Quantum Simulation of Ligand-like Molecules through Sample-based Quantum Diagonalization in Density Matrix Embedding Framework

TL;DR

The paper tackles the difficulty of accurately capturing electron correlation in extended molecular systems with classical methods, and proposes a hybrid quantum-classical approach. It integrates Density Matrix Embedding Theory (DMET) with Sample-based Quantum Diagonalization (SQD) to solve embedded Hamiltonians on near-term quantum hardware. Using a minimal STO-3G basis and a set of ligand-like molecules, the DMET-SQD energies agree with DMET-FCI within chemical accuracy, demonstrating the viability of quantum sampling combined with embedding for chemically relevant systems. The work highlights potential applications in drug discovery and functional materials, while discussing noise-related limitations and the need for compact subspaces to improve efficiency.

Abstract

The accurate treatment of electron correlation in extended molecular systems remains computationally challenging using classical electronic structure methods. Hybrid quantum-classical algorithms offer a potential route to overcome these limitations; however, their practical deployment on existing quantum computers requires strategies that both reduce problem size and mitigate hardware noise. In this work, we combine Density Matrix Embedding Theory (DMET) with Sample-based Quantum Diagonalization (SQD) to compute ground-state energies of a set of natural ligand-like molecules in the minimal Slater Type Orbital (STO-3G) basis set. DMET provides a systematic fragmentation of a molecule into embedded impurity subproblems, while SQD enables construction and classical diagonalization of reduced configuration spaces through quantum sampling enhanced by iterative configuration recovery. The resulting embedded Hamiltonians are solved on IBM's Eagle R3 superconducting quantum hardware (IBM Sherbrooke). The DMET-SQD energies obtained for all systems considered exhibit strong agreement with DMET-FCI benchmark values within chemical accuracy (1 kcal/mol). These results demonstrate that sample-based quantum methods, when integrated with a robust embedding framework, can reliably extend quantum computation towards simulation of chemically relevant molecular systems, showcasing potential applications in the field of drug discovery.

Figures (4)

• Figure 1: Quantum Circuit Diagram for performing Sample-based Quantum Diagonalization. The initial state is prepared as the Hartree-Fock configuration, and is acted upon by an LUCJ ansatz which is pre-initialized with $t_i^a$ and $t_{ij}^{ab}$ parameters obtained through CCSD calculation. Finally, measurement is performed in the $\hat{\sigma}_z$ basis.
• Figure 2: Illustrative example of bath-orbital construction for the $H_2O$ molecule in the STO-3G basis. The system is fragmented so that the orbital localized on a single hydrogen atom constitutes the fragment. (a) shows an iso-surface of this fragment orbital; (b) shows the corresponding bath orbital obtained via DMET, which is a linear combination of the remaining localized spatial orbitals in the molecular orbital basis. Together, (a) and (b) span the impurity subspace for the H-fragment.
• Figure 3: A simplified workflow for DMET-SQD
• Figure 4: Comparison of the DMET-SQD energies obtained for the set of studied molecules on IBM Sherbrooke Quantum Hardware ($4^{th}-5^{th}$ June, 2025) with DMET-FCI. All the energies obtained are within the chemical accuracy criterion (1 kcal/mol $\approx$ 0.001594 Ha), which is marked with the red-dashed line. The x-axis denotes the name of the studied molecule, the molecular formula and the molecular weight. The y-axis denotes the absolute energy difference between the energy obtained through quantum hardware using DMET-SQD ($E_{DMET-SQD}$) and the reference energy $E_{DMET-FCI}$, which is defined as $\triangle E$.