Magic Steady State Production: Non-Hermitian and Stochastic pathways

Universal quantum computers require states with both entanglement and non-stabilizerness, the latter property being commonly known as \textit{quantum magic}. Here, we introduce a protocol that prepares magic steady states by leveraging non-Hermitian dynamics, which, contrary to unitary dynamics, can host pure-state attractors. We investigate the dissipative qubit, in which we find the optimal parameters to prepare $|H\rangle$ and $|T\rangle$ states. Interestingly, this approach does not require knowledge or preparation of an initial state, since all the states of the Bloch sphere converge to these steady states. We also consider the addition of classical noise in the anti-hermitian part, and show that it does not necessarily hinder magic, rather the single trajectories show concentration around the magic steady state value.