Nonstabilizerness Mpemba Effects

TL;DR

This paper reveals a quantum Mpemba effect where states with less initial magic can generate magic faster, influenced by initial state structure and symmetry, across various quantum dynamics.

Contribution

It demonstrates the existence of quantum Mpemba effects in magic generation, independent of symmetry type or circuit randomness, highlighting a new aspect of quantum state dynamics.

Findings

States with lower initial magic can generate magic faster.

The effect depends on the spatial structure of initial states within charge sectors.

Quantum magic exhibits Mpemba effects across different symmetries and dynamics.

Abstract

Quantum state preparation can be strikingly counterintuitive: the fastest route to a target state need not start from the apparently closest initial condition. We uncover such a quantum Mpemba effect in the dynamical generation of quantum magic (nonstabilizerness), quantified by the stabilizer R\'enyi entropy, in $\mathrm{U(1)}$-symmetric random circuits initialized from tilted product states. States with lower initial magic can generate magic faster than states with higher initial magic. The acceleration is not determined solely by the conserved-charge distribution. Two initial-state families with identical initial magic and identical charge distribution exhibit qualitatively different magic-growth dynamics, depending also on the spatial structure of the initial state within each charge sector. Analogous magic Mpemba effects in $\mathrm{SU(2)}$-symmetric circuits and under nonintegrable Hamiltonian dynamics further show that the phenomenon is tied neither to Abelian symmetry nor to random-circuit dynamics, establishing quantum magic as a distinct arena for Mpemba physics.