  The quantum alternating operator ansatz (QAOA) is a prominent example of
variational quantum algorithms. We propose a generalized QAOA called CD-QAOA,
which is inspired by the counterdiabatic driving procedure, designed for
quantum many-body systems and optimized using a reinforcement learning (RL)
approach. The resulting hybrid control algorithm proves versatile in preparing
the ground state of quantum-chaotic many-body spin chains by minimizing the
energy. We show that using terms occurring in the adiabatic gauge potential as
generators of additional control unitaries, it is possible to achieve fast
high-fidelity many-body control away from the adiabatic regime. While each
unitary retains the conventional QAOA-intrinsic continuous control degree of
freedom such as the time duration, we consider the order of the multiple
available unitaries appearing in the control sequence as an additional discrete
optimization problem. Endowing the policy gradient algorithm with an
autoregressive deep learning architecture to capture causality, we train the RL
agent to construct optimal sequences of unitaries. The algorithm has no access
to the quantum state, and we find that the protocol learned on small systems
may generalize to larger systems. By scanning a range of protocol durations, we
present numerical evidence for a finite quantum speed limit in the
nonintegrable mixed-field spin-1/2 Ising and Lipkin-Meshkov-Glick models, and
for the suitability to prepare ground states of the spin-1 Heisenberg chain in
the long-range and topologically ordered parameter regimes. This work paves the
way to incorporate recent success from deep learning for the purpose of quantum
many-body control.
