Fig. 4. Repeated ancilla-based quantum logic spectroscopy.

a, We consider three ensembles of atoms: reference (Ref.) atoms (R; red), clock atoms (C; purple) and ancillas (A; blue). An entangling gate maps the state of clock atoms to the state of ancilla atoms before the MCR of the ancilla state. b, Logic spectroscopy with ancilla atoms. A Ramsey interrogation is performed in parallel on reference atoms (R) and clock atoms (C). A clock-ancilla CNOT gate (controlled on qubit state $\mid 0⟩$) maps the state onto ancilla atoms (A) for read-out. c, Ancilla-based $\widehat{X}$ measurement. A non-destructive measurement of the state ${\mid \psi ⟩}_C$ is realized by shelving clock qubits ($\widehat{S}$ operation) followed by ancilla MCR. We show that following the unshelving (${\widehat{S}}^{†}$), the state of the clock qubit is projected to a well-defined state in the measurement basis, conditioned on the ancilla state. d, N_cyc repeated rounds of quantum logic spectroscopy with minimal dead time (2.9 ms), enabled by ancilla replacement through an array reconfiguration. Each round j consists of a fixed evolution time T_j followed by ancilla-based $\widehat{X}$ measurement before a final round where the clock qubit is directly measured in a Ramsey sequence with variable time t. e, We find improved contrast in the final measurement round when conditioned on ancilla results (see text) in all previous rounds (purple markers) compared to the reference clock atoms, which are protected during MCR but do not interact with the ancillas (red markers).