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arXiv:2610.02145

A provable quantum advantage for approximate optimization via decoded quantum interferometry

Maximilian J. Kramer, Elies Gil-Fuster, Benjamin D. M. Jones, Jens Eisert, Franz J. Schreiber

quant-phcs.CCcs.DSSubmitted Oct 1, 2026• Announced Oct 2, 2026• 0 citations
v1 · Oct 1, 2026v2 · Oct 2, 2026
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Abstract

Decoded quantum interferometry (DQI) is a novel paradigm for tackling approximate optimization problems on quantum computers. This framework comes with strong performance guarantees and exploits a well-established duality between optimization and coding theory. A central question, however, is whether DQI can actually provably outperform all polynomial-time classical algorithms. In this work, we establish such an advantage in an oracle setting: we consider an optimization task called folded optimal polynomial intersection (folded OPI), where the acceptance sets are chosen randomly and accessed through membership oracles. We establish a strict gap between the approximation ratio achievable by any polynomial-time classical algorithm and the approximation ratio achieved by the DQI algorithm. Our proof builds on Jordan et al.'s DQI framework for approximate optimization and extends the classical lower-bound method underlying Yamakawa and Zhandry's exact-search oracle separation to approximation. Building on recent developments by Sun and Wootters, Horinaga and Yamakawa, and Jo, we further show that a modified version of the DQI algorithm achieves a strictly larger gap on the folded OPI problem, yielding an even stronger quantum separation. As a concrete example, for code rate $0.3$, DQI and the modified algorithm achieve expected scores of approximately $0.85$ and $0.95$, respectively. In contrast, exceeding the classical threshold of $0.65$ by any fixed amount with constant probability on sampled instances requires super-polynomially many classical membership queries.

Comments
59 pages, 3 figures

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Decoded quantum interferometry (DQI) is a novel paradigm for tackling approximate optimization problems on quantum computers. This framework comes with strong performance guarantees and exploits a well-established duality between optimization and coding theory. A central question, however, is whether DQI can actually provably outperform all polynomial-time classical algorithms. In this work, we establish such an advantage in an oracle setting: we consider an optimization task called folded optimal polynomial intersection (folded OPI), where the acceptance sets are chosen randomly and accessed through membership oracles. We establish a strict gap between the approximation ratio achievable by any polynomial-time classical algorithm and the approximation ratio achieved by the DQI algorithm. Our proof builds on Jordan et al.'s DQI framework for approximate optimization and extends the classical lower-bound method underlying Yamakawa and Zhandry's exact-search oracle separation to approximation. Building on recent developments by Sun and Wootters, Horinaga and Yamakawa, and Jo, we further show that a modified version of the DQI algorithm achieves a strictly larger gap on the folded OPI problem, yielding an even stronger quantum separation. As a concrete example, for code rate 0.30.30.3, DQI and the modified algorithm achieve expected scores of approximately 0.850.850.85 and 0.950.950.95, respectively. In contrast, exceeding the classical threshold of 0.650.650.65 by any fixed amount with constant probability on sampled instances requires super-polynomially many classical membership queries.
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