Magic of random matrix product states

Magic, or nonstabilizerness, characterizes how far away a state is from the stabilizer states, making it an important resource in quantum computing, under the formalism of the Gotteman-Knill theorem. In this paper, we study the magic of the one-dimensional (1D) random matrix product states (RMPSs) using the L 1 -norm measure. We first relate the L 1 norm to the L 4 norm. We then employ a unitary four -design to map the L 4 norm to a 24 -component statistical physics model. By evaluating partition functions of the model, we obtain a lower bound on the expectation values of the L 1 norm. This bound grows exponentially with respect to the qudit number n , indicating that the 1D RMPS is highly magical. Our numerical results confirm that the magic grows exponentially in the qubit case.