Realistic Runtime Analysis for Quantum Simplex Computation

authored by: Sabrina Ammann, Maximilian Hess, Debora Ramacciotti, Sándor P. Fekete, Paulina L. A. Goedicke, David Gross, Andreea Lefterovici, Tobias J. Osborne, Michael Perk, Antonio Rotundo, S. E. Skelton, Sebastian Stiller, Timo de Wolff
Abstract: In recent years, strong expectations have been raised for the possible power of quantum computing for solving difficult optimization problems, based on theoretical, asymptotic worst-case bounds. Can we expect this to have consequences for Linear and Integer Programming when solving instances of practically relevant size, a fundamental goal of Mathematical Programming, Operations Research and Algorithm Engineering? Answering this question faces a crucial impediment: The lack of sufficiently large quantum platforms prevents performing real-world tests for comparison with classical methods. In this paper, we present a quantum analog for classical runtime analysis when solving real-world instances of important optimization problems. To this end, we measure the expected practical performance of quantum computers by analyzing the expected gate complexity of a quantum algorithm. The lack of practical quantum platforms for experimental comparison is addressed by hybrid benchmarking, in which the algorithm is performed on a classical system, logging the expected cost of the various subroutines that are employed by the quantum versions. In particular, we provide an analysis of quantum methods for Linear Programming, for which recent work has provided asymptotic speedup through quantum subroutines for the Simplex method. We show that a practical quantum advantage for realistic problem sizes would require quantum gate operation times that are considerably below current physical limitations.
Organisation(s): Multimedia Signal Processing Section
L3S Research Centre
QUEST-Leibniz Research School
Institute of Theoretical Physics
Type: Preprint
Publication date: 16.11.2023
Publication status: Published

BibTeX

@techreport{7fe9ca45f8864876accfbc43027982e6,
title = "Realistic Runtime Analysis for Quantum Simplex Computation",
abstract = " In recent years, strong expectations have been raised for the possible power of quantum computing for solving difficult optimization problems, based on theoretical, asymptotic worst-case bounds. Can we expect this to have consequences for Linear and Integer Programming when solving instances of practically relevant size, a fundamental goal of Mathematical Programming, Operations Research and Algorithm Engineering? Answering this question faces a crucial impediment: The lack of sufficiently large quantum platforms prevents performing real-world tests for comparison with classical methods. In this paper, we present a quantum analog for classical runtime analysis when solving real-world instances of important optimization problems. To this end, we measure the expected practical performance of quantum computers by analyzing the expected gate complexity of a quantum algorithm. The lack of practical quantum platforms for experimental comparison is addressed by hybrid benchmarking, in which the algorithm is performed on a classical system, logging the expected cost of the various subroutines that are employed by the quantum versions. In particular, we provide an analysis of quantum methods for Linear Programming, for which recent work has provided asymptotic speedup through quantum subroutines for the Simplex method. We show that a practical quantum advantage for realistic problem sizes would require quantum gate operation times that are considerably below current physical limitations. ",
keywords = "quant-ph, cs.DS, math.OC",
author = "Sabrina Ammann and Maximilian Hess and Debora Ramacciotti and Fekete, {S{\'a}ndor P.} and Goedicke, {Paulina L. A.} and David Gross and Andreea Lefterovici and Osborne, {Tobias J.} and Michael Perk and Antonio Rotundo and Skelton, {S. E.} and Sebastian Stiller and Wolff, {Timo de}",
note = "39 pages, 8 figures",
year = "2023",
month = nov,
day = "16",
language = "English",
type = "WorkingPaper",
}