Towards Chemically Accurate and Scalable Quantum Simulations on IQM Quantum Hardware: A Quantum-HPC Hybrid Approach

Abstract

We present a large-scale experimental study of quantum-computing-based molecular simulation carried out on IQM's Sirius 24-qubit superconducting processor, utilizing up to 16 operational qubits. The work employs Sample-based Quantum Diagonalization (SQD) together with the Local Unitary Cluster Jastrow (LUCJ) ansatz to estimate ground-state energies for a set of benchmark molecules, including H$_2$, LiH, BeH$_2$, H$_2$O, and NH$_3$. In addition, we introduce a Linear-CNOT variant of the Unitary Coupled-Cluster Singles and Doubles (LCNot-UCCSD) ansatz within the SQD workflow, trading higher circuit depth for reduced classical preprocessing. A comparison between these ansätze is provided, clarifying their respective strengths, limitations, and suitability for near-term quantum hardware. We further explore potential energy landscapes through 1D scans for H$_2$ and HeH$^+$ using both STO-3G and 6-31G basis sets, and for LiH and BeH$_2$ in STO-3G. Extending beyond this, we demonstrate the experimental construction of a full 2D potential energy surface for the water molecule on quantum hardware, mapped over a 32 $\times$ 32 grid in bond length and bond angle. To move beyond small benchmark systems, we combine SQD(LUCJ) with Density Matrix Embedding Theory (DMET) to compute active-space energies for a set of ligand-like molecules, as well as the pharmacologically relevant amantadine system. Across all studies, the majority of quantum-computed energies agree with reference FCI results, as well as with DMET-CASCI energies for embedded systems, to within chemical accuracy for the chosen basis sets. These results demonstrate the reliability of sample-based diagonalization approaches and underscore the potential of hybrid embedding strategies for extending quantum simulations to increasingly complex molecular systems, while also highlighting their practicality on current IQM quantum hardware.

Figures (41)

• Figure 1: An illustrative depiction of the iso-spheres of the orbitals used for describing the carbon atom in (a) STO-3G basis set requiring 5 orbitals $1s, 2s, 2p_x, 2p_y, 2pz$ and in (b) 6-31G basis set which requires 9 orbitals $1s$, $2s$, $2p_x$, $2p_y$, $2p_z$, $2s'$, $2p_x'$, $2p_y'$, $2p_z'$. In addition to the orbitals which have a possibility of filling in the p-block (carbon atom), an additional orbital from the next block is picked for all the orbitals except the core orbital 1s. Hence, the additional orbitals $2s'$, $2p_x'$, $2p_y'$ and $2p_z'$ are also used. These orbitals were generated using PySCF, and visualized in Mol$^*$ (MolStar) Sehnal2021MolStar online software.
• Figure 2: The single excitation gate (left) and double excitation gate (right) represented in the Qubit Excitation Based (QEB) method Magoulas2023.
• Figure 3: Quantum circuit for a single layer of the LUCJ ansatz acting on $\alpha$ and $\beta$ spin registers. Each layer implements a sequence of localized orbital rotations $e^{\pm \hat{T}}$ and spin-resolved Jastrow correlators $e^{i\hat{J}}$, including inter-spin coupling $e^{i\hat{J}_{\alpha\beta}}$, enabling efficient encoding of one- and two-body correlations within a locality-constrained framework.
• Figure 4: Schematic representation of SQD workflows comparing the (a) LUCJ and (b) LCNot-UCCSD ansätze. The flowchart illustrates the division between Classical Pre-Processing, Quantum Computation, and Classical Post-Processing stages. Green boxes indicate computational advantages (lower algorithmic scaling), while yellow boxes highlight computational trade-offs, demonstrating the inverse relationship between classical initialization costs and quantum circuit complexity in determining the final energy, $E_{SQD}$.
• Figure 5: Molecular geometry representations of the one-dimensional potential energy surface (1D-PES) molecules under study: (a) H$_2$, (b) HeH$^+$, (c) LiH, and (d) BeH$_2$. Here, $r$ denotes the varying interatomic distance in ångströms (Å).