  We present a quantum-classical hybrid algorithm that simulates electronic
structures of periodic systems such as ground states and quasiparticle band
structures. By extending the unitary coupled cluster (UCC) theory to describe
crystals in arbitrary dimensions, for a hydrogen chain, we numerically
demonstrate that the UCC ansatz implemented on a quantum circuit can be
successfully optimized with a small deviation from the exact diagonalization
over the entire range of the potential energy curves. Furthermore, by using the
quantum subspace expansion method, in which we truncate the Hilbert space
within the linear response regime from the ground state, the quasiparticle band
structure is computed as charged excited states. Our work establishes a
powerful interface between the rapidly developing quantum technology and modern
material science.
