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arXiv · 2603.08841

Universal Non-stabilizerness Dynamics Across Quantum Phase Transitions

András Grabarits·Adolfo del Campo
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Abstract

Quantum magic, or non-stabilizerness, is an important quantum resource that characterizes computational power beyond classically simulable Clifford operations and is therefore essential for achieving quantum advantage. While previous studies have explored non-stabilizerness dynamics in random circuits and under time-independent generators, here we extend the study of its universal dynamics to time-dependent driving 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.

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András Grabarits, Adolfo del Campo. 2026-03-09. Universal Non-stabilizerness Dynamics Across Quantum Phase Transitions. https://arxiv.org/abs/2603.08841

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