Surpassing spectator qubits with photonic modes and continuous measurement for Heisenberg-limited noise mitigation.

Noise is an ever-present challenge to the creation and preservation of fragile quantum states. Recent work suggests that spatial noise correlations can be harnessed as a resource for noise mitigation via the use of spectator qubits to measure environmental noise. In this work we generalize this concept from spectator qubits to a spectator mode: a photonic mode which continuously measures spatially correlated classical dephasing noise and applies a continuous correction drive to frequency-tunable data qubits. Our analysis shows that by using many photon states, spectator modes can surpass many of the quantum measurement constraints that limit spectator qubit approaches. We also find that long-time data qubit dephasing can be arbitrarily suppressed, even for white noise dephasing. Further, using a squeezing (parametric) drive, the error in the spectator mode approach can exhibit Heisenberg-limited scaling in the number of photons used. We also show that spectator mode noise mitigation can be implemented completely autonomously using engineered dissipation. In this case no explicit measurement or processing of a classical measurement record is needed. Our work establishes spectator modes as a potentially powerful alternative to spectator qubits for noise mitigation.