# Diagonal Adaptive Non-local Observables on Quantum Neural Networks

arXiv: https://arxiv.org/abs/2605.15410 · HTML: https://mlsanity.com/paper/2605.15410/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 20 references that are in the map.
- First posted on arXiv 14 May 2026.

## Builds on (most cited first, 12 of 12)

- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [Quantum Convolutional Neural Networks for High Energy Physics Data Analysis](https://mlsanity.com/paper/2012.12177/) (2020)
- [An end-to-end trainable hybrid classical-quantum classifier](https://mlsanity.com/paper/2102.02416/) (2021)
- [Asynchronous training of quantum reinforcement learning](https://mlsanity.com/paper/2301.05096/) (2023)
- [Learning to Measure Quantum Neural Networks](https://mlsanity.com/paper/2501.05663/) (2025)
- [Adaptive Non-local Observable on Quantum Neural Networks](https://mlsanity.com/paper/2504.13414/) (2025)
- [Quantum Reinforcement Learning by Adaptive Non-local Observables](https://mlsanity.com/paper/2507.19629/) (2025)
- [Quantum Super-resolution by Adaptive Non-local Observables](https://mlsanity.com/paper/2601.14433/) (2026)
- [Breaking the cubic barrier in the Solovay-Kitaev algorithm](https://mlsanity.com/paper/2306.13158/) (2023)

## Abstract (arXiv)

Adaptive Non-local Observables (ANOs) have shown that making quantum observables dynamic can substantially enlarge the function space of Variational Quantum Algorithms, partly shifting hardware demands from circuit synthesis to measurement design. However, this advantage is accompanied by a steep increase in the number of parameters, as well as the classical optimization cost for varying general Hermitian observables. We propose a special form of ANO that significantly reduces this burden by considering only diagonal observables paired with quantum circuits. Mathematically, this is equivalent to the full ANO of a large parameter space since diagonal matrices are canonical representatives of the ANO space modulo unitary similarity. As a result, Diagonal ANO retains the same capability of full ANO while reducing k-local observable complexity from O(4k) to O(2k) and lowering the corresponding measurement-side classical computation. In this sense, diagonal ANO preserves much of the benefit of full ANO while encompassing conventional VQCs as a special case.