Batched matrix operations on distributed GPUs with application in theoretical physics

One of the most important and commonly used operations in many linear algebra functions is matrix-matrix multiplication (GEMM), which is also a key component in obtaining high performance of many scientific codes. It is a computationally intensive function requiring O(n
³
) operations, and its high computational intensity makes it well-suited to be significantly accelerated with GPUs. Today, many research problems require solving a very large number of relatively small GEMM operations that cannot utilise the entire GPU. To overcome this bottleneck, special functions have been developed that pack several GEMM operations into one and then compute them simultaneously on a GPU, which is called a batch operation. In this research work, we have proposed a different approach based on linking multiple GEMM operations to Message Passing Interface (MPI) processes and then binding multiple MPI processes to a single GPU. To increase GPU utilisation, more MPI processes (i.e. GEMM operations) are added. We implement and test this approach in the field of theoretical physics to compute entanglement properties through simulated annealing Monte Carlo simulation of quantum spin chains. For the specific use case, we were able to simulate a much larger spin system and achieve a speedup of up to 35× compared to the parallel CPU-only version.