Modified EMICoRe Eigensolver Improves Variational Quantum Eigensolver Performance

Bayesian optimisation offers a powerful approach to tuning the complex parameters within variational quantum circuits, but current methods can struggle with the inherent noise in predicting energy levels. Shreyas Dillon and Nicoli, working independently, present a refinement to a leading technique called the Expected Maximum Improvement over Confident Regions (EMICoRe) eigensolver. Their work introduces a new, more adaptable threshold for identifying promising regions of parameter space, one that considers both the uncertainty in predictions and how quickly those predictions change. This adjustment addresses a key limitation of the original method, allowing for more effective exploration and ultimately achieving improved accuracy in approximating the ground state energy of complex systems, demonstrated through benchmarks using the Ising Hamiltonian and similar models. The research paves the way for more robust and efficient optimisation of quantum circuits, potentially accelerating progress in quantum computation and materials science.

The team introduces a new threshold for defining a ‘Confident Region’ within the algorithm, basing it on both the uncertainty in initial predictions and the subsequent change in predicted energy. This modified threshold aims to improve the efficiency and robustness of Bayesian optimization for variational quantum circuits.

The new approach considers the Gaussian process prior variance and how the predicted energy changes over iterations, creating a more lenient threshold for the Confident Region. This allows for natural fluctuations in predicted energy, which the original EMI-CoRe method might incorrectly penalize. Testing with the Ising Hamiltonian demonstrates that this alternative threshold achieves comparable, and in some cases improved, performance over the original EMI-CoRe method.

PEDT Optimizes Variational Quantum Algorithms Effectively

Variational Quantum Algorithms (VQAs) offer a promising approach to solving complex problems by combining quantum and classical computation. However, these algorithms often face challenges like barren plateaus and getting trapped in suboptimal solutions, requiring efficient optimization techniques. This research introduces PEDT, which stands for Parameter Exploration with Defined Threshold, a new Bayesian Optimization algorithm designed to improve the exploration-exploitation trade-off in VQA optimization.

PEDT uses a Confident Region to focus exploration on promising areas of the parameter space while avoiding regions with high uncertainty. The key innovation lies in the threshold that determines the size and inclusivity of this region. The team demonstrates that PEDT consistently outperforms an existing algorithm when optimizing the 10-qubit Ising Hamiltonian problem. A crucial finding is that the choice of the threshold parameter is vital; a threshold that is too strict limits exploration, while one that is too lenient introduces noise. The team introduced a modified threshold for identifying a ‘Confident Region’ within the algorithm, basing this new threshold on both the initial uncertainty in predictions and the subsequent change in predicted energy. This adaptive threshold aims to improve the efficiency and robustness of the algorithm.

Results demonstrate that this alternative threshold achieves comparable, and in some cases improved, performance over the original EMICoRe method when applied to the Ising Hamiltonian. The study highlights the potential for further optimization within this new threshold framework, noting several adjustable parameters that could lead to even greater improvements, particularly when applied to more complex systems. Future work should explore the algorithm’s performance on systems beyond the Ising Hamiltonian to assess its broader robustness and applicability, paving the way for practical quantum solutions in fields like quantum chemistry and materials science.