linear Systems of Equations
Harrow, A. W., Hassidim, A., and Lloyd, S. (2009) · 2009
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Preconditioned quantum linear system algorithm
Clader, B. D., Jacobs, B. C., and Sprouse, C. R. (2013) · 2013
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Kerenidis, I. and Prakash, A. (2018) · 2018
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Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics
Gilyén, A., Su, Y., Low, G. H., and Wiebe, N. (2019) · 2019
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Improvements in Quantum SDP-Solving with Applications
van Apeldoorn, J. and Gilyén, A. (2019a) · 2019
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A quantum interior-point predictor–corrector algorithm for linear programming
Casares, P. A. M. and Martin-Delgado, M. A. (2020) · 2020
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Compilation of fault-tolerant quantum heuristics for combinatorial optimization
Sanders, Y. R., Berry, D. W., Costa, P. C., Tessler, L. W., Wiebe, N., Gidney, C., Neven, H., and Babbush, R. (2020) · 2020
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Quantum interior point methods for semidefinite optimization
Augustino, B., Nannicini, G., Terlaky, T., and Zuluaga, L. (2021) · 2021
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Focus beyond quadratic speedups for error-corrected quantum advantage
Babbush, R., McClean, J. R., Newman, M., Gidney, C., Boixo, S., and Neven, H. (2021) · 2021
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Fast quantum subroutines for the simplex method
Nannicini, G. (2021) · 2021
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Quantum tomography using state-preparation unitaries
van Apeldoorn, J., Cornelissen, A., Gilyén, A., and Nannicini, G. (2022) · 2022
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