Beyond spectator qubits: Noise mitigation with continuous measurements, photonic modes, and Heisenberg-limited performance*

There has recently been significant theoretical (see e.g., [1-3]) and experimental (see e.g., [4]) interest in the use of spectator qubits to detect spatially correlated noise fluctuations and use the acquired information to protect a distinct set of "data" qubits. Here we generalize the concept to that of a "spectator mode": a photonic mode which continuously measures the spatially correlated noise fluctuations and applies a continuous correction drive to a frequency-tunable data qubit. We show that the spectator mode approach has a key advantage over spectator qubits: measurements can be made using many photons, allowing a parametric suppression of measurement imprecision and dramatically enhanced performance. We find that long-time qubit dephasing can in principle be arbitrarily suppressed, even for Markovian dephasing noise. Furthermore, realistic spectator mode architectures can exhibit Heisenberg-limited performance in the number of photons used in the measurement. We also discuss similar performance of analogous spectator mode strategies when applied to mechanical force sensors.