  Any quantum program on a realistic quantum device must be compiled into an
executable form while taking into account the underlying hardware constraints.
Stringent restrictions on architecture and control imposed by physical
platforms make this very challenging. In this paper, based on the quantum
variational algorithm, we propose a novel scheme to train an Ansatz circuit and
realize high-fidelity compilation of a set of universal quantum gates for
singlet-triplet qubits in semiconductor double quantum dots, a fairly heavily
constrained system. Furthermore, we propose a scalable architecture for a
modular implementation of quantum programs in this constrained systems and
validate its performance with two representative demonstrations, Grover's
algorithm for the database searching (static compilation) and a variant of
variational quantum eigensolver for the Max-Cut optimization (dynamic
compilation). Our methods are potentially applicable to a wide range of
physical devices. This work constitutes an important stepping-stone for
exploiting the potential for advanced and complicated quantum algorithms on
near-term devices.
