[Paper Review] Benchmarking Variational Quantum Eigensolvers for Quantum Chemistry

Jiaqi Hu, Junning Li+7 more|arXiv (Cornell University)|Nov 23, 2022

Quantum Computing Algorithms and Architecture4 citations

TL;DR

This paper benchmarks 12 variational quantum eigensolver (VQE) ansatzes for quantum chemistry simulations across molecules from H₄ to N₂ (up to 30 qubits), evaluating energy accuracy, convergence runtime, and parameter count. The ADAPT ansatz achieves superior accuracy for small systems (<14 qubits), but UCCSD0 shows better performance and scalability for larger molecules; all ansatzes fail to reach chemical accuracy at stretched bond lengths.

ABSTRACT

Quantum chemistry is one of the most promising applications of quantum computers in the near future. For noisy intermediate-scale quantum devices, the quantum-classical hybrid framework based on the variational quantum eigensolver (VQE) has become the method of choice. In the literature, there are many different variants of VQE, but it is not known which one is optimal for a given molecule. For this purpose, we perform a thorough benchmarking on more than ten different kinds of VQE ansatzes (in systems up to 30 qubits), based on their performance on the energy accuracy, runtime until convergence, and number of parameters. Our results show that the ADAPT ansatz can be used to obtain more accurate energy for small systems (below 14 qubits), but it costs much more computational resources. For larger molecules, UCCSD0 has better performance. However, all the tested ansatzes can hardly reach chemical accuracy at stretched bond lengths. Our results were obtained using MindSpore Quantum, where the codes and the benchmarking toolkit are publicly available at Gitee.

Motivation & Objective

• To evaluate and compare the performance of multiple VQE ansatzes for quantum chemistry simulations on near-term quantum devices.
• To identify the most effective ansatz for different molecular systems based on energy accuracy, convergence speed, and parameter efficiency.
• To develop and release a reproducible benchmarking toolkit for VQE ansatz comparison using the MindSpore Quantum framework.
• To assess the scalability and limitations of VQE ansatzes, particularly at stretched bond lengths where performance degrades.
• To provide practical guidance for researchers selecting ansatzes based on system size and desired accuracy.

Proposed method

• Implemented and reproduced 12 VQE ansatzes, including fixed-circuit (UCCSD, HEA, LDCA) and adaptive (ADAPT, qubit-ADAPT) variants, using the MindSpore Quantum framework.
• Performed simulations on molecules H₄, LiH, BeH₂, H₂O, CH₄, and N₂ in the STO-3G basis set, varying bond lengths to test robustness.
• Used a hybrid quantum-classical optimization loop: quantum circuits prepare variational states, classical optimizers (e.g., SPSA) update parameters based on measured energy.
• Applied Trotterization to decompose time-evolution operators and mapped electronic Hamiltonians to qubit Hamiltonians via Jordan-Wigner or Bravyi-Kitaev transformations.
• Developed a benchmarking toolkit to record and compare energy error, convergence runtime, and number of parameters across all ansatzes.
• Conducted large-scale simulations up to 30 qubits (CO₂), achieving chemical accuracy at 41 iterations with SymUCCSD ansatz.

Experimental results

Research questions

• RQ1 Which VQE ansatz delivers the highest energy accuracy for small molecular systems (≤14 qubits) and larger systems (>14 qubits)?
• RQ2 How do convergence runtime and number of parameters vary across different ansatz types, and what trade-offs exist?
• RQ3 Can any ansatz consistently achieve chemical accuracy across all bond lengths, including stretched geometries?
• RQ4 How does the performance of adaptive ansatzes (e.g., ADAPT) scale with system size compared to fixed-circuit ansatzes?
• RQ5 What are the practical implications of these benchmarking results for selecting ansatzes in real-world quantum chemistry applications?

Key findings

• ADAPT achieves the highest energy accuracy for small molecules (e.g., H₄, BeH₂, H₂O) below 14 qubits, but requires significantly more computational resources.
• For larger molecules (e.g., CH₄, N₂), UCCSD0 outperforms other ansatzes in energy accuracy and is more scalable than ADAPT.
• All tested ansatzes fail to reach chemical accuracy at stretched bond lengths, indicating a critical limitation in current VQE implementations.
• UCCSD0 and QUCC ansatzes consistently deliver more accurate energies than other fixed-circuit ansatzes, with UCCSD0 being more accurate for larger systems.
• Adaptive ansatzes (ADAPT, qubit-ADAPT) use fewer parameters and shallower circuits than fixed-circuit ansatzes, but require longer classical optimization times.
• The benchmarking toolkit enabled large-scale simulations up to 30 qubits (CO₂), with SymUCCSD reaching chemical accuracy in 41 iterations—among the largest such simulations reported.