Compressed space quantum approximate optimization algorithm for constrained combinatorial optimization

• URL: http://arxiv.org/abs/2410.05703v1
• Date: Tue, 8 Oct 2024 05:48:46 GMT
• Title: Compressed space quantum approximate optimization algorithm for constrained combinatorial optimization
• Authors: Tatsuhiko Shirai, Nozomu Togawa,
• Abstract summary: We introduce a method for engineering a compressed space that represents the feasible solution space with fewer qubits than the original. We then propose compressed space QAOA, which seeks near-optimal solutions within this reduced space.
• Score: 6.407238428292173
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Combinatorial optimization is a promising area for achieving quantum speedup. Quantum approximate optimization algorithm (QAOA) is designed to search for low-energy states of the Ising model, which correspond to near-optimal solutions of combinatorial optimization problems (COPs). However, effectively dealing with constraints of COPs remains a significant challenge. Existing methods, such as tailoring mixing operators, are typically limited to specific constraint types, like one-hot constraints. To address these limitations, we introduce a method for engineering a compressed space that represents the feasible solution space with fewer qubits than the original. Our approach includes a scalable technique for determining the unitary transformation between the compressed and original spaces on gate-based quantum computers. We then propose compressed space QAOA, which seeks near-optimal solutions within this reduced space, while utilizing the Ising model formulated in the original Hilbert space. Experimental results on a quantum simulator demonstrate the effectiveness of our method in solving various constrained COPs.

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