Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2608.06415

Ground-State Energy Estimation of HeH$^{+}$, ArH$^{+}$, and H$_2$O via Sample-Based Quantum Diagonalization

Jubin Park, Chae-Hyun Yoon, Minkyu Lee, Myung-Ki Cheoun

Published Aug 5, 2026• 0 citations
arXivHTMLPDF

Abstract

Accurate ground-state energies are essential for understanding molecular structure, chemical bonding, and reaction energetics in quantum chemistry. In this work, we investigate the ground-state properties of the molecular systems HeH$^+$, ArH$^+$, and H$_2$O using Sample-Based Quantum Diagonalization (SQD), a hybrid quantum-classical framework designed for near-term quantum devices. Unlike variational approaches such as VQE, which require deep parameterized circuits and repeated expectation-value measurements, SQD reconstructs a low-energy determinant subspace directly from measured bitstrings. For the present calculations, bitstrings were generated on IBM quantum hardware using shallow local unitary cluster Jastrow (LUCJ) circuits whose parameters were constructed from the $t_1$ and $t_2$ amplitudes of coupled-cluster singles and doubles (CCSD) calculations based on restricted Hartree--Fock (RHF) references. From these samples, we compute ground-state potential-energy curves of HeH$^+$, ArH$^+$, and H$_2$O with the 6-31G and cc-pVDZ basis sets. For all three systems, the SQD results obtained with the cc-pVDZ basis closely follow the corresponding same-basis CCSD energies and reproduce the equilibrium-region trends of the potential-energy curves. HeH$^+$ and ArH$^+$ were chosen as simple yet astrophysically important molecular-ion benchmarks, while H$_2$O was included as a representative polyatomic molecule to assess the applicability of SQD beyond diatomic ionic systems. At the adopted equilibrium geometries, the deviations from the same-active-space CASCI references are 0.00, 2.51, and 6.34 mHa for HeH$^+$, ArH$^+$, and H$_2$O, respectively. These results demonstrate the feasibility of hardware-assisted SQD for the present benchmark systems and motivate further studies of its accuracy and computational scaling for larger molecular active spaces.

DOI
10.48550/arxiv.2608.06415

Related papers

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

Anurag K. S. V., Ashish Kumar Patra, Manas Mukherjee +5 more

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.

quant-pharXiv:2604.01983•Apr 3, 2026•0 citations

Towards utility-scale electronic structure with sample-based quantum bootstrap embedding

Joel Bierman, Yuan Liu

One of the main applications for which quantum computers are hoped to find utility is in simulating ground state energies and other observables of molecular chemical systems. The recently proposed sample-based diagonalization method is a readily implementable method for this task on current-day hardware using short circuit depths and has been demonstrated on as many as 77 qubits. In this work, we combine bootstrap embedding with sampled-based diagonalization (QBE-SQD) and present the first benchmarking study of the QBE method on real quantum hardware, ibm_pittsburgh, a heron r3 processor with 156 qubits. Our test system is a hydrogen ring with 8 hydrogen atoms in the cc-pVDZ basis. We show that for this system, QBE-SQD using an active space of (8e, 19o) per fragment with a 43 qubit footprint produces a ground state energy accuracy which exceeds that of an SQD calculation with a (8e, 30o) active space with a 67 qubit footprint by $\sim$ 1 mHa when using a comparable number of Slater determinants and a lower reliance on error mitigation. This demonstrates that the use of bootstrap embedding techniques are a promising path towards extending the capabilities of state-of-the-art quantum eigensolvers on near-term devices.

Digital Discovery•Jan 1, 2026•3 citations

Sample-Based Quantum Diagonalization for Variable Molecular Geometries

Matthieu Fortin-Deschenes, Ibrahim Shehzad

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.

quant-pharXiv:2610.38701•Oct 30, 2026•0 citations

Quantum Chemical Calculations of H₂, HeH⁺, LiH, BeH₂, H₂O, NH₃, CH₄, CO₂, and N₂ Molecules Using the Variational Quantum Eigensolver(VQE): Ground State Energies,Potential Energy Surfaces, and Quantum Circuit Analysis

Surendra babu Nambury

Abstract We present a comprehensive quantum chemical study of nine molecules H₂, HeH⁺, LiH, BeH₂, H₂O, NH₃, CH₄, CO₂, and N₂ using the Variational Quantum Eigensolver (VQE) algorithm implemented in Qiskit 2.4.1. Molecular Hamiltonians are constructed in the STO-3G minimal basis set, transformed to qubit operators via the Jordan-Wigner mapping, and optimized using the n-local hardware-efficient ansatz with the SLSQP optimizer. Ground state energies are benchmarked against Full Configuration Interaction (FCI)/STO-3G reference values from authoritative literature sources. VQE achieves accuracies from 96.46% (HeH⁺) to 99.99% (H₂), average 98.68%. Potential energy surfaces are generated for all nine molecules and compared with high level ab initio literature PES references including the Kolos-Wolniewicz H₂ curve, the Polyansky water surface, and the Bytautas-Ruedenberg N₂ FCI surface. Equilibrium bond lengths agree with experiment to within 0.000–0.006 Å. Quantum ansatz circuits are analyzed in detail for all molecules. These results confirm the viability of near-term VQE algorithms for molecular quantum chemistry across diverse bond types and geometries.

•Jun 23, 2026•1 citation

Sample-Based Quantum Diagonalization Methods for Modeling the Photochemistry of Diazirine and Diazo Compounds

Saurabh Shivpuje, Tanvi P. Gujarati, Richard Van +6 more

Diazirines and diazo compounds are widely employed as photoreactive precursors for generating carbenes, key intermediates in chemical biology and materials science. However, computationally modeling their reaction pathways remains challenging due to the need for large active spaces and the requirement to accurately capture excited-state surfaces along with transition states and conical intersections. In this work, we utilize a hybrid quantum-classical workflow for investigating carbene formation in representative diazirine-diazomethane systems. Our approach leverages Sample-based Quantum Diagonalization (SQD) and its extended variant, Extended Sample-based Quantum Diagonalization (Ext-SQD), for ground- and excited-state analysis, combined with classical tools for geometry optimization, active-space selection, and diagnostic evaluation. Quantum computations were carried out on superconducting quantum processors, and results for both aliphatic and aryl-substituted diazirine-diazomethane pairs were benchmarked against established classical methods, including density functional theory (DFT), coupled cluster with singles and doubles (CCSD), complete active space configuration interaction (CASCI), and selected configuration interaction (SCI). SQD achieves accuracy surpassing the chemical accuracy threshold for nearly all stationary points on the potential energy surface of parent diazirine relative to the CASCI(12,10) reference, and remains close to chemical accuracy for phenyl-substituted diazirine in a (30,30) active space, with an average deviation of 1.1 kcal/mol relative to the SCI benchmark. SQD closely follows CASCI and SCI trends, showing consistent agreement. The findings demonstrate the promise of quantum computing frameworks in modeling photochemical transformations of electronically complex and pharmacologically relevant molecules.

arXiv:2510.00484•Journal of Chemical Theory and Computation•Jun 30, 2026•0 citations

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

Ashish Kumar Patra, Anurag K. S. V., Sai Shankar P. +4 more

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 investigate ground-state energy calculations of ligand-like molecules using Sample-based Quantum Diagonalization (SQD) within the Density Matrix Embedding Theory (DMET) framework, focusing on low-symmetry systems with diverse bonding motifs that exhibit subsystem-dependent variations in fragment-environment entanglement. These entanglement-based variations directly influence bath orbital construction, impurity sizes, and the structure of the embedded Hamiltonians, posing nontrivial challenges for both embedding and quantum sampling. By combining DMET fragmentation with SQD-based construction of reduced configuration spaces through quantum sampling and iterative configuration recovery, we perform quantum simulations on IBM's Eagle R3 (IBM Sherbrooke) and IBM's Heron R3 (IBM Boston) superconducting quantum hardware thereby, showing that the entanglement structure across embedding subsystems plays a central role in determining the efficiency and accuracy of the simulations. Despite these complexities, we show that the DMET-SQD framework yields ground-state energies in strong agreement with DMET-FCI benchmarks, achieving chemical accuracy (1 kcal/mol) across all systems studied. These results demonstrate that SQD-based quantum simulations can be robustly extended to low-symmetry, chemically realistic, industry relevant molecules, and highlight the importance of entanglement-aware embedding strategies for scalable quantum electronic structure calculations.

quant-pharXiv:2511.22158•The Journal of Chemical Physics•Nov 28, 2025•0 citations
Ground-State Energy Estimation of HeH+^{+}+, ArH+^{+}+, and H2_22​O via Sample-Based Quantum Diagonalization
Accurate ground-state energies are essential for understanding molecular structure, chemical bonding, and reaction energetics in quantum chemistry. In this work, we investigate the ground-state properties of the molecular systems HeH+^++, ArH+^++, and H2_22​O using Sample-Based Quantum Diagonalization (SQD), a hybrid quantum-classical framework designed for near-term quantum devices. Unlike variational approaches such as VQE, which require deep parameterized circuits and repeated expectation-value measurements, SQD reconstructs a low-energy determinant subspace directly from measured bitstrings. For the present calculations, bitstrings were generated on IBM quantum hardware using shallow local unitary cluster Jastrow (LUCJ) circuits whose parameters were constructed from the t1t_1t1​ and t2t_2t2​ amplitudes of coupled-cluster singles and doubles (CCSD) calculations based on restricted Hartree--Fock (RHF) references. From these samples, we compute ground-state potential-energy curves of HeH+^++, ArH+^++, and H2_22​O with the 6-31G and cc-pVDZ basis sets. For all three systems, the SQD results obtained with the cc-pVDZ basis closely follow the corresponding same-basis CCSD energies and reproduce the equilibrium-region trends of the potential-energy curves. HeH+^++ and ArH+^++ were chosen as simple yet astrophysically important molecular-ion benchmarks, while H2_22​O was included as a representative polyatomic molecule to assess the applicability of SQD beyond diatomic ionic systems. At the adopted equilibrium geometries, the deviations from the same-active-space CASCI references are 0.00, 2.51, and 6.34 mHa for HeH+^++, ArH+^++, and H2_22​O, respectively. These results demonstrate the feasibility of hardware-assisted SQD for the present benchmark systems and motivate further studies of its accuracy and computational scaling for larger molecular active spaces.
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_22​, LiH, BeH2_22​, H2_22​O, and NH3_33​. 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_22​ and HeH+^++ using both STO-3G and 6-31G basis sets, and for LiH and BeH2_22​ 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.
One of the main applications for which quantum computers are hoped to find utility is in simulating ground state energies and other observables of molecular chemical systems. The recently proposed sample-based diagonalization method is a readily implementable method for this task on current-day hardware using short circuit depths and has been demonstrated on as many as 77 qubits. In this work, we combine bootstrap embedding with sampled-based diagonalization (QBE-SQD) and present the first benchmarking study of the QBE method on real quantum hardware, ibm_pittsburgh, a heron r3 processor with 156 qubits. Our test system is a hydrogen ring with 8 hydrogen atoms in the cc-pVDZ basis. We show that for this system, QBE-SQD using an active space of (8e, 19o) per fragment with a 43 qubit footprint produces a ground state energy accuracy which exceeds that of an SQD calculation with a (8e, 30o) active space with a 67 qubit footprint by ∼\sim∼ 1 mHa when using a comparable number of Slater determinants and a lower reliance on error mitigation. This demonstrates that the use of bootstrap embedding techniques are a promising path towards extending the capabilities of state-of-the-art quantum eigensolvers on near-term devices.
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.
Abstract We present a comprehensive quantum chemical study of nine molecules H₂, HeH⁺, LiH, BeH₂, H₂O, NH₃, CH₄, CO₂, and N₂ using the Variational Quantum Eigensolver (VQE) algorithm implemented in Qiskit 2.4.1. Molecular Hamiltonians are constructed in the STO-3G minimal basis set, transformed to qubit operators via the Jordan-Wigner mapping, and optimized using the n-local hardware-efficient ansatz with the SLSQP optimizer. Ground state energies are benchmarked against Full Configuration Interaction (FCI)/STO-3G reference values from authoritative literature sources. VQE achieves accuracies from 96.46% (HeH⁺) to 99.99% (H₂), average 98.68%. Potential energy surfaces are generated for all nine molecules and compared with high level ab initio literature PES references including the Kolos-Wolniewicz H₂ curve, the Polyansky water surface, and the Bytautas-Ruedenberg N₂ FCI surface. Equilibrium bond lengths agree with experiment to within 0.000–0.006 Å. Quantum ansatz circuits are analyzed in detail for all molecules. These results confirm the viability of near-term VQE algorithms for molecular quantum chemistry across diverse bond types and geometries.
Diazirines and diazo compounds are widely employed as photoreactive precursors for generating carbenes, key intermediates in chemical biology and materials science. However, computationally modeling their reaction pathways remains challenging due to the need for large active spaces and the requirement to accurately capture excited-state surfaces along with transition states and conical intersections. In this work, we utilize a hybrid quantum-classical workflow for investigating carbene formation in representative diazirine-diazomethane systems. Our approach leverages Sample-based Quantum Diagonalization (SQD) and its extended variant, Extended Sample-based Quantum Diagonalization (Ext-SQD), for ground- and excited-state analysis, combined with classical tools for geometry optimization, active-space selection, and diagnostic evaluation. Quantum computations were carried out on superconducting quantum processors, and results for both aliphatic and aryl-substituted diazirine-diazomethane pairs were benchmarked against established classical methods, including density functional theory (DFT), coupled cluster with singles and doubles (CCSD), complete active space configuration interaction (CASCI), and selected configuration interaction (SCI). SQD achieves accuracy surpassing the chemical accuracy threshold for nearly all stationary points on the potential energy surface of parent diazirine relative to the CASCI(12,10) reference, and remains close to chemical accuracy for phenyl-substituted diazirine in a (30,30) active space, with an average deviation of 1.1 kcal/mol relative to the SCI benchmark. SQD closely follows CASCI and SCI trends, showing consistent agreement. The findings demonstrate the promise of quantum computing frameworks in modeling photochemical transformations of electronically complex and pharmacologically relevant molecules.
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 investigate ground-state energy calculations of ligand-like molecules using Sample-based Quantum Diagonalization (SQD) within the Density Matrix Embedding Theory (DMET) framework, focusing on low-symmetry systems with diverse bonding motifs that exhibit subsystem-dependent variations in fragment-environment entanglement. These entanglement-based variations directly influence bath orbital construction, impurity sizes, and the structure of the embedded Hamiltonians, posing nontrivial challenges for both embedding and quantum sampling. By combining DMET fragmentation with SQD-based construction of reduced configuration spaces through quantum sampling and iterative configuration recovery, we perform quantum simulations on IBM's Eagle R3 (IBM Sherbrooke) and IBM's Heron R3 (IBM Boston) superconducting quantum hardware thereby, showing that the entanglement structure across embedding subsystems plays a central role in determining the efficiency and accuracy of the simulations. Despite these complexities, we show that the DMET-SQD framework yields ground-state energies in strong agreement with DMET-FCI benchmarks, achieving chemical accuracy (1 kcal/mol) across all systems studied. These results demonstrate that SQD-based quantum simulations can be robustly extended to low-symmetry, chemically realistic, industry relevant molecules, and highlight the importance of entanglement-aware embedding strategies for scalable quantum electronic structure calculations.