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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2601.17686 |
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| _version_ | 1866915753171615744 |
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| author | Choi, Vicky |
| author_facet | Choi, Vicky |
| contents | Establishing quantum speedup for computationally hard problems of practical relevance, particularly combinatorial optimization problems, remains a central challenge in quantum computation. In this work, we identify a structurally defined family of classically hard maximum independent set (MIS) instances, and design and analyze a non-stoquastic adiabatic quantum optimization algorithm that exploits this structure. The algorithm runs in polynomial time and achieves an exponential speedup over both transverse-field quantum annealing and state-of-the-art classical solvers on these instances, under assumptions supported by analytical and numerical evidence. We identify the essential quantum mechanism enabling the speedup as the use of a non-stoquastic XX-driver to access a larger sign-structured admissible subspace beyond the stoquastic regime, which allows sign-generating quantum interference to create smooth evolution paths that bypass tunneling. This identifies a distinctive quantum mechanism underlying the speedup and explains why no efficient classical analogue is likely to exist. In addition, our analysis produces scalable small-scale models, derived from our structural reduction, that capture the essential dynamics of the algorithm. These models provide a concrete opportunity for verification of the quantum advantage mechanism on currently available universal quantum computers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_17686 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exponential Quantum Speedup on Structured Hard Instances of Maximum Independent Set Choi, Vicky Quantum Physics Establishing quantum speedup for computationally hard problems of practical relevance, particularly combinatorial optimization problems, remains a central challenge in quantum computation. In this work, we identify a structurally defined family of classically hard maximum independent set (MIS) instances, and design and analyze a non-stoquastic adiabatic quantum optimization algorithm that exploits this structure. The algorithm runs in polynomial time and achieves an exponential speedup over both transverse-field quantum annealing and state-of-the-art classical solvers on these instances, under assumptions supported by analytical and numerical evidence. We identify the essential quantum mechanism enabling the speedup as the use of a non-stoquastic XX-driver to access a larger sign-structured admissible subspace beyond the stoquastic regime, which allows sign-generating quantum interference to create smooth evolution paths that bypass tunneling. This identifies a distinctive quantum mechanism underlying the speedup and explains why no efficient classical analogue is likely to exist. In addition, our analysis produces scalable small-scale models, derived from our structural reduction, that capture the essential dynamics of the algorithm. These models provide a concrete opportunity for verification of the quantum advantage mechanism on currently available universal quantum computers. |
| title | Exponential Quantum Speedup on Structured Hard Instances of Maximum Independent Set |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2601.17686 |