Quantum Approaches to the Quadratic Assignment Problem

Nathan Daly; Thomas Krauss; Julia Shapiro

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arXiv · 2505.00182

Quantum Approaches to the Quadratic Assignment Problem

Nathan Daly·Thomas Krauss·Julia Shapiro

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Abstract

The Quadratic Assignment Problem (QAP) is an NP-hard fundamental combinatorial optimization problem introduced by Koopmans and Beckmann in 1957. The problem is to assign $n$ facilities to $n$ different locations with the goal of minimizing the cost of the total distances between facilities weighted by the corresponding flows. We initiate the study of using Rydberg arrays to find optimal solutions to the QAP and provide a complementing circuit theory to facilitate an easy representation of other hard problems. We provide an algorithm for finding valid and optimal solutions to the QAP using Rydberg arrays.

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Nathan Daly, Thomas Krauss, Julia Shapiro. 2025-04-30. Quantum Approaches to the Quadratic Assignment Problem. https://arxiv.org/abs/2505.00182

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