Deterministic Construction of Arbitrary States in Permutationally-Invariant Spin Ensemble

Spin ensemble systems are capable of hosting long-lived qubits, making them promising platforms to implement quantum technologies such as sensors, repeaters, and processors. To achieve the quantum advantages of these applications, specific states are required to be prepared, but a systematic way to prepare arbitrary spin-ensemble state is missing in the literature. In this work, we propose a scheme to fill this gap. Our scheme first employs engineered dissipation to deterministically prepare the spin ensemble in any angular momentum subspace. Arbitrary superpositions of excitation can then be encoded through interacting with an auxilary qubit. As an example of application, we show that our scheme can encode a qubit into a subspace that is more robust against collective errors than in the conventional Dicke subspace.