# Learning to Program Adaptive Non-Local Observables for Machine Learning

arXiv: https://arxiv.org/abs/2609.18655 · HTML: https://mlsanity.com/paper/2609.18655/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 23 references that are in the map.
- First posted on arXiv 16 Sep 2026.

## Builds on (most cited first, 15 of 15)

- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [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)
- [Learning to Program Variational Quantum Circuits with Fast Weights](https://mlsanity.com/paper/2402.17760/) (2024)
- [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)
- [QuLTSF: Long-Term Time Series Forecasting with Quantum Machine Learning](https://mlsanity.com/paper/2412.13769/) (2024)
- [Quantum Hierarchical Reinforcement Learning via Variational Quantum Circuits](https://mlsanity.com/paper/2605.03434/) (2026)
- [Multivariate Time Series Forecasting with Adaptive Non-Local Observables](https://mlsanity.com/paper/2607.24399/) (2026)

## Abstract (arXiv)

Quantum neural networks (QNNs) are typically built from variational quantum circuits (VQCs), which are limited by local measurements. Adaptive non-local observables (ANO) address this by jointly optimizing circuit parameters and multi-qubit measurements. However, existing ANO-based VQCs learn only a single static observable that remains invariant across all inputs. We propose QFWP-ANO, a novel architecture which employs a classical hypernetwork to dynamically program VQC parameters and/or non-local observables conditioned on each input. On multivariate time-series forecasting across four ETT datasets, QFWP-ANO achieves the lowest MSE in 16 of 20 settings and second-lowest in the remaining four, surpassing ANO-based and other strong baselines. On reinforcement learning tasks, QFWP-ANO consistently surpasses ANO-VQCs. Our results establish input-conditioned ANO as an effective approach for enhancing QNNs.