Optimized Quantum Phase Estimation for Simulating Electronic States in Various Energy Regimes.

While quantum algorithms for simulations exhibit better asymptotic scaling than their classical counterparts, they currently cannot be accurately implemented on real-world devices. Instead, chemists and computer scientists rely on costly classical simulations of these quantum algorithms. In particular, the quantum phase estimation (QPE) algorithm is among several approaches that has attracted much attention in recent years due to its genuine quantum character. However, it is memory-intensive to simulate and intractable for moderate system sizes. This paper discusses the performance and applicability of QPESIM, a new simulation of the QPE algorithm designed to take advantage of modest computational resources. In particular, we demonstrate the versatility of QPESIM in simulating various electronic states by examining the ground and core-level states of HO. For these states, we also discuss the effect of the active-space size on the quality of the calculated energies. For the high-energy core-level states, we demonstrate that new QPE simulations for active spaces defined by 15 active orbitals significantly reduce the errors in core-level excitation energies compared to earlier QPE simulations using smaller active spaces.