Quantum computers promise to dramatically advance our understanding of new materials and novel chemistry. Unfortunately, many proposed algorithms have resource requirements not yet suitable for near-term quantum devices. In this talk I will focus on the application of quantum computers to hard problems in the application area of chemistry and materials, and discuss the challenges and opportunities related to current algorithms. One particular method of interest to overcome quantum resource requirements is the variational quantum eigensolver (VQE), a recently proposed hybrid quantum-classical method for solving eigenvalue problems and more generic optimizations on a quantum device leveraging classical resources to minimize coherence time requirements. I will briefly review the original VQE approach and introduce a simple extension requiring no additional coherence time to approximate excited states. Moreover, we show that this approach offers a new avenue towards mitigation of decoherence in quantum simulation requiring no additional coherence time beyond the original algorithm and utilizing no formal error correction codes.