Quantum-Enhanced Channel Mixing in RWKV Models for Time Series Forecasting (2505.13524v2)

Abstract: Recent advancements in neural sequence modeling have led to architectures such as RWKV, which combine recurrent-style time mixing with feedforward channel mixing to enable efficient long-context processing. In this work, we propose QuantumRWKV, a hybrid quantum-classical extension of the RWKV model, where the standard feedforward network (FFN) is partially replaced by a variational quantum circuit (VQC). The quantum component is designed to enhance nonlinear representational capacity while preserving end-to-end differentiability via the PennyLane framework. To assess the impact of quantum enhancements, we conduct a comparative evaluation between QuantumRWKV and its classical counterpart across ten synthetic time-series forecasting tasks, encompassing linear (ARMA), chaotic (Logistic Map), oscillatory (Damped Oscillator, Sine Wave), and regime-switching signals. Our results show that QuantumRWKV outperforms the classical model in 6 out of 10 tasks, particularly excelling in sequences with nonlinear or chaotic dynamics, such as Chaotic Logistic, Noisy Damped Oscillator, Sine Wave, Triangle Wave, Sawtooth, and ARMA. However, it underperforms on tasks involving sharp regime shifts (Piecewise Regime) or smoother periodic patterns (Damped Oscillator, Seasonal Trend, Square Wave). This study provides one of the first systematic comparisons between hybrid quantum-classical and classical recurrent models in temporal domains, highlighting the scenarios where quantum circuits can offer tangible advantages. We conclude with a discussion on architectural trade-offs, such as variance sensitivity in quantum layers, and outline future directions for scaling quantum integration in long-context temporal learning systems.

Quantum-Enhanced Channel Mixing in RWKV Models for Time Series Forecasting

The paper "Quantum-Enhanced Channel Mixing in RWKV Models for Time Series Forecasting" explores the integration of quantum computing elements into neural architectures specifically tailored for time-series analysis. Neural sequence modeling continues to be pivotal across various scientific domains; however, existing architectures struggle with balancing the requirements for scalability, efficiency, and the ability to model complex temporal patterns.

Overview

RWKV is a neural architecture designed for sequence modeling, initially devised to overcome the quadratic complexity limitations inherent in self-attention mechanisms typical to Transformer models. Rather than relying on attention, RWKV utilizes a recurrent-style time mixing combined with feedforward channel mixing. This paper proposes an augmentation to the RWKV model—the QuantumRWKV—by partially replacing its feedforward network with a variational quantum circuit (VQC), leveraging quantum computing capabilities for enhanced nonlinear representational power.

Methodology

The QuantumRWKV model retains the classical RWKV's time-mixing component but introduces a novel quantum channel-mixing module involving a dual-path feedforward structure. The quantum path employs VQCs, encoding input features using angle embeddings and using entangling layers to compute quantum state transformations. These quantum enhancements are facilitated using the PennyLane framework, preserving differentiability. This innovative setup permits the hybrid quantum-classical model to co-train effectively within classical deep learning pipelines.

Experimental Insights

A comparative evaluation was conducted involving various synthetic time-series forecasting tasks, categorized into linear, chaotic, oscillatory, and discontinuous regime tasks. Notably, the QuantumRWKV demonstrated superior performance in modeling tasks characterized by smooth nonlinearity and chaotic dynamics, such as the chaotic Logistic map and Noisy Damped Oscillator. Conversely, it exhibited limitations in tasks which involved sharp discontinuities, such as piecewise regime signals.

Implications

The results underscore the specific contexts under which quantum circuits can bolster the learning capacity of temporal models. While quantum computation showed an advantage in tasks entailing smooth nonlinear behaviors and chaotic dynamics, classical architectures remained more effective for tasks featuring discrete transitions. This suggests quantum-enhanced models like QuantumRWKV could be beneficial for domains requiring intricate temporal predictions, such as neuroscience or nutritional modeling, provided the underlying time-series data exhibit suitable characteristics.

Future Directions

Future developments could explore varying the number of qubits and circuit depth to further unlock the full potential of VQCs, conditional on managing computational overhead effectively. Furthermore, as quantum hardware matures, the deployment of hybrid architectures on real quantum devices may offer substantial performance improvements compared to simulation. Such advancements could establish large-scale quantum integration as practical in time-series domains, marrying classical scalability with quantum's nonlinear transformation capabilities.

In summary, the paper makes a significant contribution by systematically investigating the efficacy of quantum components within a recurrent model architecture for time-series forecasting. By establishing task-specific contexts where quantum advantages manifest, it effectively paves the way for further exploration into quantum hybrid models and their applicability across varied scientific fields. The insights derived from its findings promise to inform architectural design paradigms and guide future research into quantum machine learning.