Scalable Simulation of Quantum Many-Body Dynamics with Or-Represented Quantum Algebra

High-performance numerical methods are essential for advancing quantum many-body physics, as well as for enabling the integration of supercomputers with emerging quantum computing platforms. We have developed a scalable and general-purpose numerical framework for quantum simulations based on or-represented quantum algebra (ORQA). This framework applies to arbitrary spin-systems and naturally integrates with quantum circuit simulation in the Heisenberg picture, particularly relevant to recent large-scale experiments on superconducting qubit processors [Kim et al., Nature 618, 500 (2023)]. As a benchmark, we simulate the kicked Ising model on a 127-qubit heavy-hexagon lattice, successfully tracking the time-evolution of local magnetization using up to one trillion Pauli strings. Our simulations exhibit strong scaling up to 2^17 parallel processes with near-linear communication overhead. Further, we show that our framework is naturally extended to a broader range of quantum systems, superseding the capabilities of recently established Pauli propagation methods. We present possible future directions on how to utilize our algorithm.