Finite-round quantum error correction on symmetric quantum sensors

Understand

In quantum sensing using $N$ entangled probes, the variance of the estimated signal strength $\hat{\theta}$ scales like $ \Theta(N^{-2})$ at the Heisenberg limit, which is a quadratic improvement over the standard quantum limit, and is the maximum quantum advantage over classical methods.

• This limit remains elusive, however, because of the inevitable presence of noise decohering quantum sensors.
• Here, we introduce a quantum sensing protocol \texttt{ECSense} based on permutation-invariant quantum error correction (QEC) codes that support tunable code parameters to suit the physical noise model.
• We show that when the signal duration is much shorter than decoherence times, such that errors only accumulate during the $N$ qubit probe state preparation and idle stage, then the estimate's variance of $\Theta( N^{-3/2})$ is achievable in the presence of $\Theta(\sqrt{N})$ errors while the Heisenberg limit is achieved when the number of errors is a constant.