  Recent developments in quantum computing and machine learning have propelled
the interdisciplinary study of quantum machine learning. Sequential modeling is
an important task with high scientific and commercial value. Existing VQC or
QNN-based methods require significant computational resources to perform the
gradient-based optimization of a larger number of quantum circuit parameters.
The major drawback is that such quantum gradient calculation requires a large
amount of circuit evaluation, posing challenges in current near-term quantum
hardware and simulation software. In this work, we approach sequential modeling
by applying a reservoir computing (RC) framework to quantum recurrent neural
networks (QRNN-RC) that are based on classical RNN, LSTM and GRU. The main idea
to this RC approach is that the QRNN with randomly initialized weights is
treated as a dynamical system and only the final classical linear layer is
trained. Our numerical simulations show that the QRNN-RC can reach results
comparable to fully trained QRNN models for several function approximation and
time series prediction tasks. Since the QRNN training complexity is
significantly reduced, the proposed model trains notably faster. In this work
we also compare to corresponding classical RNN-based RC implementations and
show that the quantum version learns faster by requiring fewer training epochs
in most cases. Our results demonstrate a new possibility to utilize quantum
neural network for sequential modeling with greater quantum hardware
efficiency, an important design consideration for noisy intermediate-scale
quantum (NISQ) computers.
