Adaptive Non-local Observable on Quantum Neural Networks

2025-04-18

AI Summary

Conventional variational quantum circuits (VQCs) are constrained by fixed Hermitian observables, limiting their expressive power and resource efficiency. Method: This paper introduces an adaptive, nonlocal observable framework grounded in the Heisenberg picture, wherein the observable itself is treated as a trainable parameter that dynamically evolves during circuit optimization. The framework incorporates two distinct constructions of nonlocal Pauli tensor observables, markedly enhancing long-range correlations and information mixing across qubits. Contribution/Results: We prove theoretically that standard VQCs correspond to a special case of our framework under frozen observables. Numerical experiments on classification tasks demonstrate that the proposed method achieves higher accuracy with shallower circuit depths, substantially improving both model expressivity and quantum resource utilization efficiency.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Non-convex Optimization
• Computer Vision: Learning & Optimization for CV

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

Conventional Variational Quantum Circuits (VQCs) for Quantum Machine Learning typically rely on a fixed Hermitian observable, often built from Pauli operators. Inspired by the Heisenberg picture, we propose an adaptive non-local measurement framework that substantially increases the model complexity of the quantum circuits. Our introduction of dynamical Hermitian observables with evolving parameters shows that optimizing VQC rotations corresponds to tracing a trajectory in the observable space. This viewpoint reveals that standard VQCs are merely a special case of the Heisenberg representation. Furthermore, we show that properly incorporating variational rotations with non-local observables enhances qubit interaction and information mixture, admitting flexible circuit designs. Two non-local measurement schemes are introduced, and numerical simulations on classification tasks confirm that our approach outperforms conventional VQCs, yielding a more powerful and resource-efficient approach as a Quantum Neural Network.

Problem

• Enhances model complexity with adaptive non-local measurements
• Optimizes VQC rotations via dynamic observable trajectories
• Improves qubit interaction and classification performance

Innovation

• Adaptive non-local measurement framework
• Dynamical Hermitian observables with evolving parameters
• Variational rotations with non-local observables