Hybrid Quantum-Classical Recurrent Neural Networks

ICLR 2026 Conference Submission21275 Authors

Keywords: quantum computing, variational quantum models, parametrized quantum circuits, hybrid-quantum classical neural networks, recurrent neural netwroks

TL;DR: A hybrid quantum–classical RNN with a unitary PQC core and nonlinear classical control and feedback, achieving superior or competitive performance to strong classical baselines on six sequence tasks, with simulations up to 14 qubits.

Abstract: We present a new hybrid quantum-classical recurrent neural network (RNN) architecture in which the recurrent core is realized as a parametrized quantum circuit (PQC) controlled by a nonlinear classical feedforward network. The hidden state is the quantum state of the PQC, residing in an exponentially large Hilbert space $\mathbb{C}^{2^n}$ and manipulable using only $n$ qubits. The PQC is unitary by construction, making the hidden-state evolution inherently norm preserving without external constraints. To evolve the recurrence, classical embeddings of the current input are combined with mid-circuit readouts from the previous timestep’s quantum state and processed by a feedforward network. The resulting outputs parameterize the PQC, which then evolves unitarily to produce the updated hidden state. This enables per-timestep readouts while avoiding attempts to emulate nonlinearities with inherently linear quantum dynamics. We evaluate the model in simulation with up to 14 qubits on sentiment analysis, MNIST, permuted MNIST, copying memory, and language modeling, adopting projective measurements as a limiting case to obtain mid-circuit readouts while maintaining a coherent quantum memory across timesteps. We also devise a soft attention mechanism over readouts in a sequence-to-sequence model and show that the network is effective for machine translation. To our knowledge, this is the first model (RNN or otherwise) grounded in quantum operations to achieve superior or competitive performance against strong classical baselines across a broad class of sequence-learning tasks.

Primary Area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)

Submission Number: 21275