Chemical applications of variational quantum eigenvalue-based quantum algorithms: Perspective and survey

Abstract

Exploring many-body chemical systems on classical computers often involves solving the Schrödinger equation. However, this approach is frequently limited by the exponential increase in the dimensionality of the Hamiltonian as the number of degrees of freedom increases. In contrast, quantum computing, specifically through the variational quantum eigensolver (VQE) framework, shows promise in overcoming this exponential cost. VQE can utilize the collective properties of quantum states to model the wavefunction in polynomial time. Despite the current limitations of quantum hardware, significant advances have been made in the development of VQE-based algorithms. In this review, we provide an overview of emerging protocols, focusing on their applications in simulating the ground state, excited state, and vibrational properties of chemical systems. By examining notable algorithmic advancements and applications, this review aims to shed light on the challenges and potential of VQE-based algorithms in addressing relevant chemical problems.