Range of Applicability of the Strassen Algorithm in Physics Computations

Conventional matrix multiplication has time complexity of O(n³) while the Strassen algorithm has that of O(n^log₂7), where n is the largest dimension involved. This algorithm is not implemented in many libraries for scientific computation due to the historical advantage of conventional methods. With the increasing need to compute matrix multiplications and tensor contractions for large systems the Strassen algorithm may be a powerful tool due to its beneficial time complexity.

We will present on an implementation of the Strassen algorithm and quantify when it achieves a computational advantage over conventional matrix multiplication. The algorithm will be applied to tensor network computations for quantum systems, with the results giving a benchmark for application in scientific computations and simulations. The version of the Strassen algorithm presented will be released for public use in a lightweight Julia package.