Journal Article

FZJ-2024-02715

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Unbalanced penalization: a new approach to encode inequality constraints of combinatorial problems for quantum optimization algorithms

Montanez-Barrera, J. A. (Corresponding author)FZJ* ; Willsch, D.FZJ* ; Maldonado-Romo, A. ; Michielsen, K.FZJ*

2024
IOP Publishing Philadelphia, PA

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Please use a persistent id in citations: doi:10.1088/2058-9565/ad35e4  doi:10.34734/FZJ-2024-02715

Abstract: Solving combinatorial optimization problems of the kind that can be codified by quadratic unconstrained binary optimization (QUBO) is a promising application of quantum computation. Some problems of this class suitable for practical applications such as the traveling salesman problem (TSP), the bin packing problem (BPP), or the knapsack problem (KP) have inequality constraints that require a particular cost function encoding. The common approach is the use of slack variables to represent the inequality constraints in the cost function. However, the use of slack variables considerably increases the number of qubits and operations required to solve these problems using quantum devices. In this work, we present an alternative method that does not require extra slack variables and consists of using an unbalanced penalization function to represent the inequality constraints in the QUBO. This function is characterized by larger penalization when the inequality constraint is not achieved than when it is. We evaluate our approach on the TSP, BPP, and KP, successfully encoding the optimal solution of the original optimization problem near the ground state cost Hamiltonian. Additionally, we employ D-Wave Advantage and D-Wave hybrid solvers to solve the BPP, surpassing the performance of the slack variables approach by achieving solutions for up to 29 items, whereas the slack variables approach only handles up to 11 items. This new approach can be used to solve combinatorial problems with inequality constraints with a reduced number of resources compared to the slack variables approach using quantum annealing or variational quantum algorithms.

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Contributing Institute(s):

1. Jülich Supercomputing Center (JSC)

Research Program(s):

1. 5111 - Domain-Specific Simulation & Data Life Cycle Labs (SDLs) and Research Groups (POF4-511) (POF4-511)
2. BMBF 13N16149 - QSolid (BMBF-13N16149) (BMBF-13N16149)

Appears in the scientific report 2024

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Database coverage:
; ; ; Clarivate Analytics Master Journal List ; Current Contents - Physical, Chemical and Earth Sciences ; Essential Science Indicators ; SCOPUS ; Science Citation Index Expanded ; Web of Science Core Collection

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