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

TL;DR

This paper introduces a non-Hermitian dissipative protocol for preparing magic steady states in quantum systems, enabling convergence from any initial state and robustness against noise, with potential implementation in cat qubits.

Contribution

It presents a novel non-Hermitian dissipative method to generate magic states, expanding quantum state engineering techniques beyond unitary dynamics.

Findings

Optimal parameters for $|H angle$ and $|T angle$ steady states identified.

All Bloch sphere states converge to the target steady state.

High magic states achievable despite classical noise.

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 $|H\rangle$ and $|T\rangle$ 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.