  The development of tailored materials for specific applications is an active
field of research in chemistry, material science and drug discovery. The number
of possible molecules that can be obtained from a set of atomic species grow
exponentially with the size of the system, limiting the efficiency of classical
sampling algorithms. On the other hand, quantum computers can provide an
efficient solution to the sampling of the chemical compound space for the
optimization of a given molecular property. In this work we propose a quantum
algorithm for addressing the material design problem with a favourable scaling.
The core of this approach is the representation of the space of candidate
structures as a linear superposition of all possible atomic compositions. The
corresponding `alchemical' Hamiltonian drives then the optimization in both the
atomic and electronic spaces leading to the selection of the best fitting
molecule, which optimizes a given property of the system, e.g., the interaction
with an external potential in drug design. The quantum advantage resides in the
efficient calculation of the electronic structure properties together with the
sampling of the exponentially large chemical compound space. We demonstrate
both in simulations and in IBM Quantum hardware the efficiency of our scheme
and highlight the results in a few test cases. These preliminary results can
serve as a basis for the development of further material design quantum
algorithms for near-term quantum computers.
