Challenges in the Use of Quantum Computing Hardware-Efficient Ansätze in Electronic Structure Theory

Area of Science:

• Quantum computing
• Computational chemistry
• Electronic structure theory

Background:

• Heuristic quantum algorithms are advancing for electronic structure calculations.
• Characterizing performance and limitations of these methods is essential.
• Hardware-efficient Ansätze are commonly used in variational quantum simulations.

Purpose of the Study:

• To identify and discuss potential pitfalls of hardware-efficient Ansätze in variational quantum simulations.
• To analyze the interplay between different limitations of these Ansätze.
• To compare hardware-efficient Ansätze with established methods and quantization strategies.

Main Methods:

• Comparative analysis of hardware-efficient Ansätze against unitary coupled cluster and full configuration interaction.
• Evaluation of second- and first-quantization strategies for encoding fermionic degrees of freedom.
• Illustrating limitations such as Hamiltonian symmetry breaking and non-differentiable potential energy curves.

Main Results:

• Hardware-efficient Ansätze can inadvertently break Hamiltonian symmetries.
• These Ansätze may lead to non-differentiable potential energy curves, complicating optimization.
• The optimization of variational parameters remains a significant challenge.

Conclusions:

• Hardware-efficient Ansätze present specific limitations that must be addressed for reliable quantum simulations.
• Understanding these pitfalls is key to developing more robust and accurate quantum electronic structure algorithms.
• Further research is needed to improve the design and application of quantum algorithms for electronic structure problems.