Advantage of utilizing nonlocal magic resource in Haar-random circuits

Abstract Magic resources and entanglement are fundamental components for achieving the universal quantum computation, so is the interplay between them. Herein, we uncover an intrinsic scaling law of the magic resource and bond dimension of matrix product states in Haar-random quantum circuits, that is, the magic resource is converged on a bond dimension in logarithmic scale with the system size. From a practical perspective, this finding substantially enhances the classical simulability of nonstabilizerness. It also allows us to utilize the bond dimension as a bridge to link the entanglement and the nonlocal magic resource, which extends the capacity perspective that the entanglement plays the role of container for the nonlocal magic resource. Furthermore, the intrinsic scaling enables an information separation between the nonlocal magic resource and the extra entanglement. This, in turn, leads to the conclusion that, any dynamical relation between magic and entanglement resources is ruled out. In other words, it is inappropriate to regard the entanglement as the driving force of the growth and spreading of nonlocal magic resource.