Efficiency in solving random k-SAT problems is explored through structured quantum search algorithms. The paper discusses the transition from solubility to insolubility in classical computing and introduces a family of algorithms for efficient solutions. By focusing on satisfiable instances, exponential acceleration is proven for specific conditions.
The content delves into the complexity of random k-SAT beyond established thresholds, emphasizing the importance of structural information in quantum searches. It introduces adiabatic quantum computation principles and their application to improve efficiency in solving max-k-SSAT instances. The study establishes that by modifying existing algorithms, polynomial average complexity can be achieved for certain conditions.
Key points include the theoretical foundation of k-local quantum search, algorithm design specifics, and proof of main theorems regarding efficiency improvements. The analysis extends to refined landscape exploration and performance evaluations based on different metrics.
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by Mingyou Wu at arxiv.org 03-07-2024
https://arxiv.org/pdf/2403.03237.pdfDeeper Inquiries