The Shape of Speed: Impacts of Partition Geometry and Rank Density in Distributed Quantum Circuit Simulations

Abstract

In distributed quantum circuit simulation, a poorly shaped partition can halve performance before computation begins. Evaluation on Fugaku across 764 validated configurations (twelve algorithms, thirteen torus partition geometries, and six rank densities for 39-qubit simulations on 1,024 nodes) shows that partition geometry dominates runtime. All twelve algorithms run 1.73-2.31x slower on flat partitions than on near-cubic ones despite identical data transfer, proving the slowdown stems from network delivery rather than communication volume. This penalty scales with the 3D torus partition aspect ratio (runtime $\propto a^{0.39}$, $r = 0.72$). Rank density is secondary, cutting runtime by 11% at 16 ranks per node only on compact geometries. Ultimately, requesting a near-cubic partition with 16 ranks per node roughly halves time-to-solution relative to flat partitions, which also consume 1.82x more energy. A simulator-free all-to-all microbenchmark confirms a similar geometry penalty for collective-dominated workloads.