# Beyond Heisenberg Limit Quantum Metrology through Quantum Signal Processing

arXiv: https://arxiv.org/abs/2209.11207 · HTML: https://mlsanity.com/paper/2209.11207/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 29 references that are in the map.
- First posted on arXiv 22 Sep 2022.

## Builds on (most cited first, 2 of 2)

- [Universal Quantum Control through Deep Reinforcement Learning](https://mlsanity.com/paper/1803.01857/) (2018)
- [Efficient phase-factor evaluation in quantum signal processing](https://mlsanity.com/paper/2002.11649/) (2020)

## Abstract (arXiv)

Leveraging quantum effects in metrology such as entanglement and coherence allows one to measure parameters with enhanced sensitivity. However, time-dependent noise can disrupt such Heisenberg-limited amplification. We propose a quantum-metrology method based on the quantum-signal-processing framework to overcome these realistic noise-induced limitations in practical quantum metrology. Our algorithm separates the gate parameter varphi~(single-qubit Z phase) that is susceptible to time-dependent error from the target gate parameter θ~(swap-angle between |10> and |01> states) that is largely free of time-dependent error. Our method achieves an accuracy of 10-4 radians in standard deviation for learning θ in superconducting-qubit experiments, outperforming existing alternative schemes by two orders of magnitude. We also demonstrate the increased robustness in learning time-dependent gate parameters through fast Fourier transformation and sequential phase difference. We show both theoretically and numerically that there is an interesting transition of the optimal metrology variance scaling as a function of circuit depth d from the pre-asymptotic regime d ll 1/θ to Heisenberg limit d → ∞. Remarkably, in the pre-asymptotic regime our method's estimation variance on time-sensitive parameter varphi scales faster than the asymptotic Heisenberg limit as a function of depth, Var(hatvarphi)≈ 1/d4. Our work is the first quantum-signal-processing algorithm that demonstrates practical application in laboratory quantum computers.