ORIGINAL RESEARCH article
Front. Quantum Sci. Technol.
Sec. Quantum Computing and Simulation
Volume 4 - 2025 | doi: 10.3389/frqst.2025.1636042
This article is part of the Research TopicAdvancing Quantum Computation: Optimizing Algorithms and Error Mitigation in NISQ DevicesView all 4 articles
Encodings of the weighted MAX k-CUT problem on qubit systems
Provisionally accepted
- 1SINTEF Digital, Trondheim, Norway
- 2Universitetet i Oslo, Oslo, Norway
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The weighted MAX k-CUT problem involves partitioning a weighted undirected graph into k subsets, or colors, to maximize the sum of the weights of edges between vertices in different subsets. This problem has significant applications across multiple domains. This paper explores encoding methods for MAX k-CUT on qubit systems, utilizing quantum approximate optimization algorithms (QAOA) and addressing the challenge of encoding integer values on quantum devices with binary variables. We examine various encoding schemes and evaluate the efficiency of these approaches. The paper presents a systematic and resource efficient method to implement phase separation operator for the cost function of the MAX k-CUT problem. When encoding the problem into the full Hilbert space, we show the importance of encoding the colors in a balanced way. We also explore the option to encode the problem into a suitable subspace, by designing suitable state preparations and constrained mixers (LX-and Grover-mixer). Numerical simulations on weighted and unweighted graph instances demonstrate the effectiveness of these encoding schemes, particularly in optimizing circuit depth, approximation ratios, and computational efficiency.
Keywords: Quantum Optimization Algorithm, Quantum Circuit Compilation, QAOA (Quantum Approximate Optimization Algorithm), Quantum Technologies, Variational quantum circuits
Received: 27 May 2025; Accepted: 15 Aug 2025.
Copyright: © 2025 Pariente, Fuchs and Lien. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Ruben Pariente, SINTEF Digital, Trondheim, Norway
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