Quantum Computation of Molecules Benefits from Improved Initial State Preparation.

Researchers demonstrate an algorithm to efficiently prepare initial states for quantum computation of strongly correlated molecules, notably iron-sulfur clusters. Employing entanglement-minimised orbitals with spin-adapted matrix product states improves initial state overlap by up to two orders of magnitude, reducing computational resource requirements for complex systems like nitrogenase.

The accurate simulation of molecular behaviour remains a substantial challenge for computational chemistry, particularly when dealing with strongly correlated systems exhibiting complex electronic structures. Current quantum algorithms, such as phase estimation, promise accelerated calculations, but their efficiency hinges on the precise preparation of an initial quantum state closely resembling the molecule’s true ground state. Researchers now demonstrate a method to optimise this initial state preparation, significantly reducing the computational resources required for simulating complex molecules. Zhendong Li, from the Key Laboratory of Theoretical and Computational Photochemistry at Beijing Normal University, and colleagues, detail their approach in the article, “Entanglement-minimized orbitals enable faster quantum simulation of molecules”, where they present an algorithm to identify ‘entanglement-minimized orbitals’ (EMOs). These EMOs, generated using spin-adapted matrix product states (MPS), provide a more compact representation of the ground state, improving initial state overlap and scalability for systems including iron-sulfur clusters and the complex catalytic centres found in nitrogenase.

Simulations reveal that entanglement-optimized orbitals (EMOs) substantially improve the efficiency of density matrix renormalization group (DMRG) calculations, particularly for strongly correlated systems. Researchers consistently achieve higher wavefunction purity, quantified by the p0 metric, when employing EMOs compared to calculations utilising either site basis or natural orbitals (NOs). Wavefunction purity, in this context, indicates how closely the calculated wavefunction approximates the true ground state of the system. This enhancement in purity translates to a more accurate representation of the ground state and facilitates faster convergence of calculations, establishing EMOs as a powerful tool for computational physics and chemistry.

The observed superiority of EMOs stems from their design, which explicitly minimises entanglement within the wavefunction, thereby reducing the computational burden on the DMRG algorithm. DMRG is a numerical method used to find the ground state of quantum many-body systems, and its efficiency is heavily influenced by the choice of orbital basis. By lessening the demands on computational resources, researchers achieve more efficient calculations and improved accuracy, surpassing the performance of traditional orbital bases.

Specifically, research highlights a near order of magnitude improvement in wavefunction purity when using EMOs compared to NOs for the investigated four-site Hubbard model, demonstrating a significant advancement in computational methodology. This advantage extends to more complex systems, such as iron-sulfur clusters, where EMOs yield substantial enhancements in initial state overlap, crucial for quantum computation algorithms like phase estimation. Improvements of factors of 10 and 20 were achieved for iron-sulfur clusters with four and eight iron centres respectively, when compared to calculations employing localized orbitals, solidifying their impact on quantum simulations.

Researchers developed an efficient classical algorithm to generate EMOs using spin-adapted matrix product states (MPS) with small bond dimensions, addressing a critical bottleneck in quantum computation. MPS are a representation of the wavefunction that allows for efficient calculations of properties of the system. This algorithm eases the difficulty of preparing an initial state with high overlap with the true ground state, enabling more accurate and efficient quantum simulations. By providing a means to generate a more compact ground-state representation, the algorithm significantly reduces the demands on initial state preparation, paving the way for more complex computations.

Investigations demonstrate EMOs consistently outperform both site basis and natural orbitals in achieving higher p0 values and lower energies, establishing their effectiveness in representing complex quantum systems.

Researchers attribute the suboptimal performance of natural orbitals to their delocalized nature, suggesting a more localized basis set, such as that provided by EMOs, is better suited to capturing the essential physics within the DMRG framework. Quantitative results demonstrate the magnitude of these improvements, with EMOs achieving a p0 of approximately 8 x 10^-6 for CSF at D=6000, while natural orbitals reach 3 x 10^-6 and the site basis performs even lower. These values directly quantify the efficiency with which each orbital basis represents the wavefunction, highlighting the superior performance of EMOs.

This work demonstrates employing explicitly maximized orbitals significantly enhances the efficiency of DMRG calculations, achieving a higher p0 with a smaller bond dimension. Fewer states require retention, reducing computational cost and enabling more accurate results, establishing EMOs as a valuable technique for improving performance across a wide range of systems. The findings underscore the critical importance of orbital basis selection for DMRG calculations, solidifying EMOs as a powerful tool for computational scientists.

Future research will focus on extending the EMO algorithm to even larger and more complex systems, exploring its potential for applications in materials science, chemistry, and condensed matter physics. Researchers also plan to investigate the use of EMOs in conjunction with other advanced computational techniques, such as machine learning, to further enhance the accuracy and efficiency of quantum simulations. The development of EMOs represents a significant step forward in the field of computational physics and chemistry, paving the way for new discoveries and innovations.