# Inference-Based Quantum Sensing

arXiv: https://arxiv.org/abs/2206.09919 · HTML: https://mlsanity.com/paper/2206.09919/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 52 references that are in the map.
- First posted on arXiv 20 Jun 2022.

## Builds on (most cited first, 6 of 6)

- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Noise-Induced Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2007.14384/) (2020)
- [Absence of Barren Plateaus in Quantum Convolutional Neural Networks](https://mlsanity.com/paper/2011.02966/) (2020)
- [Stochastic gradient descent for hybrid quantum-classical optimization](https://mlsanity.com/paper/1910.01155/) (2019)
- [Trainability of Dissipative Perceptron-Based Quantum Neural Networks](https://mlsanity.com/paper/2005.12458/) (2020)
- [Can Error Mitigation Improve Trainability of Noisy Variational Quantum Algorithms?](https://mlsanity.com/paper/2109.01051/) (2021)

## Built on by (most cited first, 7 of 7)

- [Does provable absence of barren plateaus imply classical simulability?](https://mlsanity.com/paper/2312.09121/) (2023)
- [Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networks](https://mlsanity.com/paper/2210.09974/) (2022)
- [A Primer on Quantum Machine Learning](https://mlsanity.com/paper/2511.15969/) (2025)
- [Effects of noise on the overparametrization of quantum neural networks](https://mlsanity.com/paper/2302.05059/) (2023)
- [On the universality of Sn-equivariant k-body gates](https://mlsanity.com/paper/2303.00728/) (2023)
- [Separable Power of Classical and Quantum Learning Protocols Through the Lens of No-Free-Lunch Theorem](https://mlsanity.com/paper/2405.07226/) (2024)
- [Optical Quantum Sensing for Agnostic Environments via Deep Learning](https://mlsanity.com/paper/2311.07203/) (2023)

## Abstract (arXiv)

In a standard Quantum Sensing (QS) task one aims at estimating an unknown parameter θ, encoded into an n-qubit probe state, via measurements of the system. The success of this task hinges on the ability to correlate changes in the parameter to changes in the system response R(θ) (i.e., changes in the measurement outcomes). For simple cases the form of R(θ) is known, but the same cannot be said for realistic scenarios, as no general closed-form expression exists. In this work we present an inference-based scheme for QS. We show that, for a general class of unitary families of encoding, R(θ) can be fully characterized by only measuring the system response at 2n+1 parameters. This allows us to infer the value of an unknown parameter given the measured response, as well as to determine the sensitivity of the scheme, which characterizes its overall performance. We show that inference error is, with high probability, smaller than δ, if one measures the system response with a number of shots that scales only as Omega(log3(n)/δ2). Furthermore, the framework presented can be broadly applied as it remains valid for arbitrary probe states and measurement schemes, and, even holds in the presence of quantum noise. We also discuss how to extend our results beyond unitary families. Finally, to showcase our method we implement it for a QS task on real quantum hardware, and in numerical simulations.