phase2: Full-State Vector Simulation of Quantum Time Evolution at Scale

Abstract: Large-scale classical simulation of quantum computers is crucial for benchmarking quantum algorithms, establishing boundaries of quantum advantage and exploring heuristic quantum algorithms. We present a full-state vector simulation algorithm and software implementation designed to perform HPC simulation of layers of rotations around a string of Pauli operators. We demonstrate robust scalability of the simulation method on large distributed CPU and GPU systems. Our distributed computation harnessed up to $16\,384$ CPU cores and $512$ NVIDIA H100 GPUs, using $32$ TB of memory. The simulator significantly outperforms other high-performance libraries, showing a typical speedup of $10-100$ for large-scale multi-GPU workloads. As a first application of our approach, we report a numerical experiment aimed at simulating exactly Hamiltonian dynamics of up to 40 qubits to investigate the Trotter error for a quantum chemistry problem. Bounding the Trotter error is important for evaluating the cost of quantum algorithms for chemistry, and rigorous bounds are often conservative, as our simulations confirm. Our software, specifically designed for quantum time evolution applications, is also well equipped to manage circuits that utilize standard gate sets.