Momentum space nonstabilizerness for the transverse field quantum Ising model
Phys. Rev. B 112, 125427 – Published 29 September, 2025
DOI: https://doi.org/10.1103/mx8t-l4hf
Abstract
Stabilizer entropies have been extensively explored in real-space formulations of quantum systems within the framework of resource theory. However, interesting and transparent physics often emerges in momentum space, such as Cooper pairing. Motivated by this, we investigate the momentum space structure of Pauli strings and stabilizer entropies in the one-dimensional transverse field quantum Ising model. By mapping the Ising chain onto momentum space qubits, where the stabilizer state corresponds to the paramagnetic state, we analyze the evolution of the Pauli string distribution for 40 spins. In the ferromagnetic phase, the distribution is broad, whereas in the paramagnetic phase, it develops a two-peak structure. We demonstrate that all ferromagnetic states possess the same degree of nonstabilizerness in the thermodynamic limit, while stabilizer entropies are nonanalytic at the critical point and decrease with increasing transverse field. The momentum space approach to nonstabilizerness not only complements its real-space counterpart but also provides advantages in terms of reducing nonstabilizerness and enhancing classical simulability.
