  Adaptive gating plays a key role in temporal data processing via classical
recurrent neural networks (RNN), as it facilitates retention of past
information necessary to predict the future, providing a mechanism that
preserves invariance to time warping transformations. This paper builds on
quantum recurrent neural networks (QRNNs), a dynamic model with quantum memory,
to introduce a novel class of temporal data processing quantum models that
preserve invariance to time-warping transformations of the (classical)
input-output sequences. The model, referred to as time warping-invariant QRNN
(TWI-QRNN), augments a QRNN with a quantum-classical adaptive gating mechanism
that chooses whether to apply a parameterized unitary transformation at each
time step as a function of the past samples of the input sequence via a
classical recurrent model. The TWI-QRNN model class is derived from first
principles, and its capacity to successfully implement time-warping
transformations is experimentally demonstrated on examples with classical or
quantum dynamics.
