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

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.

16 pages, 9 figures, supplemental information included as an ancillary file

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• Is the Trotterized UCCSD Ansatz chemically well-defined?
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• Simulation of a Diels-Alder Reaction on a Quantum Computer
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• Variational Quantum Subspace Construction via Symmetry-Preserving Cost Functions