Longitudinal-field suppression of quantum-magic backflow in an Ising chain

Abstract Quantum quenches can generate substantial nonstabilizerness, but generating a large amount
of magic does not by itself guarantee its later retention. We study an open transverse-field Ising
chain perturbed by a longitudinal field that removes the free-fermion integrable structure of the
G = 0 model. Exact finite-size calculations compare symmetry-resolved level statistics, stabilizer
R´enyi entropy, Pauli-spectrum memory, and a time-averaged magic-backflow measure. A weak
longitudinal field increases the generated magic and suppresses large Pauli-spectrum revivals, while
the field minimizing memory does not coincide with the largest finite-size adjacent-gap ratio. For the
exact stabilizer state |+⟩⊗N , a broad intermediate-field window strongly reduces magic backflow.
At fixed G/J = 0.09 and 0.12, this suppression remains approximately 80% through N = 11;
extending the N = 11 evolution from τf = 24 to 32 leaves the suppression essentially unchanged.
Pauli-spectrum revivals are reduced more modestly. Thus the data establish a robust finite-size and
finite-time separation between resource retention and Pauli-spectrum memory.....