A measurement-driven quantum algorithm for SAT: Performance guarantees via spectral gaps and measurement parallelization

• URL: http://arxiv.org/abs/2511.09647v1
• Date: Fri, 14 Nov 2025 01:02:16 GMT
• Title: A measurement-driven quantum algorithm for SAT: Performance guarantees via spectral gaps and measurement parallelization
• Authors: Franz J. Schreiber, Maximilian J. Kramer, Alexander Nietner, Jens Eisert,
• Abstract summary: This work presents a rigorous worst-case runtime analysis of a measurement-driven quantum SAT solver.<n>We show that this quantum algorithm does not exclusively rely on Grover-type methods and shows promising numerical performance.<n>We also develop a new readout routine that efficiently finds a solution even for instances with multiple satisfying assignments.
• Score: 39.146761527401424
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Boolean satisfiability problem (SAT) is of central importance in both theory and practice. Yet, most provable guarantees for quantum algorithms rely exclusively on Grover-type methods that cap the possible advantage at only quadratic speed-ups, making the search for approaches that surpass this quadratic barrier a key challenge. In this light, this work presents a rigorous worst-case runtime analysis of a recently introduced measurement-driven quantum SAT solver. Importantly, this quantum algorithm does not exclusively rely on Grover-type methods and shows promising numerical performance. Our analysis establishes that the algorithm's runtime depends on an exponential trade-off between two key properties: the spectral gap of the associated Hamiltonian and the success probability of the driving measurements. We show that this trade-off can be systematically controlled by a tunable rotation angle. Beyond establishing a worst-case runtime expression, this work contributes significant algorithmic improvements. First, we develop a new readout routine that efficiently finds a solution even for instances with multiple satisfying assignments. Second, a measurement parallelization scheme, based on perfect hash families, is introduced. Third, we establish an amplitude-amplified version of the measurement-driven algorithm. Finally, we demonstrate the practical utility of our framework: By suitably scheduling the algorithm's parameters, we show that its runtime collapses from exponential to polynomial on a special class of SAT instances, consistent with their known classical tractability. A problem we leave open is to establish a non-trivial lower bound on the spectral gap as a function of the rotation angle. Resolving this directly translates into an improved worst-case runtime, potentially realizing a super-quadratic quantum advantage.

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