Challenges in the use of quantum computing hardware-efficient Ansatze in electronic structure theory

TL;DR

This paper examines the limitations of hardware-efficient Ansatze in quantum algorithms for electronic structure, highlighting issues like symmetry breaking and optimization difficulties, and compares them with other encoding strategies.

Contribution

It provides a detailed analysis of the pitfalls of hardware-efficient Ansatze and compares their performance with unitary coupled cluster and full configuration interaction methods.

Findings

Hardware-efficient Ansatze can break Hamiltonian symmetries.

They may produce non-differentiable potential energy curves.

Optimization of variational parameters remains challenging.

Abstract

Advances in quantum computation for electronic structure, and particularly heuristic quantum algorithms, create an ongoing need to characterize the performance and limitations of these methods. Here we discuss some potential pitfalls connected with the use of hardware-efficient Ansatze in variational quantum simulations of electronic structure. We illustrate that hardware-efficient Ansatze may break Hamiltonian symmetries and yield non-differentiable potential energy curves, in addition to the well-known difficulty of optimizing variational parameters. We discuss the interplay between these limitations by carrying out a comparative analysis of hardware-efficient Ansatze versus unitary coupled cluster and full configuration interaction, and of second- and first-quantization strategies to encode fermionic degrees of freedom to qubits. Our analysis should be useful in understanding potential limitations and in identifying possible areas of improvement in hardware-efficient Ansatze.