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Near-term quantum computers are expected to facilitate material and chemicalresearch through accurate molecular simulations. Several developments havealready shown that accurate ground-state energies for small molecules can beevaluated on present-day quantum devices. Although electronically excitedstates play a vital role in chemical processes and applications, the search fora reliable and practical approach for routine excited-state calculations onnear-term quantum devices is ongoing. Inspired by excited-state methodsdeveloped for the unitary coupled-cluster theory in quantum chemistry, wepresent an equation-of-motion-based method to compute excitation energiesfollowing the variational quantum eigensolver algorithm for ground-statecalculations on a quantum computer. We perform numerical simulations on H$_2$,H$_4$, H$_2$O, and LiH molecules to test our quantum self-consistentequation-of-motion (q-sc-EOM) method and compare it to other currentstate-of-the-art methods. q-sc-EOM makes use of self-consistent operators tosatisfy the vacuum annihilation condition, a critical property for accuratecalculations. It provides real and size-intensive energy differencescorresponding to vertical excitation energies, ionization potentials andelectron affinities. We also find that q-sc-EOM is more suitable forimplementation on NISQ devices as it is expected to be more resilient to noisecompared with the currently available methods.

Quantum self-consistent equation-of-motion method for computing  molecular excitation energies, ionization potentials, and electron affinities  on a quantum computer