[Paper Review] Quantum Recurrent Unit: A Parameter-Efficient Quantum Neural Network Architecture for NISQ Devices

Tzong-Daw Wu, Hsi-Sheng Goan|arXiv (Cornell University)|Jan 26, 2026

Quantum Computing Algorithms and Architecture0 citations

TL;DR

The paper introduces the Quantum Recurrent Unit (QRU), a parameter-efficient quantum neural network using C-SWAP gates for NISQ devices, with constant depth and parameters across sequence length, and demonstrates strong performance on oscillation prediction, cancer classification, and MNIST.

ABSTRACT

The rapid growth of modern machine learning (ML) models presents fundamental challenges in parameter efficiency and computational resource requirements. This study introduces the Quantum Recurrent Unit (QRU), a novel quantum neural network (NN) architecture specifically designed to address these challenges while remaining compatible with Noisy Intermediate-Scale Quantum (NISQ) devices. QRU leverages quantum controlled-SWAP (C-SWAP; Fredkin) gates to implement an information selection mechanism inspired by classical Gated Recurrent Units (GRUs), enabling selective processing of temporal information via quantum operations. Through its innovative recurrent architecture featuring measurement results feedforward state propagation and shared parameters across time steps, QRU achieves constant circuit depth and constant parameter count regardless of input sequence length, effectively circumventing stringent NISQ hardware constraints. We systematically validate QRU through three progressive experiments: (1) oscillatory behavior prediction, where 72-parameter QRU matches 197-parameter classical GRU performance; (2) Wisconsin Diagnostic Breast Cancer classification, where 35 parameters achieve 96.13% accuracy comparable to 167-parameter artificial NNs; and (3) MNIST handwritten digit recognition, where 132 parameters reach 98.05% accuracy, outperforming a 27,265-parameter convolutional NN. These results demonstrate that QRU consistently achieves comparable or superior performance with significantly fewer parameters than classical NNs while maintaining constant quantum circuit depth. The architecture's quantum-native design, combining C-SWAP-based information selection with novel recurrent processing, suggests QRU's potential as a fundamental building block for next-generation ML systems, offering a promising pathway toward more efficient and scalable quantum ML architectures.

Motivation & Objective

• Motivate the need for parameter-efficient ML on NISQ hardware.
• Propose QRU as a quantum recurrent architecture with constant depth and parameter count across sequence length.
• Demonstrate QRU performance on oscillation prediction, Wisconsin Breast Cancer classification, and MNIST.
• Show that QRU can match or surpass classical NN performance with far fewer parameters.

Proposed method

• Use quantum controlled-SWAP (C-SWAP) gates to implement information selection inspired by gated recurrent units.
• Employ a recurrent architecture with measurement results feeding forward state propagation.
• Share parameters across time steps to maintain constant parameter count.
• Achieve constant circuit depth independent of input sequence length.

Experimental results

Research questions

• RQ1 Can QRU achieve competitive or superior performance to classical RNNs with a fixed, small parameter budget on NISQ devices?
• RQ2 Does QRU maintain constant circuit depth and parameter count as input sequences grow longer?
• RQ3 How does QRU perform on standard benchmarks (oscillatory prediction, breast cancer classification, MNIST) compared to larger classical networks?

Key findings

• In oscillatory prediction, a 72-parameter QRU matches a 197-parameter classical GRU.
• In Wisconsin Diagnostic Breast Cancer classification, 35 QRU parameters achieve 96.13% accuracy, comparable to a 167-parameter artificial NN.
• In MNIST recognition, 132 QRU parameters reach 98.05% accuracy, outperforming a 27,265-parameter convolutional NN.
• Across tasks, QRU delivers competitive or superior performance with substantially fewer parameters and constant depth.