# Learning to Measure Quantum Neural Networks

arXiv: https://arxiv.org/abs/2501.05663 · HTML: https://mlsanity.com/paper/2501.05663/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 41 references that are in the map.
- First posted on arXiv 10 Jan 2025.

## Builds on (most cited first, 27 of 27)

- [Variational Quantum Circuits for Deep Reinforcement Learning](https://mlsanity.com/paper/1907.00397/) (2019)
- [Quantum Long Short-Term Memory](https://mlsanity.com/paper/2009.01783/) (2020)
- [Parametrized quantum policies for reinforcement learning](https://mlsanity.com/paper/2103.05577/) (2021)
- [Quantum Convolutional Neural Networks for High Energy Physics Data Analysis](https://mlsanity.com/paper/2012.12177/) (2020)
- [The Dawn of Quantum Natural Language Processing](https://mlsanity.com/paper/2110.06510/) (2021)
- [Quantum Architecture Search via Deep Reinforcement Learning](https://mlsanity.com/paper/2104.07715/) (2021)
- [An end-to-end trainable hybrid classical-quantum classifier](https://mlsanity.com/paper/2102.02416/) (2021)
- [Variational Quantum Reinforcement Learning via Evolutionary Optimization](https://mlsanity.com/paper/2109.00540/) (2021)
- [When BERT Meets Quantum Temporal Convolution Learning for Text Classification in Heterogeneous Computing](https://mlsanity.com/paper/2203.03550/) (2022)
- [Quantum Architecture Search: A Survey](https://mlsanity.com/paper/2406.06210/) (2024)
- [QTN-VQC: An End-to-End Learning framework for Quantum Neural Networks](https://mlsanity.com/paper/2110.03861/) (2021)
- [PQLM -- Multilingual Decentralized Portable Quantum Language Model for Privacy Protection](https://mlsanity.com/paper/2210.03221/) (2022)
- [Quantum Multi-Agent Reinforcement Learning via Variational Quantum Circuit Design](https://mlsanity.com/paper/2203.10443/) (2022)
- [Quantum deep recurrent reinforcement learning](https://mlsanity.com/paper/2210.14876/) (2022)
- [Learning to Program Variational Quantum Circuits with Fast Weights](https://mlsanity.com/paper/2402.17760/) (2024)
- [Slimmable Quantum Federated Learning](https://mlsanity.com/paper/2207.10221/) (2022)
- [Applying QNLP to sentiment analysis in finance](https://mlsanity.com/paper/2307.11788/) (2023)
- [Quantum Architecture Search via Continual Reinforcement Learning](https://mlsanity.com/paper/2112.05779/) (2021)
- [Federated Quantum Long Short-term Memory (FedQLSTM)](https://mlsanity.com/paper/2312.14309/) (2023)
- [Differentiable Quantum Architecture Search in Asynchronous Quantum Reinforcement Learning](https://mlsanity.com/paper/2407.18202/) (2024)
- [Differentiable Quantum Architecture Search for Quantum Reinforcement Learning](https://mlsanity.com/paper/2309.10392/) (2023)
- [QEEGNet: Quantum Machine Learning for Enhanced Electroencephalography Encoding](https://mlsanity.com/paper/2407.19214/) (2024)
- [Quantum Machine Learning Architecture Search via Deep Reinforcement Learning](https://mlsanity.com/paper/2407.20147/) (2024)
- [Quantum-Trained Convolutional Neural Network for Deepfake Audio Detection](https://mlsanity.com/paper/2410.09250/) (2024)
- [Quantum Gradient Class Activation Map for Model Interpretability](https://mlsanity.com/paper/2408.05899/) (2024)
- [Reinforcement Learning for Variational Quantum Circuits Design](https://mlsanity.com/paper/2409.05475/) (2024)
- [Evolutionary Optimization for Designing Variational Quantum Circuits with High Model Capacity](https://mlsanity.com/paper/2412.12484/) (2024)

## Built on by (most cited first, 15 of 15)

- [Adaptive Non-local Observable on Quantum Neural Networks](https://mlsanity.com/paper/2504.13414/) (2025)
- [Differentiable Quantum Architecture Search in Quantum-Enhanced Neural Network Parameter Generation](https://mlsanity.com/paper/2505.09653/) (2025)
- [Learning to Program Quantum Measurements for Machine Learning](https://mlsanity.com/paper/2505.13525/) (2025)
- [Quantum Reinforcement Learning by Adaptive Non-local Observables](https://mlsanity.com/paper/2507.19629/) (2025)
- [Quantum Long Short-term Memory with Differentiable Architecture Search](https://mlsanity.com/paper/2508.14955/) (2025)
- [Quantum Super-resolution by Adaptive Non-local Observables](https://mlsanity.com/paper/2601.14433/) (2026)
- [Exploring the Potential of QEEGNet for Cross-Task and Cross-Dataset Electroencephalography Encoding with Quantum Machine Learning](https://mlsanity.com/paper/2503.00080/) (2025)
- [QuKAN: A Quantum Circuit Born Machine approach to Quantum Kolmogorov Arnold Networks](https://mlsanity.com/paper/2506.22340/) (2025)
- [Kernel-based optimization of measurement operators for quantum reservoir computers](https://mlsanity.com/paper/2602.14677/) (2026)
- [Neural Architecture Search for Quantum Autoencoders](https://mlsanity.com/paper/2511.19246/) (2025)
- [Multivariate Time Series Forecasting with Adaptive Non-Local Observables](https://mlsanity.com/paper/2607.24399/) (2026)
- [Dataset Distillation for Quantum Neural Networks](https://mlsanity.com/paper/2503.17935/) (2025)
- [Differential equation quantum solvers: engineering measurements to reduce cost](https://mlsanity.com/paper/2503.22656/) (2025)
- [Diagonal Adaptive Non-local Observables on Quantum Neural Networks](https://mlsanity.com/paper/2605.15410/) (2026)
- [Learning to Program Adaptive Non-Local Observables for Machine Learning](https://mlsanity.com/paper/2609.18655/) (2026)

## Abstract (arXiv)

The rapid progress in quantum computing (QC) and machine learning (ML) has attracted growing attention, prompting extensive research into quantum machine learning (QML) algorithms to solve diverse and complex problems. Designing high-performance QML models demands expert-level proficiency, which remains a significant obstacle to the broader adoption of QML. A few major hurdles include crafting effective data encoding techniques and parameterized quantum circuits, both of which are crucial to the performance of QML models. Additionally, the measurement phase is frequently overlooked-most current QML models rely on pre-defined measurement protocols that often fail to account for the specific problem being addressed. We introduce a novel approach that makes the observable of the quantum system-specifically, the Hermitian matrix-learnable. Our method features an end-to-end differentiable learning framework, where the parameterized observable is trained alongside the ordinary quantum circuit parameters simultaneously. Using numerical simulations, we show that the proposed method can identify observables for variational quantum circuits that lead to improved outcomes, such as higher classification accuracy, thereby boosting the overall performance of QML models.