  Despite remarkable successes in solving various complex decision-making
tasks, training an imitation learning (IL) algorithm with deep neural networks
(DNNs) suffers from the high computation burden. In this work, we propose
quantum imitation learning (QIL) with a hope to utilize quantum advantage to
speed up IL. Concretely, we develop two QIL algorithms, quantum behavioural
cloning (Q-BC) and quantum generative adversarial imitation learning (Q-GAIL).
Q-BC is trained with a negative log-likelihood loss in an off-line manner that
suits extensive expert data cases, whereas Q-GAIL works in an inverse
reinforcement learning scheme, which is on-line and on-policy that is suitable
for limited expert data cases. For both QIL algorithms, we adopt variational
quantum circuits (VQCs) in place of DNNs for representing policies, which are
modified with data re-uploading and scaling parameters to enhance the
expressivity. We first encode classical data into quantum states as inputs,
then perform VQCs, and finally measure quantum outputs to obtain control
signals of agents. Experiment results demonstrate that both Q-BC and Q-GAIL can
achieve comparable performance compared to classical counterparts, with the
potential of quantum speed-up. To our knowledge, we are the first to propose
the concept of QIL and conduct pilot studies, which paves the way for the
quantum era.
