Quantum computing has the potential to significantly impact the field of chemistry by solving problems beyond the reach of classical computers. However, identifying high-utility problem instances and estimating the timeline for practical quantum applications remains challenging. This talk reports on recent progress in anticipating the first useful quantum computations and the software tools aiding this exploration. The variational quantum eigensolver (VQE) algorithm has been considered a candidate for the first useful quantum algorithm for quantum chemistry. Unfortunately, mounting evidence points to the inadequacy of VQE for estimating ground state energies of molecules. In light of these findings, we will introduce a collection of recently developed quantum algorithms designed for early fault-tolerant quantum computers. I will contextualize these algorithms along the spectrum of near-term (variational quantum eigensolver) to far-term (quantum phase estimation), highlighting their capabilities and limitations. Finally, I will present resource estimates for running these algorithms on superconducting qubits and ion trap systems and discuss the implications for the development of quantum algorithms and quantum hardware towards tackling challenges in quantum chemistry.
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