Quantum computers have the potential to revolutionise our understanding of the microscopic behaviour of materials and chemical processes by enabling high-accuracy electronic structure calculations to scale more efficiently than is possible using classical computers. Current quantum computing hardware devices suffer from the dual challenges of noise and cost, which raises the question of what practical value these devices might offer before full fault tolerance is achieved and economies of scale enable cheaper access. Here we examine the practical value of noisy quantum computers as tools for high-accuracy electronic structure, by using a Quantinuum ion-trap quantum computer to predict the ionisation potential of helium. By combining a series of techniques suited for use with current hardware including qubit-efficient encoding coupled with chemical insight, low-cost variational optimisation with hardware-adapted quantum circuits, and moments-based corrections, we obtain an ionisation potential of 24.5536 (+0.0011, -0.0005) eV, which agrees with the experimentally measured value to within true chemical accuracy, and with high statistical confidence. The methods employed here can be generalised to predict other properties and expand our understanding of the value that might be provided by near-term quantum computers.
Quantum computers have the potential to revolutionise our understanding of the microscopic behaviour of materials and chemical processes by enabling high-accuracy electronic structure calculations to scale more efficiently than is possible using classical computers. Current quantum computing hardware devices suffer from the dual challenges of noise and cost, which raises the question of what practical value these devices might offer before full fault tolerance is achieved and economies of scale enable cheaper access. Here we examine the practical value of noisy quantum computers as tools for high-accuracy electronic structure, by using a Quantinuum ion-trap quantum computer to predict the ionisation potential of helium. By combining a series of techniques suited for use with current hardware including qubit-efficient encoding coupled with chemical insight, low-cost variational optimisation with hardware-adapted quantum circuits, and moments-based corrections, we obtain an ionisation potential of 24.5536 (+0.0011, -0.0005) eV, which agrees with the experimentally measured value to within true chemical accuracy, and with high statistical confidence. The methods employed here can be generalised to predict other properties and expand our understanding of the value that might be provided by near-term quantum computers.
Quantum computing offers a promising path toward accurate electronic structure calculations, especially for systems where classical methods face limitations. However, most quantum demonstrations to date have focused on simplified systems, lacking the quantitative precision required for direct comparison with experiment. In this work, we present a method tailored for implementation on existing and near-term quantum hardware. Our focus is on predicting a quantity that can be directly compared with experiment, enabling a meaningful benchmark of quantum hardware for chemical applications. We use a compact representation that is achieved through physically motivated simplifications of the wavefunction, reflecting a general strategy of adapting the representation to known properties of the system, even though the degree of simplification is system-dependent. We validate this approach by computing the total energy of neutral helium using the Quantinuum H1-1 ion-trap quantum computer, enabling us to determine the ionization potential to within true chemical accuracy of the experimental value. This represents a meaningful step toward practical quantum computational chemistry and establishes a framework for benchmarking future quantum hardware using real-world chemical systems.
The predictive simulation of molecules and materials has had a broad and significant impact. It nevertheless remains constrained by the cost of accurately treating electronic correlation, excited states, and complex energy landscapes. Quantum computing offers a fundamentally different computational paradigm in which quantum states are encoded and manipulated directly rather than approximated on classical hardware. Here we discuss where this approach may provide a genuine scientific advantage in chemistry, materials science, and biochemistry. Promising directions include the high-accuracy treatment of correlated active spaces, improved excited-state simulations, and accelerated exploration of combinatorial structure spaces. The central challenge is therefore not qubit scaling alone, but demonstrably chemically meaningful gains in predictive reliability. We argue that near-term value is most likely to come from disciplined workflow integration rather than wholesale replacement of classical methods. Noisy physical devices, error-mitigated utility experiments, early fault-tolerant devices, and fully fault-tolerant quantum computers offer different scientific prospects, and claims of usefulness must be tied to the specific regime being discussed. Quantum computing will become scientifically valuable when it demonstrably reduces uncertainty in computed energies, rates, spectra, or materials stability after the full costs of state preparation, measurement, error handling, and coupling to classical simulation are included.
Accurate prediction of molecular structures and properties is vital for chemistry; materials science, and drug discovery, yet classical electronic-structure methods often fail for strongly correlated systems, large basis sets, and complex potential-energy landscapes. Quantum technology encompassing quantum computing, quantum machine learning, and hybrid quantum classical strategies offers a fundamentally new paradigm by encoding many-electron wave functions directly on qubits and exploiting superposition and entanglement to explore exponentially large Hilbert spaces. This review synthesizes recent algorithmic and hardware advances relevant to molecular modelling, including the Variational Quantum Eigensolver (VQE), Quantum Phase Estimation (QPE), quantum unitary coupled-cluster (q-UCC) families, equation-of-motion and subspace methods for excited states, tensor-network hybrids, and quantum kernel and variational QML approaches. We examine noise-aware hybrid workflows, error-mitigation techniques, symmetry-preserving ansätze, and operator-factorization methods that reduce measurement and gate overhead. Representative applications are discussed: ground- and excited-state energy prediction, potential-energy surface mapping, geometry and transition-state optimization, spectroscopic property estimation (IR, UV–Vis, NMR, EPR), and reaction-dynamics scenarios where non-adiabatic effects and conical intersections dominate. Resource estimates and scaling analyses clarify current NISQ limitations qubit counts, circuit depth, shot complexity and delineate the roadmap to fault-tolerant QPE for chemical accuracy. We compare quantum approaches with classical baselines (DFT, CCSD (T), multireference methods), identifying domains where quantum methods already show promise (strong correlation, multi-reference dissociation, spin-state ordering) and where classical methods remain competitive. Finally, we highlight near-term industrial opportunities in drug design, catalysis, CO2 capture, and energy materials, and outline critical research directions: algorithmic reductions in measurement/precision cost, hardware improvements in fidelity and connectivity, scalable ansatz design, and integrated software stacks for reproducible hybrid simulations. Together, these developments indicate that while practical, large-scale quantum advantage for general chemistry remains future work, quantum technologies are rapidly maturing into powerful tools for targeted molecular problems that are intractable with existing classical techniques.
One of the most important application areas of molecular quantum chemistry is the study and prediction of chemical reactivity. Large-scale, fully error-tolerant quantum computers could provide exact or near-exact solutions to the underlying electronic structure problem with exponentially less effort than a classical computer thus enabling highly accurate predictions for comparably large molecular systems. In the nearer future, however, only “noisy” devices with a limited number of qubits that are subject to decoherence will be available. For such near-term quantum computers the hybrid quantum-classical variational quantum eigensolver algorithm in combination with the unitary coupled-cluster ansatz (UCCSD-VQE) [Peruzzo et al. Nat. Commun. 2014, 5, 4213 and McClean et al. New J. Phys. 2016, 18, 023023] has become an intensively discussed approach that could provide accurate results before the dawn of error-tolerant quantum computing. In this work we present an implementation of UCCSD-VQE that allows for the first time to treat both open- and closed-shell molecules. We study the accuracy of the obtained energies for nine small molecular systems as well as for four exemplary chemical reactions by comparing to well-established electronic structure methods like (nonunitary) coupled-cluster and density functional theory. Finally, we roughly estimate the required quantum hardware resources to obtain “useful” results for practical purposes.
The advancements in classical computational components such as CPUs and GPUs have had a reverberating impact on the democratization of computational power available, with the field of computational chemistry reaping significant benefits from the propulsion of the limits of systems studied. The accurate prediction of chemical properties and reaction dynamics through computational simulation is now a centerpiece of modern chemical research, significantly accelerating discoveries research areas of materials science and drug development, as well as industrially relevant processes such as the emission of aldehydes from soft foams, flame retardants and pyrolysis and the carbonylation of epoxides. These achievements of computational chemistry still are overshadowed in the face of fundamental bottlenecks where classical methods remain constrained by the exponential scaling when treating large and/or strongly correlated quantum many-body systems. This innate computational complexity often constitutes chemically accurate calculations based on first principles impractical, or plain impossible, for systems beyond modest sizes. Quantum computing offers a potential pathway around these limitations, originally formally formulated by David Deutsch as a tool for simulating quantum systems, with the first quantum algorithms indicating speed-ups compared to classical counterparts arising from Peter Shor and Lov Grover for the prime factorization of an integer number and unstructured search respectively. Relying on fundamental theorems by Claude Shannon, it has been demonstrated that through the use of error-correcting codes fault-tolerant quantum computers are able to safeguard information against noise and decoherence, strongly indicating towards exponential speedups in solving central computational chemistry problems, such as determining ground state energies or reaction pathways of chemical systems. Substantial strides in experimental quantum computing over the past decade, including proof-of-principle demonstrations of quantum error correction, mean to bring full-scale fault-tolerant quantum computing within the grasp of humanity. The breakthroughs needed to attain scalable, error-corrected quantum computation with capabilities exceeding those of classical methods in real-world scenarios is likely still some years away. While striving to address the engineering challenges standing in the way of achieving fault tolerant quantum computing, substantial effort has been focused toward developing and benchmarking hybrid algorithms tailored for the Noisy Intermediate- Scale Quantum (NISQ) devices, available now to researchers. These hybrid quantum-classical algorithms, with the most notable being the Variational Quantum Eigensolver (VQE), allow the probing of quantum computing’s utility in computational chemistry even in the face of significant hardware noise and limited coherence times. The work presented in this thesis introduces several key additions the VQE framework, geared especially towards to NISQ hardware, where the mindful use of available resources is imperative. First, the implementation of the Conjugate Model Search optimizer is described, an optimization method that integrates simple models that are surrogate to the original function, combined with conjugate gradient optimization to navigate effectively parameter landscapes typical of variational algorithms, prone to noise. Second, this thesis contains the proposal and extensive study of a hyperparameter tuning procedure employing genetic algorithms, allowing for comprehensive simulation benchmarks that augment the robustness and efficiency of VQE implementations with respect to convergence time through real wall-time models of quantum processors. Continuing, a bridge is presented between quantum simulation and quantum chemistry, through qubit-to-fermion mappings of existing quantum gates, further enabling the direct and accurate modeling of chemical systems on trapped atom quantum hardware with the added arsenal provided by techniques designed for qubit architectures. Additionally, experimental data contained in this thesis include detailed benchmarking data collected from state-of-the-art trapped ion quantum processors available at the Johannes Gutenberg Universität Mainz, demonstrating the actual viability and performance of various methodologies for extracting results. Lastly, the state of VQE is examined, as it served as a springboard for a plethora of advancements in the development of quantum computing hardware, as well as the direction the field of simulation of computational quantum chemistry via quantum devices is headed towards in the coming years.
Abstract Quantum computers have the potential to perform accurate and efficient electronic structure calculations, enabling the simulation of properties of materials. However, today’s noisy, intermediate-scale quantum (NISQ) devices have a limited number of qubits and gate operations due to the presence of errors. Here, we propose a systematically improvable end-to-end pipeline to alleviate these limitations. Our proposed resource-efficient pipeline combines problem decomposition techniques for compact molecular representations, circuit optimization methods for compilation, solving the eigenvalue problem on advanced quantum hardware, and error-mitigation techniques in post-processing the results. Using the density matrix embedding theory for compact representation, and an ion-trap quantum computer, we simulate a ring of 10 hydrogen atoms taking into account all electrons equally and explicitly in the electronic structure calculation. In our experiment, we simulated the largest molecular system on a quantum computer within chemical accuracy with respect to total molecular energy calculated by the full CI method. Our methods reduce the number of qubits required for high-accuracy quantum simulations by an order of magnitude in the present work, enabling the simulation of larger, more industrially relevant molecules using NISQ devices. They are further systematically improvable as devices’ computational capacity continues to grow.