  Variational methods offer a highly promising route to exploiting quantum
computers for chemistry tasks. Here we employ methods described in a sister
paper to the present report, entitled ab initio machine synthesis of quantum
circuits, in order to solve problems using adaptively evolving quantum
circuits. Consistent with prior authors we find that this approach can
outperform human-designed circuits such as the coupled-cluster or
hardware-efficient ans\"atze, and we make comparisons for larger instances up
to 14 qubits. Moreover we introduce a novel approach to constraining the
circuit evolution in the physically relevant subspace, finding that this
greatly improves performance and compactness of the circuits. We consider both
static and dynamics properties of molecular systems. The emulation environments
used is QuESTlink; all resources are open source and linked from this paper.
