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With the advent of near-term quantum computers, it is now possible to simulate solid-state properties using quantum algorithms. By an adequate description of the system's Hamiltonian, variational methods enable to fetch of the band structure and other fundamental properties as transition probabilities. Here, we describe semiconductor structures of the III-V family using k·p Hamiltonians and obtain their band structures using a state vector solver, a probabilistic simulator, and a real noisy-device simulator. The resulting band structures are in good agreement with those obtained by direct diagonalization of the Hamiltonian. The simulation times depend on the optimizer, circuit depth, and simulator used. Finally, with the optimized eigenstates, we convey the inter-band absorption probability, demonstrating the possibility of analyzing the fundamental properties of crystalline systems using quantum computers.