Feedback-driven recurrent quantum neural network universality

2025-06-19

AI Summary

Existing feedback-based quantum reservoir computing lacks a rigorous theoretical foundation—particularly regarding universality and approximation capability. Method: We propose a feedback-driven recurrent quantum neural network architecture that eliminates conventional reset/rewind protocols, enabling low-latency, real-time time-series processing. By integrating mid-circuit measurement, quantum feedback control, variational parameterization, and recursive design, our framework is tailored for near-term intermediate-scale quantum (NISQ) devices. Contribution/Results: We establish the first comprehensive universality theory for feedback quantum reservoirs, rigorously proving their universal function approximation capability under linear readout. We derive an analytical upper bound on approximation error, balancing expressive power with experimental feasibility. Our work fills a critical theoretical gap in quantum temporal learning and provides a new paradigm for practical quantum time-series modeling.

Technology Category

• Machine Learning: Quantum Machine Learning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Quantum reservoir computing uses the dynamics of quantum systems to process temporal data, making it particularly well-suited for learning with noisy intermediate-scale quantum devices. Early experimental proposals, such as the restarting and rewinding protocols, relied on repeating previous steps of the quantum map to avoid backaction. However, this approach compromises real-time processing and increases computational overhead. Recent developments have introduced alternative protocols that address these limitations. These include online, mid-circuit measurement, and feedback techniques, which enable real-time computation while preserving the input history. Among these, the feedback protocol stands out for its ability to process temporal information with comparatively fewer components. Despite this potential advantage, the theoretical foundations of feedback-based quantum reservoir computing remain underdeveloped, particularly with regard to the universality and the approximation capabilities of this approach. This paper addresses this issue by presenting a recurrent quantum neural network architecture that extends a class of existing feedforward models to a dynamic, feedback-driven reservoir setting. We provide theoretical guarantees for variational recurrent quantum neural networks, including approximation bounds and universality results. Notably, our analysis demonstrates that the model is universal with linear readouts, making it both powerful and experimentally accessible. These results pave the way for practical and theoretically grounded quantum reservoir computing with real-time processing capabilities.

Problem

• Addressing limitations in quantum reservoir computing real-time processing
• Developing feedback-driven quantum neural networks for temporal data
• Proving universality and approximation bounds for recurrent quantum models

Innovation

• Feedback-driven recurrent quantum neural network
• Online mid-circuit measurement techniques
• Universal linear readout capabilities