Exponential Quantum Speedup on Structured Hard Instances of Maximum Independent Set

• URL: http://arxiv.org/abs/2601.17686v1
• Date: Sun, 25 Jan 2026 04:18:35 GMT
• Title: Exponential Quantum Speedup on Structured Hard Instances of Maximum Independent Set
• Authors: Vicky Choi,
• Abstract summary: We identify a family of classically hard maximum independent set (MIS) instances, and design and analyze a non-stoquastic adiabatic quantum optimization algorithm.<n>The algorithm runs in time and achieves an exponential speedup over both transverse-field quantum and state-of-the-art classical solvers.<n>This identifies a distinctive quantum mechanism underlying the speedup and explains why no efficient classical analogue is likely to exist.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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