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Learning to Program Adaptive Non-Local Observables for Machine Learning
Yu-Ting Lee, Samuel Yen-Chi Chen, Huan-Hsin Tseng
TL;DR
VQC-based QNNs rely on local measurements, while existing ANO models keep their observable static across inputs. QFWP-ANO uses a classical hypernetwork to condition circuit parameters and/or non-local observables on each input, and performs strongly in forecasting and reinforcement learning.
Problem
VQC-based QNNs rely on local measurements, and existing ANO-based QNNs use an observable that remains invariant across inputs.
Source: §1 · p. 1Method
QFWP-ANO uses a classical hypernetwork to program VQC parameters, non-local observables, or both, conditioned on each input.
Source: §1 · p. 1Results
Across four ETT datasets, QFWP-ANO ranks first in MSE in 16 of 20 forecasting settings and second in the remaining four; it also outperforms ANO-VQCs in reinforcement learning.
Source: §1 · p. 1Takeaways & Limitations
The results establish input-conditioned ANO as a promising route to more capable quantum models.
Source: §5 · p. 4
Abstract
from arXiv · showhide
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.
1. INTRODUCTION
Local measurements constrain VQC-based QNNs, and existing ANO models use observables that remain static across inputs. QFWP-ANO conditions circuit parameters and/or non-local observables on each input, with strong results in forecasting and reinforcement learning.
1. INTRODUCTION
- Existing ANO-based QNNs rely on a static observable per task, leaving measurements invariant to the input data stream.VQC-based QNNs also rely on local measurements, which limit their ability to learn complex data distributions.Source: §1 · p. 1
- QFWP-ANO uses a classical hypernetwork to program circuit parameters, non-local observables, or both conditioned on each input.The architecture builds on quantum fast weight programmers.Source: §1 · p. 1
- QFWP-ANO ranks first in MSE in 16 of 20 ETT forecasting settings and second in the remaining four, outperforming standard ANO-VQCs in 17 of 20 cases.The reported results cover four ETT datasets.Source: §1 · p. 1
- In standard reinforcement-learning environments, QFWP-ANO outperforms ANO-VQCs, and programming non-local observables can accelerate learning.Source: §1 · p. 1
2. METHODOLOGY
The methodology replaces fixed VQC measurements with trainable multi-qubit observables and uses a classical hypernetwork to generate circuit and observable parameters from each input.
2.1. Variational Quantum Circuits
- VQCs encode classical input into an n-qubit state, evolve it with a parameterized unitary, and measure a fixed Hermitian observable to extract classical information.Source: §2.1 · pp. 1–2
2.2. Adaptive Non-Local Observables
- ANO replaces a fixed observable with a trainable k-local Hermitian operator that couples k qubits and can mix features beyond common Pauli-Z measurements.A conventional VQC with a fixed local observable is a special case of ANO.Source: §2.2 · p. 2
2.3. QFWP-ANO
- QFWP-ANO's encoder-decoder hypernetwork maps each input independently to rotation angles and/or ANO parameters, without accumulated recurrent state.A shared MLP encoder produces latent z; separate decoders generate rotation angles and ANO parameters.Source: §2.3 · p. 2
- The QFWP-ANO circuit uses data re-uploading with parameterized Rz/Ry rotations, circular CNOT gates, and trainable k-local observables for measurement.The architecture figure depicts these circuit layers and measurement observables.Source: §2.3 · p. 2, Figure 1 · p. 2
3. EXPERIMENTAL SETTINGS
The experiments evaluate QFWP-ANO on multivariate time-series forecasting and reinforcement learning, using ETT datasets and A3C environments. The setups specify the forecasting data split and metrics, as well as the RL tasks and training conditions.
3. EXPERIMENTAL SETTINGS
- The MTSF experiments compare QFWP-ANO variants that program rotation angles, ANO parameters, or both.All three variants are evaluated on forecasting and RL tasks.Source: §3 · p. 2
3.1. Multivariate Time Series Forecasting
- MTSF predicts future values from a multivariate lookback window; experiments use four ETT datasets, a 6:2:2 split, and MSE and MAE metrics.The study sweeps circuit depth and non-locality, reporting the best result over those settings.Source: §3.1 · pp. 2–3
3.2. Reinforcement Learning
- For RL, separate QFWP-ANO instances approximate the A3C policy and value functions, with each hypernetwork reading the state directly.Experiments use Acrobot and MiniGrid-SimpleCrossingS9N1, compare against ANO-VQC, and average results over 10 seeds.Source: §3.2 · p. 3
4. EXPERIMENTS
Across MTSF and RL benchmarks, QFWP-ANO performs strongly against ANO-VQCs. Forecasting results favor observable-programming variants, while RL learning curves and analyses of non-locality and circuit depth show setting-dependent outcomes.
4.1. MTSF Results
- QFWP-ANO ranks first in MSE in 16 of 20 MTSF settings and second in the remaining four; it outperforms standard ANO-VQCs in 17 of 20 cases.The results use lookback L = 16 and prediction horizons H ∈ {1, 5, 16, 32, 48}.Source: §4.1 · p. 3, Table 2 · p. 4
4.2. RL Results
- In Acrobot, QFWP-ANO variants outperform ANO-VQC from episodes 1000–4000, and observable-programming variants reach peak performance around episode 1000; in SimpleCrossingS9N1, QFWP-ANO-RO leads throughout training.The figure plots reward over episodes, with bands showing ± standard deviation.Source: §4.2 · pp. 3–4, Figure 2 · p. 3
4.3. Impact of ANO Non-Locality and VQC Depth
- Moderate non-locality performs best across variants, while shallower circuits match or outperform deeper circuits in most settings.At k = 7, QFWP-ANO-R dominates across horizons, whereas QFWP-ANO-RO and QFWP-ANO-O achieve the lowest MSE for k ≤ 4.Source: §4.3 · p. 4, Table 3 · p. 4
5. CONCLUSION
The conclusion presents QFWP-ANO as a hypernetwork-based QNN architecture that dynamically programs VQCs and non-local observables. Its reported forecasting and RL results support input-conditioned ANO as a promising route to more capable quantum models.
5. CONCLUSION
- QFWP-ANO uses a classical hypernetwork to dynamically program VQCs along with non-local observables.Source: §5 · p. 4
- On MTSF benchmarks, QFWP-ANO ranks first in MSE in 16 of 20 settings and second in the remaining four.Source: §5 · p. 4
- In RL environments, QFWP-ANO consistently outperforms ANO-VQCs, and programming non-local observables can accelerate learning.Source: §5 · p. 4