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Expressibility and Trainability Analysis of Hardware-Efficient Ansatz Variants in Variational Quantum Eigensolver
Rasyid Ustman Ramadhan1,2, Luthfiya Kurnia Permatahati3,2, Teguh Budi Prayitno1
1Department of Physics, Faculty of Mathematics and Natural Science, Jakarta State University, East Jakarta 13220, Indonesia.
The Journal of Physical Chemistry. A
|April 3, 2026
Summary
Selecting the right hardware-efficient ansatz (HEA) is crucial for variational quantum eigensolver (VQE) performance. Some HEAs offer high expressibility but risk barren plateaus, while complex ansatzes ensure stable optimization.
Area of Science:
- Quantum Computing
- Computational Chemistry
- Algorithm Analysis
Background:
- The Variational Quantum Eigensolver (VQE) is a leading hybrid quantum-classical algorithm for near-term quantum devices.
- Hardware-Efficient Ansatz (HEA) design is critical for VQE performance, influencing expressibility and trainability.
- Barren plateaus, characterized by vanishing gradients, pose a significant challenge to VQE optimization.
Purpose of the Study:
- To analyze the expressibility and gradient distribution of nine HEAs within the VQE framework.
- To evaluate the impact of ansatz structure on optimization performance and barren plateau susceptibility.
- To identify optimal ansatz choices for VQE implementations based on expressibility-trainability trade-offs.
Main Methods:
- Utilized Kullback-Leibler divergence (DKL) to quantify ansatz expressibility.
- Measured gradient variance to assess barren plateau phenomena.
- Employed the L-BFGS optimization algorithm for parameter updates in a hydrogen molecular system.
Main Results:
- Ansatzes like SRy, TRy, RyRx, and RyRz showed high expressibility but suffered from low gradient variance, indicating barren plateau issues.
- More complex ansatzes (HRy, Ry, XRy) demonstrated stable gradient distributions and consistent optimization performance.
- Findings align with the linear mixing expressibility-trainability model, highlighting that increased expressibility doesn't guarantee easier optimization.
Conclusions:
- The choice of HEA significantly impacts VQE optimization performance and barren plateau risk.
- Complex ansatzes with mixed rotation bases offer better trainability and more reliable optimization.
- This study provides a foundation for selecting effective ansatzes to enhance future variational quantum algorithm implementations.
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