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

We present a scalable high-performance framework for quantum simulations, based on or-represented quantum algebra. This framework applies to arbitrary spin systems and naturally integrates with quantum circuit simulation in the Heisenberg picture, in the spirit of Pauli propagation techniques. We demonstrate our method on simulations of the kicked Ising model on a 127-qubit heavy-hexagon lattice, inspired by recent large-scale experiments [Kim et al., Nature 618, 500 (2023)]. Throughout these simulations, our method tracks the time-evolution of local magnetization by retaining up to one trillion Pauli strings. Executed on the supercomputer Fugaku, our method exhibits weak and strong scaling for up to 2^17 parallel processes with near-linear communication overhead. Further, the general nature of the framework we have developed allows us to extend it to other classes of quantum many-body dynamics, leveraging the same scaling behavior to explore a larger range of problems.