We describe two algorithms for multiplying n x n matrices using time and energy n^2 polylog(n) under basic models of classical physics. The first algorithm is for multiplying integer-valued matrices, and the second, quite different algorithm, is for Boolean matrix multiplication. We hope this work inspires a deeper consideration of physically plausible/realizable models of computing that might allow for algorithms which improve upon the runtimes and energy usages suggested by the parallel RAM model in which each operation requires one unit of time and one unit of energy.

翻译：我们描述了两种在经典物理学基本模型下，使用 n² polylog(n) 时间与能量进行 n×n 矩阵乘法的算法。第一种算法用于整数矩阵乘法，而第二种截然不同的算法用于布尔矩阵乘法。我们希望这项工作能激发对物理上可行/可实现的计算模型的深入思考，这些模型可能允许算法超越并行RAM模型所暗示的运行时间和能量消耗（该模型中每个操作消耗一个单位时间与一个单位能量）。