Quantifying nonstabilizerness of matrix product states

Nonstabilizerness, also known as magic, quantifies the number of non-Clifford operations needed to prepare a quantum state. As typical measures either involve minimization procedures or computational cost exponential in qubits $N$, it is notoriously hard characterize for many-body states. In this paper, we show that nonstabilizerness, quantified by recently introduced stabilizer R\'enyi entropies (SREs), can be computed efficiently matrix product states (MPSs). Specifically, given an MPS bond dimension $\ensuremath{\chi}$ and integer index $n>1$, SRE expressed terms norm with ${\ensuremath{\chi}}^{2n}$. For translation-invariant states, allows us extract from single tensor, transfer matrix, while generic MPSs construction yields linear $N$ polynomial $\ensuremath{\chi}$. We exploit observation revisit study ground-state nonstabilizerness Ising chain, providing accurate numerical results up large system sizes. analyze near criticality investigate its dependence on local basis, showing is, general, not maximal at critical point.