Abstract The simulation of molecular electronic structure is an important application of quantum devices. Recently, it has been shown that quantum devices can be effectively combined with classical supercomputing centers in the context of the sample-based quantum diagonalization (SQD) algorithm. This allowed the largest electronic structure quantum simulation to date (77 qubits) and opened near-term devices to practical use cases in chemistry toward the hundred-qubit mark. However, the description of many important physical and chemical properties of those systems, such as photo-absorption/-emission, requires a treatment that goes beyond the ground state alone. In this work, we extend the SQD algorithm to determine low-lying molecular excited states. The extended-SQD method improves over the original SQD method in accuracy, at the cost of an additional computational step. It also improves over quantum subspace expansion based on single and double electronic excitations, a widespread approach to excited states on pre-fault-tolerant quantum devices, in both accuracy and efficiency. We employ the extended SQD method to compute the first singlet (S 1) and triplet (T 1) excited states of the nitrogen molecule with a correlation-consistent basis set, and the ground- and excited-state properties of the [2Fe-2S] cluster.
Abstract The simulation of molecular electronic structure is an important application of quantum devices. Recently, it has been shown that quantum devices can be effectively combined with classical supercomputing centers in the context of the sample-based quantum diagonalization (SQD) algorithm. This allowed the largest electronic structure quantum simulation to date (77 qubits) and opened near-term devices to practical use cases in chemistry toward the hundred-qubit mark. However, the description of many important physical and chemical properties of those systems, such as photo-absorption/-emission, requires a treatment that goes beyond the ground state alone. In this work, we extend the SQD algorithm to determine low-lying molecular excited states. The extended-SQD method improves over the original SQD method in accuracy, at the cost of an additional computational step. It also improves over quantum subspace expansion based on single and double electronic excitations, a widespread approach to excited states on pre-fault-tolerant quantum devices, in both accuracy and efficiency. We employ the extended SQD method to compute the first singlet (S 1) and triplet (T 1) excited states of the nitrogen molecule with a correlation-consistent basis set, and the ground- and excited-state properties of the [2Fe-2S] cluster.
Computing ground-state properties of molecules is a promising application for quantum computers operating in concert with classical high-performance computing resources. Quantum embedding methods are a family of algorithms particularly suited to these computational platforms: they combine high-level calculations on active regions of a molecule with low-level calculations on the surrounding environment, thereby avoiding expensive high-level full-molecule calculations and allowing to distribute computational cost across multiple and heterogeneous computing units. Here, we present the first density matrix embedding theory (DMET) simulations performed in combination with the sample-based quantum diagonalization (SQD) method. We employ the DMET-SQD formalism to compute the ground-state energy of a ring of 18 hydrogen atoms, and the relative energies of the chair, half-chair, twist-boat, and boat conformers of cyclohexane. The full-molecule 41- and 89-qubit simulations are decomposed into 27- and 32-qubit active-region simulations, that we carry out on the ibm_cleveland device, obtaining results in agreement with reference classical methods. Our DMET-SQD calculations mark a tangible progress in the size of active regions that can be accurately tackled by near-term quantum computers, and are an early demonstration of the potential for quantum-centric simulations to accurately treat the electronic structure of large molecules, with the ultimate goal of tackling systems such as peptides and proteins.
Quantum and hybrid quantum-classical algorithms have the potential to improve the accuracy and scale of quantum chemistry and impact a broad range of applications such as drug discovery and catalysis. In particular, subspace methods such as sample-based quantum diagonalization (SQD) can already tackle classically challenging systems. However, practical algorithms that go beyond the computation of electronic ground and excited states are still scarce. Here, we introduce the variable-geometry sample-based quantum diagonalization (VGSQD) algorithm, which extends SQD to variable molecular geometries by reusing quantum samples from a reference geometry at displaced ones, thus significantly reducing quantum computational cost. Using circuits of up to 124 qubits on ibm-quebec, an IBM Heron r2 quantum processor, we determine the equilibrium geometry and energy of the weakly bound, strongly correlated beryllium dimer, as well as the water molecule. Finally, we extend VGSQD to chemical reactions and compute the minimum energy path and energy barrier of a hydrogen exchange reaction. The results are comparable with state-of-the-art classical methods such as CCSD(T) and DMRG. This work broadens the scope of quantum algorithms for chemistry, from energies to geometry optimization and reaction pathways, both essential for practical applications.
Sample-based quantum diagonalization (SQD) offers a powerful route to accurate quantum chemistry on noisy intermediate-scale quantum (NISQ) devices by combining quantum sampling with classical diagonalization. Here we introduce HSQD, a novel half-qubit SQD approach that halves the qubit requirement for simulating a chemical system and drastically reduces overall circuit depth and gate counts, suppressing hardware noise. When modeling the dissociation of the nitrogen molecule with a (10e, 26o) active space, HSQD matches the accuracy of SQD on IBM quantum hardware using only half the number of qubits and 40% fewer measurements. We further enhance HSQD with a heat-bath configuration interaction (HCI) inspired selection of the samples, forming HCI-HSQD. This yields sub-millihartree accuracy across the N2 potential energy surface and produces subspaces up to 39% smaller than those from classical HCI, showing a significant improvement in the compactness of the ground-state representation. Finally, we demonstrate the scalability of HCI-HSQD using iron-sulfur clusters, reaching active spaces of up to (54e, 36o) while using only half as many qubits as the original SQD. For these systems, HCI-HSQD reduces SQD energy errors by up to 76% for [2Fe-2S] and 26% for [4Fe-4S], while also reducing subspace sizes, halving measurement requirements, and eliminating expensive post-processing. Together, these results establish half-qubit SQD as a noise-resilient and resource-efficient pathway toward practical quantum advantage in strongly correlated chemistry.
Computing ground-state properties of molecules is a promising application for quantum computers operating in concert with classical high-performance computing resources. Quantum embedding methods are a family of algorithms particularly suited to these computational platforms: they combine high-level calculations on active regions of a molecule with low-level calculations on the surrounding environment, thereby avoiding expensive high-level full-molecule calculations and allowing the distribution of computational cost across multiple and heterogeneous computing units. Here, we present the first density matrix embedding theory (DMET) simulations performed in combination with a sample-based quantum diagonalization (SQD) method. We employ the DMET-SQD formalism to compute the ground-state energy of a ring of 18 hydrogen atoms and the relative energies of the chair, half-chair, twist-boat, and boat conformers of cyclohexane. The full-molecule 41- and 89-qubit simulations are decomposed into 27- and 32-qubit active-region simulations, which we carry out on the ibm_cleveland device, obtaining results in agreement with reference classical methods. Our DMET-SQD calculations mark tangible progress in the size of active regions that can be accurately tackled by near-term quantum computers and are an early demonstration of the potential for quantum-centric simulations to accurately treat the electronic structure of large molecules, with the ultimate goal of tackling systems such as peptides and proteins.
Quantum computers offer the potential to simulate chemical systems beyond the capabilities of classical computers. However, current quantum computing approaches to ab initio molecular dynamics (AIMD) and vibrational analysis largely rely on the Variational Quantum Eigensolver (VQE), whose circuit depth, iterative optimization, and measurement overhead hinder the practical simulation of molecular systems. Here, we extend Sample-based Quantum Diagonalization (SQD), a quantum sampling-based electronic-structure method, to AIMD and vibrational analysis on noisy quantum hardware. The resulting framework enables nuclear forces and Hessians to be derived from quantum-computed electronic energies, facilitating molecular dynamics and characterization of potential energy surfaces. We demonstrate the approach using diverse molecular processes, including H2 bond vibration, the proton-exchange reaction (H+ + H2), the bimolecular nucleophilic substitution (SN2) reaction (Cl- + CH3Cl), and proton-transfer dynamics between two water molecules involving transient formation of the Zundel cation (H2O···H+···OH2). Across these systems, SQD-AIMD trajectories and vibrational frequencies obtained with noisy quantum hardware/noise-models show excellent agreement with classical reference calculations and substantially improved accuracy relative to previously reported VQE-based simulations. Importantly, the SQD-based approach eliminates costly variational optimization and significantly reduces measurement requirements relative to VQE, enabling AIMD simulations spanning approximately 500 timesteps (∼200 fs), substantially longer than previously reported AIMD simulations on quantum hardware. These results establish SQD-AIMD and SQD-vibrational analysis as practical and scalable frameworks for simulating chemical reaction dynamics and elucidating reaction mechanisms on near-term quantum hardware, extending quantum computing applications beyond static electronic structure calculations.
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 H2, LiH, BeH2, H2O, and NH3. 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 H2 and HeH+ using both STO-3G and 6-31G basis sets, and for LiH and BeH2 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 × 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.