  Band structure is a cornerstone to understand electronic properties of
materials. Accurate band structure calculations using a high-level
quantum-chemistry theory can be computationally very expensive. It is promising
to speed up such calculations with a quantum computer. In this study, we
present a quantum algorithm for band structure calculation based on the
equation-of-motion (EOM) theory. First, we introduce a new variational quantum
eigensolver algorithm named ADAPT-C for ground-state quantum simulation of
solids, where the wave function is built adaptively from a complete set of
anti-Hermitian operators. Then, on top of the ADAPT-C ground state,
quasiparticle energies and the band structure can be calculated using the EOM
theory in a quantum-subspace-expansion (QSE) style, where the projected
excitation operators guarantee that the killer condition is satisfied. As a
proof of principle, such an EOM-ADAPT-C protocol is used to calculate the band
structures of silicon and diamond using a quantum computer simulator.
