Accurate quantum chemistry calculations using NISQ era quantum computers

Accurate quantum simulation of molecular excited states is necessary to realize the quantum advantage in describing complex chemical phenomena. In this regard, we have developed an equation of motion (EOM) based quantum algorithm which is theoretically rigorous, requires fewer quantum resources and is expected to be more robust to noise than the current state-of-the art methods We demonstrate the usefulness of our approach by calculating ionization potentials, electron affinities and excitation energies of small molecular systems. Based on the insights developed from the EOM work, we recently developed an efficient quantum version of linear response theory (qLR) to calculate response properties like polarizabilities, specific rotation, etc. We illustrate the advantages associated with qLR theory by comparing it against the classical approaches. However, a quantitative description of these properties requires large number of basis functions or qubits. This is clearly a major bottleneck due to the limited qubit connectivity, short coherence times and sizable gate error rates associated with the contemporary quantum hardware. To overcome this, we have developed a transcorrelated Hamiltonian approach where we downfold the effects of a large basis set into a Hamiltonian in the space of a much smaller basis set. Thus, the transcorrelated Hamiltonian can provide desired quantitative accuracies with a much smaller Hilbert space, resulting in a massive reduction in the required quantum resources.