  Development of quantum architectures during the last decade has inspired
hybrid classical-quantum algorithms in physics and quantum chemistry that
promise simulations of fermionic systems beyond the capability of modern
classical computers, even before the era of quantum computing fully arrives.
Strong research efforts have been recently made to obtain minimal depth quantum
circuits which could accurately represent chemical systems. Here, we show that
unprecedented methods used in quantum chemistry, designed to simulate molecules
on quantum processors, can be extended to calculate properties of periodic
solids. In particular, we present minimal depth circuits implementing the
variational quantum eigensolver algorithm and successfully use it to compute
the band structure of silicon on a quantum machine for the first time. We are
convinced that the presented quantum experiments performed on cloud-based
platforms will stimulate more intense studies towards scalable electronic
structure computation of advanced quantum materials.
