  We show that currently available noisy intermediate-scale quantum (NISQ)
computers can be used for versatile quantum simulations of chaotic systems. We
introduce a novel classical-quantum hybrid approachfor exploring the dynamics
of the chaotic quantum kicked top (QKT) on a universal quantum computer. The
programmability of this approach allows us to experimentally explore the
complete range of QKT chaoticity parameter regimes inaccessible to previous
studies. Furthermore, the number of gates in our simulation does not increase
with the number of kicks, thus making it possible to study the QKT evolution
for arbitrary number of kicks without fidelity loss. Using a publicly
accessible NISQ computer (IBMQ), we observe periodicities in the evolution of
the 2-qubit QKT, as well as signatures of chaos in the time-averaged 2-qubit
entanglement. We also demonstrate a connection between entanglement and
delocalization in the 2-qubit QKT, confirming theoretical predictions.
