Quantum Computing for Chemistry Beyond Toy Molecules: Error Mitigation, Excited States, and Embedding Methods

Abstract

Quantum computing offers a transformative approach to computational chemistry, promising to simulate molecular systems with accuracy unattainable by classical methods. This article provides a comprehensive examination of the current state and future trajectory of quantum chemistry simulations, focusing on the critical transition from demonstrating basic quantum algorithms to achieving chemically meaningful results on complex molecular systems. We analyse three interconnected research frontiers essential for this transition: advanced error mitigation strategies including Zero-Noise Extrapolation (ZNE), Probabilistic Error Cancellation (PEC), and symmetry verification; algorithms for computing excited states and molecular dynamics; and embedding techniques such as Density Matrix Embedding Theory (DMET) and DFT embedding.