Quantum Algorithms Now Simulate Molecules and Predict Their Behaviour Accurately

Scientists are increasingly exploring the potential of quantum computing to enhance atomistic simulations, and a new study details a significant step towards this goal. Wilke Dononelli from the Institute for Physical and Theoretical Chemistry, University of Bremen, and colleagues demonstrate the successful integration of variational quantum algorithms, specifically the Variational Quantum Eigensolver (VQE) and its adaptive variant (ADAPT-VQE) , into the widely used Atomic Simulation Environment (ASE). This coupling facilitates hybrid quantum-classical workflows for diverse applications including geometry optimisation and molecular dynamics, offering a pathway to calculate properties of complex systems beyond the reach of conventional methods. By achieving results comparable to high-level classical calculations for systems like BeH2, the research establishes that adaptive variational quantum algorithms can generate stable forces within atomistic modelling, paving the way for accelerated materials discovery and design.

Quantum computation of forces for atomistic materials modelling offers potential speedups for simulations

Scientists are developing workflows for force-driven atomistic simulations utilising quantum computing. These results demonstrate that adaptive variational quantum algorithms can deliver stable and chemically meaningful forces within an atomistic modelling workflow, enabling downstream applications such as molecular dynamics and active-learning, accelerated simulations.
Advances in quantum algorithms have generated intense interest in their potential to complement classical approaches to electronic structure problems, particularly in regimes where the steep scaling of high-level methods becomes prohibitive. In atomistic modelling, wide-ranging applications such as catalysis design, battery material discovery, and molecular spectroscopy rely on accurate solutions to the electronic Schrödinger equation.

High-level classical methods such as coupled cluster with singles and doubles (CCSD) or with perturbative triples [CCSD(T)], often considered the gold standard of quantum chemistry, achieve near-chemical accuracy but scale steeply with system size, typically as O(N6) and O(N7) respectively. This scaling sharply limits application to small molecules in practice.
Early quantum algorithms for chemistry, such as quantum phase estimation (QPE), promised exact eigenvalues but required circuit depths far beyond the capabilities of noisy intermediate-scale quantum (NISQ) devices. The variational quantum eigensolver (VQE) emerged as a hybrid quantum, classical strategy that dramatically reduces circuit depth by combining state preparation and measurement on a quantum processor with classical optimisation of a parametrised wavefunction ansatz.

Chemically motivated ansätze such as unitary coupled cluster with singles and doubles (UCCSD) have been widely adopted, alongside hardware-efficient forms and low-depth generalisations such as k-UpCCGSD. Further refinements like the quantum subspace expansion and qubit coupled cluster balance expressivity against circuit resources.

In practice, however, many demonstrations have been confined to so-called “toy systems”, minimal basis calculations on very small molecules, where the quantum measurement is exact and the parameter convergence is trivial. Such examples validate implementations but fall short of showcasing chemistry-level utility.

For workflow-oriented applications, accurate and stable forces and vibrational properties in multi-electron systems must be obtained under the constraints of finite sampling (shots), noisy measurement, and challenging classical optimisation. In particular, molecular dynamics and structure exploration place stringent demands on the consistency of forces across many geometries, making force robustness, rather than single-point energy accuracy alone, a central bottleneck for quantum algorithms in atomistic modelling.

For larger systems, these challenges are further exacerbated by the substantial measurement overhead required for expectation-value, based variational algorithms and by optimization pathologies such as barren plateaus in high-dimensional parameter landscapes. Recent algorithmic advances in the NISQ era have focussed on reducing required quantum resources and improving convergence for realistic quantum chemical problems.

Among the promising tools are adaptive ansatz constructions such as the Adaptive Derivative-Assembled Pseudo-Trotter VQE (ADAPT, VQE), which iteratively builds the ansatz by selecting the most important excitation operators based on energy gradients. This approach yields compact, system-specific circuits which have demonstrated improved accuracy and convergence, especially in strongly correlated regimes.

Parallel efforts have aimed at further circuit compression and more accurate wavefunction representations, for example, by using transcorrelated (TC) Hamiltonians, which incorporate explicit electron-electron correlation via Jastrow factor transformations. Recent work shows that combining the TC approach with adaptive quantum algorithms such as AVQITE and VQE can significantly reduce quantum circuit depth and width, enhance convergence, and improve noise resilience, thereby facilitating their use in iterative atomistic workflows that require repeated and reliable force evaluations.

At the software ecosystem level, Qiskit Nature, part of the Qiskit SDK, provides robust implementations of VQE, ADAPT, VQE, and related algorithms, interfacing with molecular integrals from classical quantum chemistry packages such as PySCF. However, its current scope is limited to isolated quantum chemistry calculations; it does not directly offer the broader atomistic modelling functionality, geometry optimisation, vibrational analysis, and molecular dynamics, that underpin materials and molecular simulation workflows.

Related efforts have explored interfacing variational quantum algorithms with atomistic environments, primarily focusing on single-point energies or force evaluations, but without addressing the demands of long-time dynamical simulations. Previous studies have explored interfacing variational quantum eigensolvers with atomistic simulation environments, including force evaluations within ASE frameworks.

In contrast, the present work focuses on enabling computationally tractable molecular dynamics by combining ADAPT, VQE forces with on-the-fly active learning. This allows the electronic structure step in ASE’s geometry optimisation, vibrational frequency analysis, strain evaluation, and molecular dynamics to be performed using VQE or ADAPT, VQE, with results from a simulator returned to ASE’s property interface.

The integration permits drop-in replacement of classical electronic structure calculators with quantum counterparts, while preserving the surrounding atomistic workflow. Previous studies have explored interfacing variational quantum eigensolvers with atomistic simulation environments, including force evaluations within ASE frameworks.

These efforts primarily focused on proof-of-concept geometry optimisations or single-point force evaluations, without addressing the challenges posed by long-time molecular dynamics or force-driven workflows. In contrast, this present work emphasises the use of adaptive variational quantum algorithms in combination with on-the-fly active learning to enable computationally tractable molecular dynamics simulations.

By combining the general workflow integration with advanced quantum algorithms such as ADAPT, VQE, scientists aim to demonstrate that stable and chemically meaningful forces can be obtained for multi-electron, polyatomic systems within a hybrid quantum, classical framework. This, in turn, enables downstream applications including geometry optimisation, vibrational analysis, and molecular dynamics, rather than limiting quantum algorithms to isolated single-point calculations.

The following sections detail the implementation, benchmark results against classical CCSD, and representative applications ranging from simple diatomics to triatomics and force-driven dynamical simulations. Note however, that all calculations in this study are performed in the limit of using a minimal basis set, but the finding should be transferable to the usage of bigger basis set sizes and therefore, the here presented workflows are ready to be transferred to bigger system sizes in the future.

In this context, embedding and partitioning approaches, in which only chemically relevant subsystems are treated quantum mechanically while the environment is handled classically, provide a promising route toward extending such workflows to larger and more complex systems, although they are out of the scope of the here underlying study. Although the code is able to run in a hybrid mode on real NISQ devices, researchers focus on simulated devices and on the VQE and ADAPT, VQE algorithms.

This choice allows systematic investigation of convergence behaviour and force stability relevant to dynamical simulations, while future work could extend the framework to more advanced algorithms and real-device executions. The code is publicly available at https://github.com/thequantumchemist/ase_quantum_vqe/ and can be used and modified.

The core of this work is a custom ASE Calculator that wraps a Qiskit Nature electronic structure calculation within ASE’s standard interface. In this implementation, the geometry described by the ASE Atoms object is passed to the PySCFDriver in Qiskit Nature, which computes the one- and two-electron integrals for the system using the specified Gaussian basis set.

The resulting second-quantised fermionic Hamiltonian is mapped to qubit operators via the Jordan, Wigner mapping. A variational quantum eigensolver (VQE) is then prepared using the unitary coupled cluster ansatz with single and double excitations (UCCSD), combined with a Hartree, Fock reference state.

In addition to this, the calculator supports adaptive ansatz construction via ADAPT, VQE, in which excitation operators are iteratively selected based on energy gradients and appended to the variational circuit. The variational parameters are optimised by a classical optimizer (SLSQP if not stated otherwise) with the cost function given by expectation values obtained from the Qiskit Estimator.

The calculator is flexible in that it can employ either qiskit-aer’s statevector simulator aer or connect to an IBMQ backend via the Qiskit Runtime service, allowing tokens and backend selection to be specified at runtime. A detailed workflow is provided in Fig. The total energy computed in atomic units is converted to eV for ASE.

Forces are determined numerically by central finite differences, displacing each atomic coordinate by a small step and recomputing the energy. To ensure force consistency across geometry optimisation, vibrational analysis, and molecular dynamics, all displaced geometries in a force evaluation reuse identical electronic structure settings and convergence thresholds, thereby minimising numerical noise between successive force calls.

Dipole moments are extracted in atomic units from Qiskit Nature’s internal auxiliary operators and converted to Debye for compatibility with ASE’s dipole property, enabling direct use of the Infrared module for IR spectra. Specifically, the ADAPT-VQE algorithm was applied to multi-electron systems, beginning with BeH2, to determine vibrational and structural properties. These quantum-derived properties were then rigorously compared against high-level classical Coupled Cluster calculations, specifically CCSD, performed within a minimal basis set.

This direct comparison validated the accuracy and reliability of the adaptive variational quantum algorithms in producing stable and chemically meaningful forces essential for atomistic modelling. The study demonstrated that ADAPT-VQE can deliver consistent forces, a critical requirement for downstream applications like molecular dynamics and active-learning accelerated simulations.

The research further focused on achieving stable forces under challenging conditions, including finite sampling, noisy measurement, and complex classical optimisation landscapes. ADAPT-VQE iteratively constructs the wavefunction ansatz by selecting the most important excitation operators based on energy gradients, resulting in compact, system-specific circuits.

This adaptive approach improved both accuracy and convergence, particularly in strongly correlated regimes, and facilitated the use of these algorithms in iterative atomistic workflows demanding repeated and reliable force evaluations. The study demonstrates that adaptive variational quantum algorithms can deliver stable and chemically meaningful forces essential for atomistic modelling workflows.

These forces enable downstream applications such as molecular dynamics and active-learning accelerated simulations, expanding the scope of quantum computation in materials science. By utilising ADAPT-VQE, the research team obtained results in agreement with classical CCSD calculations, validating the accuracy of the quantum approach for complex systems.

This work addresses a key limitation of previous demonstrations, which often focused on small molecules and trivial convergence scenarios. The integration with ASE allows for the exploration of more realistic chemical systems and the performance of iterative atomistic workflows demanding consistent and reliable force evaluations. Limitations acknowledged by the researchers include the constraints imposed by small basis sets and the use of simulated quantum hardware.

Future work will concentrate on incorporating analytic gradients, developing tailored algorithms for specific chemical groups, and enhancing error-mitigation techniques for use with actual quantum hardware. This framework also offers potential for embedding and multiscale modelling, selectively applying quantum resources to chemically important areas while treating the surrounding environment classically.