Improved real-space parallelizable matrix-product state compression and its application to unitary quantum dynamics simulation

In this presentation, I will introduce our newly developed real-space parallelizable matrix-product state (MPS) compression method, which can efficiently compress all the virtual dimensions of the MPS in a constant time against increasing the system size and simultaneously stabilize the wavefunction norm without triggering sequential renormalization procedures. Moreover, the deviated canonical form is partially recovered by appended parallel regauging steps. Based on this method, we propose the parallel time-evolving block-decimation (pTEBD) algorithm for the simulation of unitary quantum dynamics. After benchmarking the pTEBD algorithm with extensive simulations of typical one- and two-dimensional quantum circuits containing up to over 1000 qubits on Supercomputer Fugaku, we demonstrate that the pTEBD algorithm can realize the same simulation precision as compared with the current state-of-the-art MPS algorithm in an exponentially shorter time and a nearly perfect performance weak scaling.