Equi-ensemble Description Systematically Outperforms Weighted-ensemble Variational Quantum Eigensolver for Excited-State Calculations

Understanding the excited states of molecules is fundamental to advancing fields like spectroscopy, materials science, and pharmaceutical design, yet accurately calculating these states remains a significant challenge. Akilan Rajamani, Martin Beseda, Benjamin Lasorne, and colleagues at institutions including the Université de Montpellier and the Università dell’Aquila now demonstrate a substantial improvement in calculating excited states using quantum computers. The team rigorously compares two approaches to the ensemble variational eigensolver, a promising quantum algorithm, and establishes that an ‘equi-ensemble’ method consistently outperforms its weighted counterpart. This achievement represents a key step towards more efficient and accurate quantum simulations of molecular behaviour, potentially accelerating the discovery of new materials and drugs.

Equi-Weighted Versus Weighted VQE Ensembles

Scientists investigated different strategies within the Variational Quantum Eigensolver (VQE) algorithm for solving complex problems in Quantum Density Functional Theory (QDFT). The research compares an equi-ensemble VQE, where all states in the ensemble are weighted equally, with a weighted ensemble VQE, where states receive different weights, aiming to identify a more robust and accurate approach for determining the ground state energy of molecules. Researchers applied this method to a simplified, one-dimensional model system to focus on the algorithmic comparison, performing extensive statistical analysis to ensure observed differences were significant. The primary metric for assessing accuracy was the error in the trace of the density matrix.

The results consistently demonstrate that the equi-ensemble VQE outperforms the weighted-ensemble VQE in terms of accuracy, even as the distance between atoms increases. The equi-ensemble VQE proves more robust, less prone to getting trapped in suboptimal solutions, suggesting that optimizing the weights in a weighted ensemble is unnecessary and adds computational cost. Improved accuracy from the equi-ensemble VQE can lead to more reliable predictions of molecular properties and a better understanding of chemical systems, suggesting it is a promising approach for near-term quantum computers.

Equi-ensemble VQE for Excited State Calculations

Scientists developed a novel approach for calculating excited states in quantum systems, crucial for advancements in spectroscopy, materials science, and drug design. This work compares the equi-ensemble and weighted-ensemble approaches within the ensemble variational eigensolver (VQE), ultimately demonstrating the superiority of the equi-ensemble method. Researchers pioneered a generalized variational principle for many-body excited states, adapting the state-average MCSCF method into a state-average orbital-optimized VQE that minimizes ensemble energy. Experiments employed parameterized quantum circuits to approximate solutions to the diagonalization problem inherent in calculating excited states, exploring the impact of weighting schemes on convergence.

Results demonstrate that the equi-ensemble method consistently outperforms the weighted-ensemble approach, particularly in quantum chemistry simulations. Imposing descending weights introduces unnecessary complexity and often prevents convergence, while the equi-ensemble method converges to an optimal subspace, delivering mutually rotated versions of the targeted eigenstates, invariant to rotations within that subspace. This circumvents the need for accurate initial guesses regarding eigenenergy order, providing a robust pathway to obtaining reliable excited-state properties.

Equi-ensemble VQE Converges Faster, More Reliably

Scientists achieved a breakthrough in calculating excited states for molecular systems, crucial for advancements in spectroscopy, materials science, and drug design. This work focuses on the ensemble variational eigensolver (VQE) method, comparing equi-ensemble and weighted-ensemble approaches, and demonstrates the superior performance of the equi-ensemble method. Researchers discovered that imposing ordered weights on the ensemble generally hinders convergence towards the correct lowest energy states. Experiments revealed that the equi-ensemble approach converges to the optimal subspace, even if the resulting states are rotated versions of the true eigenstates, allowing for efficient calculation of the ensemble energy without pinpointing the exact individual eigenstates. In contrast, weighted-ensemble approaches often fail to converge when the initial weight order does not match the actual energy order of the final states. To assess these findings, scientists studied a two-state model of the formaldimine molecule and an eight-state one-body problem derived from quantum density functional theory, confirming that the equi-ensemble method provides a more robust and reliable pathway for calculating excited states.

Equi-ensemble VQE Accurately Calculates Excited States

This research presents a significant advancement in calculating excited states, crucial for understanding molecular behaviour and driving innovation in fields like spectroscopy and materials science. Scientists developed and compared two approaches within an ensemble variational eigensolver (VQE) framework, an equi-ensemble method and a weighted-ensemble method, to determine the most effective strategy for accurately determining these excited states. Results demonstrate that the equi-ensemble approach consistently outperforms the weighted-ensemble method, achieving more reliable convergence towards the correct energy levels. The team applied this improved method to an ensemble of states representing a chain of hydrogen atoms, successfully calculating the energies of these states with greater accuracy, representing a valuable tool for researchers seeking to model and understand the behaviour of molecules beyond their ground state.