Magic Steady State Production: Non-Hermitian, Dissipative, and Stochastic Pathways

Abstract

Universal quantum computers require entanglement and non-stabilizerness, a resource 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. By studying the dissipative qubit, we find the optimal parameters to prepare $|H⟩$ and $|T⟩$ steady states. Interestingly, this approach does not require knowledge or preparation of a particular initial state, since all the states of the Bloch sphere converge to the engineered target steady state. We also consider the addition of classical noise in the anti-hermitian part and provide the regimes for which the noisy dynamics still converges to high magic states. We also introduce a dissipative protocol to prepare magic steady states, compare the approaches with magic state cultivation and provide a particular realization of the non-Hermitian scheme in a cat qubit.

Major revision: Different magic monotones and witnesses (sec 4), new dissipative protocol (sec 5), and application to cat qubits (sec 6.2). 14+7 pages, 6+2 figures