Challenges in the Use of Quantum Computing Hardware-Efficient Ansa?tze in Electronic Structure Theory

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 Ansa''tze in variational quantum simulations of electronic structure. We illustrate that hardware efficient Ansa''tze may break Hamiltonian symmetries and yield nondifferentiable potential energy curves, in addition to the wellknown difficulty of optimizing variational parameters. We discuss the interplay between these limitations by carrying out a comparative analysis of hardware-efficient Ansa''tze 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 Ansa''tze.

Automated summary

In this paper, we discuss potential issues associated with using hardware-efficient Ansa''tze in variational quantum simulations of electronic structure, including breaking Hamiltonian symmetries, obtaining nondifferentiable potential energy curves, and the difficulty of optimizing variational parameters. By comparing with unitary coupled cluster and full configuration interaction, and different strategies to encode Fermionic degrees of freedom to qubits, we explore the interplay between these limitations. Our analysis provides insights into the potential limitations of hardware-efficient Ansa''tze and identifies possible areas for improvement.