Exact solution of long-range stabilizer Rényi entropy in the dual-unitary XXZ model

Abstract: Quantum systems can not be efficiently simulated classically due to the presence of entanglement and nonstabilizerness, also known as quantum magic. Here we study the generation of magic under evolution by a quantum circuit. To be able to provide exact solutions, we focus on the dual-unitary XXZ model and a measure of magic called stabilizer R\'enyi entropy (SRE). Moreover, we focus also on long-range SRE, which cannot be removed by short-depth quantum circuits. To obtain exact solutions we use a ZX-calculus representation and graphical rules for the evaluation of the required expressions. We obtain exact results for SRE after short-time evolution in the thermodynamic limit and for long-range SRE for all times and all R\'enyi parameters for a particular partition of the state. Since the numerical evaluation of these quantities is exponentially costly in the R\'enyi parameter, we verify this numerically for low R\'enyi parameters and accessible system sizes and provide numerical results for the long-range SRE in other bipartitions.