Sixteen Qubits Estimate Energies of Small Molecules with Quantum Simulation

A one-trillion-determinant barrier in molecular simulation has been overcome, achieved through experiments on IQM’s Sirius 24-qubit processor. For the first time, a full two-dimensional potential energy surface for the water molecule has been experimentally constructed, mapped over a 32×32 grid, representing a sharp leap forward in quantum chemistry. Anurag K. S. V. and colleagues at Qclairvoyance Quantum Labs in collaboration with National University of Singapore, Ahmedabad University, The University of Arizona and BITS Pilani, used Sample-based Quantum Diagonalization, combined with the Local Unitary Cluster Jastrow (LUCJ) ansatz and Density Matrix Embedding Theory, to compute energies for a set of benchmark molecules, including H₂, LiH, BeH₂, H₂O, and NH₃, and successfully processed a system with 1.31×10¹² determinants.

The energy landscape of a water molecule has been mapped with unprecedented detail, calculating how the energy changes as the molecule’s bonds stretch and bend, using up to 16 qubits on IQM’s Sirius processor. Scientists have achieved a breakthrough in molecular simulation, exceeding the one-trillion-determinant barrier previously limiting the size of accurately modelled systems. This advance used IQM’s Sirius 24-qubit processor to construct a detailed two-dimensional ‘potential energy surface’ for the water molecule, illustrating the energy of the molecule as its bonds stretch and bend. Sample-based Quantum Diagonalization accomplished this by taking numerous ‘samples’ from the quantum computer, analogous to conducting a statistical survey to determine public opinion. The more samples taken, the more accurate the resulting energy estimation becomes. Complementing this, Density Matrix Embedding Theory breaks down complex molecules into smaller, more manageable parts for simulation, akin to a team of specialists each focusing on a specific aspect of a larger project. This allows for a reduction in the computational resources required to model the entire system, while still maintaining a reasonable level of accuracy.

Quantum simulation exceeds one trillion determinants enabling water’s full potential energy surface

Calculations now reach 1.31×10¹² determinants, surpassing the one-trillion-determinant barrier in molecular simulation. Previously, accurate modelling was limited to systems of approximately ten to fourteen correlated electrons, due to the exponential scaling of computational cost with system size in traditional quantum chemistry methods. This breakthrough, achieved on IQM’s Sirius 24-qubit processor, represents the first experimental construction of a full two-dimensional potential energy surface for the water molecule, detailing how its energy changes as bonds stretch and bend. The potential energy surface is crucial for understanding molecular behaviour, as it dictates the vibrational frequencies and reaction pathways of the molecule.

A combination of Sample-based Quantum Diagonalization with Density Matrix Embedding Theory extended these simulations to larger molecules, including the drug amantadine, demonstrating a pathway towards modelling complex systems currently beyond classical computational reach. Chemically accurate results for eight ligand-like molecules were achieved, utilising a four-electron-in-four-orbital active-space. This active space represents the most important electrons and orbitals contributing to the molecule’s chemical properties. These energies were verified against established full configuration interaction (FCI) and Density Matrix Embedding Theory (DMET)-CASCI calculations, providing a benchmark for the accuracy of the quantum simulation. FCI is considered the ‘gold standard’ in quantum chemistry, but is computationally intractable for all but the smallest systems. DMET-CASCI offers a compromise between accuracy and computational cost, and serves as a valuable validation tool.

Current simulations, however, are limited by the number of qubits and coherence times available, meaning scaling to truly complex systems like large proteins still requires substantial advances in quantum hardware and error correction. Qubit coherence refers to the duration for which a qubit maintains its quantum state, and is crucial for performing complex calculations. Error correction is essential to mitigate the effects of noise and imperfections in the quantum hardware. The method’s potential for pharmaceutical applications was demonstrated by extending calculations to include amantadine, a drug used to treat influenza. This highlights the possibility of applying the technique to more complex systems, but also underscores the need for continued development in quantum hardware to overcome existing limitations and achieve fault-tolerant quantum computation.

Balancing quantum computation speed and precision for molecular energy surface mapping

Computational cost remains a key factor in the ability to map molecular potential energy surfaces with increasing accuracy. While successful demonstrations extended calculations to molecules of increasing complexity, up to amantadine, the method currently relies on a trade-off between precision and speed. The data reveals that stable results with the Density Matrix Embedded Time-dependent Density Functional Theory (DMET-TDDFT) calculations require a substantial number of ‘shots’, or repeated measurements, on the quantum computer. Each shot provides an estimate of the system’s energy, and averaging over many shots reduces the statistical error.

Increasing the number of shots improves convergence, but also dramatically increases the runtime. This is because each shot requires the quantum computer to perform a measurement, which is a time-consuming process. Quantum simulation now extends beyond simple energy calculations, experimentally constructing a full two-dimensional potential energy surface for the water molecule directly on quantum hardware. A 32×32 grid defining bond length and angle was used to map this detailed field, resulting in 1024 data points representing the energy at different molecular geometries. Despite the need for further optimisation, the demonstrated agreement with established methods confirms the viability of this approach. Combining quantum computation with embedding theory, such as DMET, offers a promising pathway to tackle larger, more complex molecules relevant to drug discovery and materials science. The demonstrated reliability of these sample-based approaches, alongside hybrid embedding strategies, paves the way for simulating increasingly intricate molecular systems on available quantum hardware, opening new avenues for computational chemistry and drug discovery. Future work will focus on improving the efficiency of the quantum algorithms and reducing the number of shots required to achieve a desired level of accuracy, as well as exploring the use of more advanced error mitigation techniques.

The researchers successfully computed ground-state energies for molecules including water and amantadine using a quantum computer with up to 16 qubits. This demonstrates the potential to model molecular systems directly on quantum hardware, offering a complementary approach to classical computational chemistry. By combining quantum algorithms with techniques like Density Matrix Embedding Theory, they were able to extend calculations to larger molecules, generating a two-dimensional potential energy surface for water with 1024 data points. Future work aims to improve the efficiency of these calculations and reduce the need for repeated measurements.