Emerging hybrid quantum-classical algorithms for quantum chemistry

Digital quantum computers provide a computational framework for solving the Schrodinger equation for a variety of many-particle systems. 

Quantum computing algorithms for the quantum simulation of these systems have recently witnessed remarkable growth, especially as a tool for electronic structure computations in molecules [1]. The limitations of existing quantum hardware have led to the conception of hybrid quantum-classical algorithms, which combine classical and quantum computing resources to approximately describe quantum correlations in many-particle systems.

As an illustrative application, we present the classical entanglement forging method [2], derived and implemented to perform quantum simulation of electronic problems.

Theoretical foundations and conditions for applicability of hybrid quantum-classical algorithms are discussed, and their strengths, limitations, and advances towards larger and more complex problems are presented.

[1] M. Motta and J. Rice, arXiv:2109.02873 (2021)

[2] A. Eddins et al, arXiv:2104.10220 (2021)