Lazy Qubit Reordering for Accelerating Parallel State-Vector-based Quantum Circuit Simulation

This paper proposes two quantum operation scheduling methods for accelerating parallel state-vector-based quantum circuit simulation using multiple graphics processing units (GPUs). The proposed methods reduce all-to-all communication caused by qubit reordering (QR), which can dominate the overhead of parallel simulation. Our approach eliminates redundant QRs by introducing intentional delays in QR communications such that multiple QRs can be aggregated into a single QR. The delays are carefully introduced based on the principles of time-space tiling, or a cache optimization technique for classical computers, which we use to arrange the execution order of quantum operations. Moreover, we present an extended scheduling method for the hierarchical interconnection of GPU cluster systems to avoid slow inter-node communication. We develop these methods tailored for two primary procedures in variational quantum eigensolver (VQE) simulation: quantum state update (QSU) and expectation value computation (EVC). Experimental validation on 32-GPU executions demonstrates acceleration in QSU and EVC -- up to 54$\times$ and 606$\times$, respectively -- compared to existing methods. Moreover, our extended scheduling method further reduced communication time by up to 15\% in a two-layered interconnected cluster system. Our approach is useful for any quantum circuit simulations, including QSU and/or EVC.