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

Abstract: High-performance numerical methods are essential not only for advancing quantum many-body physics but also for enabling integration with emerging quantum computing platforms. We present a scalable and general-purpose parallel algorithm 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, tracking the time evolution of local magnetization using up to one trillion Pauli strings. Executed on the supercomputer Fugaku, our simulations exhibit strong scaling up to $2^{17}$ parallel processes with near-linear communication overhead. These results establish ORQA as a practical and high-performance tool for quantum many-body dynamics, and highlight its potential for integration into hybrid quantum-classical computational frameworks, complementing recent advances in tensor-network and surrogate simulation techniques.