Repetitive Readout and Real-Time Control of Nuclear Spin Qubits in 171Yb Atoms

We demonstrate high-fidelity repetitive measurements of nuclear spin qubits in an array of neutral ytterbium-171 (171Yb) atoms. We show that the qubit state can be measured with a spin-flip probability of 0.004(4) for a single tweezer and 0.012(3) averaged over the array. This is accomplished by high cyclicity of one of the nuclear spin qubit states with an optically excited state under a magnetic field of B=58 G, resulting in a spin-flip probability of approximately 10-5 per scattered photon during fluorescence readout. The performance improves further as ∼1/B2. The state discrimination fidelity is 0.993(4) with a state-averaged readout survival of 0.994(3), limited by off-resonant scattering to dark states. We combine our measurement technique with high-contrast rotations of the nuclear spin qubit via an ac magnetic field to explore two paradigmatic scenarios, including the noncommutativity of measurements in orthogonal bases, and the quantum Zeno mechanism in which measurements "freeze"coherent evolution. Finally, we employ real-time feedforward to repetitively and deterministically prepare the qubit in the +z or -z direction after initializing it in a different basis and performing a measurement in the Z basis. These capabilities constitute an important step towards adaptive quantum circuits with atom arrays.