A canonical approach to approximating the partition function of a Gibbs distribution via sampling is simulated annealing. This method has led to efficient reductions from counting to sampling, including: $\bullet$ classic non-adaptive (parallel) algorithms with sub-optimal cost (Dyer-Frieze-Kannan '89; Bezáková-Štefankovič-Vazirani-Vigoda '08); $\bullet$ adaptive (sequential) algorithms with near-optimal cost (Štefankovič-Vempala-Vigoda '09; Huber '15; Kolmogorov '18; Harris-Kolmogorov '24). We present an algorithm that achieves both near-optimal total work and efficient parallelism, providing a reduction from counting to sampling with logarithmic depth and near-optimal work. As consequences, we obtain work-efficient parallel counting algorithms for several important models, including the hardcore and Ising models within the uniqueness regime.

翻译：通过采样近似吉布斯分布配分函数的经典方法是模拟退火。该方法已产生从计数到采样的高效归约，包括：$\bullet$ 经典非自适应（并行）算法，具有次优代价（Dyer-Frieze-Kannan '89；Bezáková-Štefankovič-Vazirani-Vigoda '08）；$\bullet$ 自适应（顺序）算法，具有近最优代价（Štefankovič-Vempala-Vigoda '09；Huber '15；Kolmogorov '18；Harris-Kolmogorov '24）。我们提出一种算法，同时实现了近最优总工作量与高效并行性，提供了从计数到采样的对数深度与近最优工作量的归约。作为结果，我们获得了若干重要模型的工作高效并行计数算法，包括唯一性区域内的硬核模型与伊辛模型。