Robustness of excited-state methods to sampling errors in quantum computers

Molecular excited state calculations are essential to model many chemical processes and applications, including those in spectroscopy, photochemistry and photophysics. Several algorithms have been proposed for accurate excited-state calculations using quantum computers, where subspace diagonalization-based Quantum Subspace Expansion (QSE), Quantum Equation-Of-Motion (qEOM) and Quantum Self-Consistent Equation-Of-Motion (q-sc-EOM) have shown promise. However, when we take into consideration practical factors like statistical sampling errors inherent in quantum mechanics and gate noise, the eigenstates can be affected greatly. This study explores the impact of sampling errors on excited states using state-of-the-art diagonalization-based molecular excited-state methods and finds that q-sc-EOM is the preferred choice in practical scenarios. In this talk, we will point out the difficulties brought by sampling errors in quantum algorithms and affirm the robustness of the q-sc-EOM method for molecular excited state calculations.