  Quantum computing promises to provide machine learning with computational
advantages. However, noisy intermediate-scale quantum (NISQ) devices pose
engineering challenges to realizing quantum machine learning (QML) advantages.
Recently, a series of QML computational models inspired by the noise-tolerant
dynamics on the brain have emerged as a means to circumvent the hardware
limitations of NISQ devices. In this article, we introduce a quantum version of
a recurrent neural network (RNN), a well-known model for neural circuits in the
brain. Our quantum RNN (qRNN) makes use of the natural Hamiltonian dynamics of
an ensemble of interacting spin-1/2 particles as a means for computation. In
the limit where the Hamiltonian is diagonal, the qRNN recovers the dynamics of
the classical version. Beyond this limit, we observe that the quantum dynamics
of the qRNN provide it quantum computational features that can aid it in
computation. To this end, we study a qRNN based on arrays of Rydberg atoms, and
show that the qRNN is indeed capable of replicating the learning of several
cognitive tasks such as multitasking, decision making, and long-term memory by
taking advantage of several key features of this platform such as interatomic
species interactions, and quantum many-body scars.
