  Quantum metrology is a promising practical use case for quantum technologies,
where physical quantities can be measured with unprecedented precision. In lieu
of quantum error correction procedures, near term quantum devices are expected
to be noisy, and we have to make do with noisy probe states. We prove that, for
a set of carefully chosen symmetric probe states that lie within certain
quantum error correction codes, quantum metrology exhibits an advantage over
classical metrology even after the probe states are corrupted by a constant
number of erasure and dephasing errors. These probe states prove useful for
robust metrology not only in the NISQ regime, but also in the asymptotic
setting where they achieve Heisenberg scaling. This brings us closer towards
making robust quantum metrology a technological reality.
