Scientists have shown that bosonic quantum sensors can maintain Heisenberg‑limited accuracy at interrogation times longer than the noise‑dominated regime of ordinary bosonic detectors. The new protocol encodes the sensor’s harmonic‑oscillator state into an odd‑length repetition code of qubit ancillae. Controlled displacements couple the oscillator to the encoded qubits, and repeated parity measurements along with conditional logical corrections reset the oscillator between sensing slots. These actions remove background dephasing noise without erasing the logical phase that carries the measurement signal.

Under realistic circuit‑level bit‑flip noise, a code of distance d reduces logical failure probability to the order of p^[(d+1)/2]. For a decay rate γ_A, total sensing time T, and mean photon‑number budget N, the Fisher information—an indicator of achievable precision—scales as N T² when the interrogation time is about γ_A^{–(d+1)/2}. This represents a clear advance over the non‑fault‑tolerant strategy, whose Heisenberg scaling ceases after a total time of order γ_A^{–1}.

However, the scheme is not immune to measurement imperfections. If each boson‑parity outcome is misidentified with probability q, the logical visibility falls as (1–2q)^{2M}, where M is the number of measurement cycles. Consequently, the interval over which the quadratic 1/T² scaling holds is limited; Heisenberg performance persists only for M roughly equal to 1/q cycles. This sets a practical bound on how many cycles can be used before the advantage erodes.