Variational Quantum Eigensolver Mitigation Strategies, Tested on 14 Qubits, Demonstrate Improved Convergence with Pretrained Ansatz at 2.2x

Variational Quantum Eigensolver algorithms, a promising route to simulating molecular behaviour using quantum computers, frequently encounter barren plateaus, where the signal needed for computation vanishes as systems grow more complex. Mostafa Atallah from the University of Tennessee, Knoxville and Cairo University, alongside Nouhaila Innan and Muhammad Kashif from New York University Abu Dhabi, and Muhammad Shafique, now present a systematic investigation into strategies for overcoming this critical limitation. Their work clarifies how different mitigation techniques perform under varying computational constraints, revealing that simply preserving gradients is not enough to guarantee success. By benchmarking approaches such as Local-Global, Adiabatic, State Efficient Ansatz, and Pretrained methods on molecular systems containing up to 14 qubits, the team demonstrates that the optimal strategy depends on both the size of the problem and the number of computational steps available, achieving near-exact energies and high fidelities for smaller systems and offering crucial insights for scaling these algorithms to tackle more complex challenges. The study clarifies how different mitigation techniques perform under varying computational constraints, revealing that simply preserving gradients is not enough to guarantee success.

The team benchmarked four approaches: standard VQE, pretraining using classical machine learning, advanced parameter initialization, and a strategy focused on preserving gradients during optimization.

Results demonstrate that the effectiveness of each strategy depends on the size of the quantum system being simulated and the number of computational steps available. For smaller systems, all methods perform reasonably well, but for larger systems, gradient-preserving methods make meaningful progress.

This research reveals a crucial relationship between iteration budget and convergence success; pretraining is effective for early progress with limited computational resources, while maintaining gradients throughout the process is vital for long-term performance.,. Benchmarking VQE Mitigation Strategies for Molecular Systems The study addresses a critical challenge in variational quantum eigensolver (VQE) algorithms: the emergence of barren plateaus, where gradients vanish as system size and circuit depth increase. To systematically investigate mitigation strategies, scientists benchmarked four approaches, standard VQE, a pretraining method, and two techniques focused on gradient preservation, on molecular systems ranging from 4 to 14 qubits. The research involved constructing molecular Hamiltonians and preparing them for quantum computation using established methods. Experiments employed an optimization algorithm, iterating up to 1000times to minimize the energy expectation value. Scientists meticulously analyzed gradient statistics, scaling depth from 1 to 50 layers, and calculated gradient variance and norm to assess the robustness of each mitigation strategy.

Results demonstrate that the impact of gradient preservation is dependent on the number of iterations. For the 14-qubit BeH2 system, pretraining initially outperformed gradient preservation at 100 iterations, but gradient preservation achieved greater accuracy after 1000 iterations. For smaller systems, gradient preservation achieved near-exact energies and high fidelities, demonstrating its effectiveness with sufficient iterations. Researchers systematically benchmarked four mitigation strategies, standard VQE, a pretraining method, and two techniques focused on gradient preservation, using molecular systems ranging from 4 to 14 qubits and exploring circuit depths up to 50 layers. The study reveals a crucial iteration-dependent relationship between gradient preservation and convergence success. Initial optimization benefits from initialization quality, while long-term performance relies on maintaining gradients throughout the process. Experiments with the 14-qubit BeH2 molecule showed that pretraining outperformed gradient preservation at 100 iterations, but gradient preservation achieved greater accuracy after 1000 iterations. For smaller systems, gradient preservation achieved near-exact energies and high fidelities, significantly surpassing the performance of standard methods.

The team quantified performance using metrics such as energy error, state fidelity, and gradient variance, analyzing how these change with circuit depth. They discovered that the effectiveness of each mitigation strategy is not solely determined by gradient variance, but is strongly linked to both system size and the available computational budget. The results demonstrate that optimization performance is not solely determined by preserving gradients, but also depends critically on the available computational budget, specifically the number of iterations performed. For the 14-qubit BeH2 system, a pretraining approach initially outperformed gradient preservation, but gradient preservation ultimately achieved superior accuracy with extended optimization, highlighting the differing roles of initialization and gradient preservation. System size further influences effectiveness; all methods successfully solved the smallest system, H2, while gradient preservation achieved near-exact accuracy on LiH. Meaningful progress on the larger BeH2 system, however, was only possible with gradient-preserving methods. Gradient preservation consistently achieved the highest accuracy and fastest runtime overall, leading the researchers to recommend its use for iteration budgets exceeding 500. For limited budgets, the pretraining approach proved more effective on systems above 10 qubits, while standard VQE remains suitable only for very small systems. This work underscores the importance of jointly optimizing both the choice of mitigation strategy and the computational budget, rather than relying solely on metrics like gradient variance, to achieve effective results in VQE calculations. 👉 More information 🗞 Investigating Different Barren Plateaus Mitigation Strategies in Variational Quantum Eigensolver 🧠 ArXiv: https://arxiv.org/abs/2512.11171 Tags: