Toward Large-Scale Distributed Quantum Long Short-Term Memory with Modular Quantum Computers

In this work, we introduce a Distributed Quantum Long Short-Term Memory (QLSTM) framework that leverages modular quantum computing to address scalability challenges on Noisy Intermediate-Scale Quantum (NISQ) devices. By embedding variational quantum circuits into LSTM cells, the QLSTM captures long-range temporal dependencies, while a distributed architecture partitions the underlying Variational Quantum Circuits (VQCs) into smaller, manageable subcircuits that can be executed on a network of quantum processing units. We assess the proposed framework using nontrivial benchmark problems such as damped harmonic oscillators and Nonlinear Autoregressive Moving Average sequences. Our results demonstrate that the distributed QLSTM achieves stable convergence and improved training dynamics compared to classical approaches. This work underscores the potential of modular, distributed quantum computing architectures for large-scale sequence modelling, providing a foundation for the future integration of hybrid quantum-classical solutions into advanced Quantum High-performance computing (HPC) ecosystems.