  The architecture of circuital quantum computers requires computing layers
devoted to compiling high-level quantum algorithms into lower-level circuits of
quantum gates. The general problem of quantum compiling is to approximate any
unitary transformation that describes the quantum computation, as a sequence of
elements selected from a finite base of universal quantum gates. The existence
of an approximating sequence of one qubit quantum gates is guaranteed by the
Solovay-Kitaev theorem, which implies sub-optimal algorithms to establish it
explicitly. Since a unitary transformation may require significantly different
gate sequences, depending on the base considered, such a problem is of great
complexity and does not admit an efficient approximating algorithm. Therefore,
traditional approaches are time-consuming tasks, unsuitable to be employed
during quantum computation. We exploit the deep reinforcement learning method
as an alternative strategy, which has a significantly different trade-off
between search time and exploitation time. Deep reinforcement learning allows
creating single-qubit operations in real time, after an arbitrary long training
period during which a strategy for creating sequences to approximate unitary
operators is built. The deep reinforcement learning based compiling method
allows for fast computation times, which could in principle be exploited for
real-time quantum compiling.
