Decoherence-free subspace of nuclear spins coupled to a rare-earth ion qubit

Nuclear spins surrounding solid-state qubits are a crucial resource for quantum information processing and storage. However, initialization, readout and control of the primary qubit usually lead to decoherence of the nuclear spin state. Encoding information into decoherence-free subspaces allows the independent operation of these two quantum subsystems.

Previously, we demonstrated polarization and coherent control of vanadium lattice nuclear spins surrounding optically addressable ytterbium qubits inside a yttrium orthovanadate host crystal.

Via high fidelity quantum control, we can engineer an interaction between Yb and the V nuclear spin ensemble, efficiently creating a highly entangled Yb-V GHZ state. Crucially, we identify the decoherence-free subspace of the collective nuclear spin state, which is insensitive to the correlated magnetic field noise generated by the Yb dipolar field. The common-mode noise rejection is a result of the symmetrical position of V ions relative to Yb, leading to long coherence times for these particular spin-ensemble states.

We verify the presence of the decoherence-free states by examining the Zeeman sensitivity to applied static fields and by testing their robustness against a range of different Yb-induced noise processes. These noise-insensitive states open up an opportunity to sense nuclear spin-nuclear spin interactions and demonstrate the first step toward decoherence-protected memories for quantum network applications.