A subgradient approach for constrained binary optimization via quantum adiabatic evolution

Outer approximation method has been proposed for solving the Lagrangian dual of a constrained binary quadratic programming problem via quantum adiabatic evolution in the literature. This should be an efficient prescription for solving the Lagrangian dual problem in the presence of an ideally noise-f...

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Bibliographic Details
Published in:Quantum information processing Vol. 16; no. 8; pp. 1 - 21
Main Authors: Karimi, Sahar, Ronagh, Pooya
Format: Journal Article
Language:English
Published: New York Springer US 01.08.2017
Springer Nature B.V
Subjects:
Adiabatic flow
Approximation
Coefficients
Constraints
Data Structures and Information Theory
Evolution
Mathematical analysis
Mathematical Physics
Mathematical programming
Microprocessors
Noise prediction
Nonlinear programming
Optimization
Physics
Physics and Astronomy
Quadratic programming
Quantum Computing
Quantum Information Technology
Quantum Physics
Spintronics
Lagrangian duality
Gradient descent
Adiabatic quantum computation
Constrained integer programming
Subgradient method
ISSN:1570-0755, 1573-1332
Online Access:Get full text
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Summary:Outer approximation method has been proposed for solving the Lagrangian dual of a constrained binary quadratic programming problem via quantum adiabatic evolution in the literature. This should be an efficient prescription for solving the Lagrangian dual problem in the presence of an ideally noise-free quantum adiabatic system. However, current implementations of quantum annealing systems demand methods that are efficient at handling possible sources of noise. In this paper, we consider a subgradient method for finding an optimal primal–dual pair for the Lagrangian dual of a constrained binary polynomial programming problem. We then study the quadratic stable set (QSS) problem as a case study. We see that this method applied to the QSS problem can be viewed as an instance-dependent penalty-term approach that avoids large penalty coefficients. Finally, we report our experimental results of using the D-Wave 2X quantum annealer and conclude that our approach helps this quantum processor to succeed more often in solving these problems compared to the usual penalty-term approaches.
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ISSN:1570-0755
1573-1332
DOI:10.1007/s11128-017-1639-2