# Robust quantum metrology with explicit symmetric states

## TL;DR

This paper demonstrates that certain symmetric quantum states within error correction codes enable robust quantum metrology, maintaining high precision even with noise, and achieve Heisenberg scaling in both NISQ and asymptotic regimes.

## Contribution

It introduces symmetric probe states within quantum error correction codes that enable noise-resilient quantum metrology with Heisenberg scaling.

## Key findings

- Robustness of symmetric states against erasure and dephasing errors.
- Quantum advantage persists despite noise in near-term devices.
- Achieves Heisenberg scaling in asymptotic limits.

## Abstract

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.