Universal Non-stabilizerness Dynamics Across Quantum Phase Transitions

TL;DR

This paper explores how non-stabilizerness, a quantum resource, evolves dynamically during quantum phase transitions, revealing universal scaling laws and distribution properties across different models.

Contribution

It extends the study of non-stabilizerness from equilibrium to dynamic quantum phase transitions, uncovering universal behaviors and distribution characteristics.

Findings

Power-law scaling of stabilizer Rènyi entropies with driving rate

Logarithmic Pauli spectrum approaches Gaussian distribution

Universal behaviors demonstrated in Ising and Kitaev models

Abstract

Quantum magic and non-stabilizerness are important quantum resources that characterize computational power beyond classically simulable Clifford operations and are therefore essential for achieving quantum advantage. While non-stabilizerness has so far been investigated only at equilibrium, here we extend its dynamics to time-dependent drivings across quantum phase transitions. In particular, we show that the stabilizer R\'enyi entropies and the cumulants of the Pauli spectrum exhibit universal power-law scaling with the driving rate in slow processes. Moreover, we show that the logarithmic Pauli spectrum is asymptotically Gaussian, implying a lognormal distribution for the Pauli spectrum values. Our results are explicitly demonstrated by exact results in the transverse-field Ising model and by analytical approximations in long-range Kitaev models.