Determining molecular properties like geometry and reaction pathways using quantum computers previously required extensive computational resources; each new configuration demanded a full circuit execution. Variable-geometry sample-based quantum diagonalization (VGSQD) reuses data from initial calculations across different molecule shapes, sharply reducing processing demands while maintaining accuracy, demonstrated by circuits utilising up to 124 qubits on an ibm-quebec processor. The algorithm efficiently calculates not only molecular energy but also their three-dimensional shape and how they evolve during chemical reactions.
Variable-geometry sample-based quantum diagonalization (VGSQD) cleverly reuses data from initial calculations on one molecule structure when examining similar forms, reducing processing demands. This technique efficiently determines not only molecular energy but also their three-dimensional shape and how they change during chemical reactions; this is key for applications like designing new drugs or catalysts. VGSQD tackles a vital challenge: reducing the computational demands of simulating molecules on quantum computers.
It achieves this by reusing data from calculations performed on one molecule structure when examining similar arrangements, akin to focusing on key “samples” representing its behaviour rather than calculating everything all at once. Using circuits with up to 124 qubits on an ibm-quebec processor, VGSQD successfully determined properties of beryllium dimer and water, as well as modelling the minimum energy path, imagine rolling a ball down a hill, for a hydrogen exchange reaction; but can it scale to more complex systems.
VGSQD achieves high accuracy molecular simulations via sample reuse on Heron r2
Previously requiring full circuit executions for each molecular configuration change, VGSQD, variable-geometry sample-based quantum diagonalization, now reuses quantum samples across geometries. Calculations utilising up to 124 qubits on a Heron r2 processor showed that barrier heights from its application to hydrogen exchange were within 0.2 kcal/mol of the highly accurate FCI reference point, a level of precision unattainable with prior methods. This breakthrough enables detailed modelling of chemical reactions and structural relaxation beyond simple energy estimations, previously limited by computational cost.
At, researchers successfully determined equilibrium geometry and energies for beryllium dimer and water molecules using this new approach, expanding what’s possible with near-term quantum hardware in practical chemistry applications like drug discovery or catalyst design. Water molecule bond lengths and angles converged to within 0.002 Å and 0.5° respectively when employing the larger cc-pVTZ basis set; these results further demonstrate its precision. Calculations on beryllium dimer utilising cc-pVDZ basis sets yielded relaxed bond lengths comparable with experimental values, alongside data obtained via CCSD(T), a state-of-the-art classical method.
These computations utilised circuits scaling up to 124 qubits on’s Heron r2 processor at ibm-quebec, coupled with high performance computing resources for data processing. While these findings broaden the scope of quantum algorithms for molecular geometry optimisation and reaction pathways, they currently focus on relatively small molecules, further development is needed to demonstrate scalability or error mitigation sufficient for tackling complex systems relevant to applications like drug discovery.
Demonstrating tangible performance improvements is vital despite expanded modelling capabilities
This new variable-geometry sample-based quantum diagonalization algorithm expands what’s possible with near-term quantum computers by moving beyond simple energy calculations to include geometry optimisation and reaction pathways; however, it doesn’t yet address how much computational benefit it delivers over existing methods. Repeating standard subspace diagonalization multiple times could potentially achieve similar results, a point the team acknowledges. Quantifying these efficiency gains, determining if reusing “quantum samples” truly reduces processing demands versus recalculating them, remains a key challenge for assessing VGSQD’s practical value.
Still, even acknowledging doubts about demonstrable speed advantages over repeated classical calculations, this work represents strong progress in expanding what near-term quantum computers can achieve. Future algorithms will likely build upon this approach to improve simulations in areas like materials design or pharmaceutical development because it reduces computational demands without sacrificing accuracy; successful simulations of beryllium dimer and water molecules demonstrate its potential using circuits scaling up to 124 qubits on an Heron r2 quantum processor. The team extended existing subspace methods by reusing quantum samples from a reference geometry at displaced ones. Further application could broaden the scope of quantum algorithms for chemistry, enabling essential calculations such as determining molecular geometries and modelling chemical reactions.
The researchers developed a new algorithm called variable-geometry sample-based quantum diagonalization (VGSQD) that allows quantum computers to calculate not only the energy of molecules but also their optimal shape and how they change during chemical reactions. This expands the capabilities of current quantum computing techniques beyond simple energy estimations, offering a method applicable to weakly bound systems like beryllium dimer and water molecules using circuits up to 124 qubits on an IBM Heron r2 processor.
The VGSQD algorithm achieves this by reusing data from initial simulations at different molecular configurations, reducing computational demands while maintaining accuracy comparable with classical methods such as CCSD(T) and DMRG. Future work will focus on improving scalability for more complex systems.
👉 More information
🗞 Sample-Based Quantum Diagonalization for Variable Molecular Geometries
✍️ Matthieu Fortin-Deschenes and Ibrahim Shehzad (Thomas J. Watson Research Center)
🧠 ArXiv: https://arxiv.org/abs/2610.38701




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