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.
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.
Hybrid artificial intelligence–quantum (AI–Q) models arise at the intersection of two rapidly advancing computational paradigms, promising unprecedented capabilities for real-time molecular structure prediction. In classical computational chemistry, the accurate determination of ground-state energies and optimized geometries relies on ab initio methods such as density functional theory (DFT) and coupled-cluster approaches, which, while highly precise, exhibit steep polynomial or exponential scaling with system size. Conversely, deep neural networks (DNNs) have demonstrated remarkable success in learning potential energy surfaces (PES) from large datasets, achieving rapid inference but sometimes lacking the ultimate chemical accuracy required for predictive applications in drug discovery or materials design. On the other hand, variational quantum eigensolvers (VQEs) leverage the intrinsic parallelism of quantum hardware to approximate electronic structure problems, yet they remain constrained by qubit coherence times, gate fidelities, and circuit depth limitations inherent to noisy intermediate-scale quantum (NISQ) devices.
Quantum chemistry models atoms and molecules using quantum mechanics, with the electronic structure problem at its core. This problem, which determines the energy and properties of electrons in a molecule, is exponentially hard to solve exactly on classical computers. To approximate solutions, effective models introduce layers of simplifications. However, these approximations can fail for strongly correlated systems, necessitating alternative approaches. Quantum computers, capable of processing quantum information natively, offer a promising path to simulate molecular systems beyond classical reach, with potential applications in catalysis, materials science, and photochemistry. Despite rapid advancements in quantum hardware, practical quantum computations remain challenging due to limited resources. This thesis optimizes quantum resource usage in computational chemistry, introducing novel embedding techniques and exploring applications beyond ground-state energies. Chapter 1 establishes the foundation by reviewing quantum chemistry methods, from Hartree-Fock and Density Functional Theory (DFT) to active space approaches. It also provides an introduction to quantum computing for chemistry, focusing on near-term algorithms. The following chapters present novel methods aimed at reducing quantum resource requirements and tackling problems classical methods struggle with. Chapter 2 introduces a technique to reduce the λ-norm of the electronic structure Hamiltonian, a key measure of quantum resource demand. By transforming molecular orbitals, this method enhances sampling efficiency in Noisy Intermediate-Scale Quantum (NISQ) algorithms and reduces runtime in Fault-Tolerant Quantum Computing (FTQC). Localized orbitals outperform canonical ones, and an orbital-optimization scheme is proposed to minimize the λ-norm. Benchmarks on hydrogen chains, FeMoco, and Ruthenium complexes demonstrate its effectiveness. Chapter 3 presents the FragPT2 framework for simulating large systems with multiple interacting fragments. This method embeds each fragment in the mean field of others and applies multi-reference perturbation theory to capture inter-fragment correlations such as dispersion and charge transfer efficiently. The approach reduces computational overhead and enables scalable simulations, as shown in applications to \ce{N2} dimers, aromatic dimers, and butadiene. Chapter 4 focuses on photochemical systems, where multiple electronic states must be treated equally. The state-averaged orbital-optimized variational quantum eigensolver (SAOOVQE) is extended with analytical energy gradients and non-adiabatic couplings, enabling geometry optimizations and simulations of non-adiabatic dynamics on quantum hardware. This is demonstrated by locating the conical intersection in formaldimine, highlighting SAOOVQE’s potential for studying photoisomerization in biomolecules. Building on this, Chapter 5 develops a quantum algorithm to detect conical intersections, where the Born-Oppenheimer approximation breaks down. These intersections are characterized by a discrete Berry phase (0 or π), representing their topological nature. The algorithm extracts this phase as a single bit of information, ensuring resilience to noise. Analytical proof and numerical validation using a toy molecular model illustrate its effectiveness for studying light-perception biochemistry and related photochemical processes. Finally, Chapter 6 explores machine learning density functionals trained on noisy quantum data. While DFT is computationally efficient, its accuracy depends on approximated exchange-correlation functionals. This work proposes a neural network-based approach to learn the exact functional from quantum data, showing that training on noisy outputs from NISQ devices can mitigate sampling errors. Applications to the Fermi-Hubbard model and other systems demonstrate its potential to generalize and provide accurate results under noise. This thesis advances quantum computational chemistry by optimizing quantum resource usage, developing new embedding strategies, and expanding the scope of quantum simulations beyond ground-state properties. These contributions pave the way for practical quantum algorithms that could revolutionize molecular simulations in the near future.
However, accurately simulating molecular interactions constitutes the central, but open question of computer chemistry. This is a core task for efforts in drug development, catalyst design, and materials science. Most classical algorithms perform well on smaller systems, but incumbent exponential scaling penalties are unavoidable as models grow larger and more complex to describe quantum behaviour. An entirely new paradigm for this problem is now introduced by quantum computing: superposition and entanglement resources natively encode quantum states and model their electronic structures. The paper will thus take a high-level view of the leading quantum algorithms, with particular regard to those called Variational Quantum Eigensolver (VQE) and Quantum Phase Estimation (QPE), while evaluating their performance on today's Noisy Intermediate Scale Quantum (NISQ) devices. Next will follow discussions on algorithm design and current hardware capabilities, before which open challenges on scalability, error mitigation, and algorithm design will be outlined. Emphasis shall also be placed on the ethics and accessibility issues as well as the timelines with which quantum computing might gain a practical advantage. Linking together the recent advances and limitations, this paper posits how quantum computer implementation may change the face of chemical modelling and scientific discovery.
Computational chemistry has entered a new era where machine learning (ML) models—particularly graph neural networks and machine learning force fields—routinely deliver quantum mechanical accuracy at classical speeds, scaling to millions of atoms and reshaping workflows in drug discovery, catalysis, and materials design. At the same time, quantum computing is promoted as chemistry’s “killer application,” with the promise of solving many body problems beyond classical reach. Between these poles lies quantum machine learning (QML), a rapidly developing field that integrates quantum algorithms with ML paradigms. But is QML today a revolution, or merely hype? This article surveys the current state of classical ML in computational chemistry, highlighting its extraordinary successes and real limitations of transferability, interpretability, and generalization. We then examine the current landscape of quantum computing hardware and algorithms, clarifying what has actually been achieved with NISQ devices and where fundamental roadblocks remain. Building from this foundation, we analyze the foundations of QML algorithms—quantum kernels, variational quantum circuits, and hybrid workflows—and their putative advantages in polynomial scaling and Hilbert space expressivity. To ground discussion in practice, we present a case study of H₂ molecular energies, contrasting classical ML’s near instantaneous accuracy with quantum algorithms like the Variational Quantum Eigensolver. The outcome is telling: performance parity, not advantage, achieved only for toy systems under heavy simplification. This provides proof of principle for QML’s viability while simultaneously underscoring the severe constraints of current hardware. From this synthesis, we conclude that QML is presently characterized more by hype than utility, given the industrial dominance of classical ML. Yet in the long term—likely the mid 2030s and beyond—fault tolerant quantum hardware could transform computational chemistry, especially for strongly correlated systems where classical surrogates fail. The future lies not in premature claims, but in hybrid strategies, honest benchmarks, interpretable models, and sustainable integration across classical ML and quantum approaches. QML is not today’s solution. It is tomorrow’s horizon. And whether it becomes a true game changer will depend not on marketing cycles, but on the community’s ability to bridge hype with the patient, long term engineering of methods and machines.
The variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm designed for noisy intermediate-scale quantum (NISQ) hardware to estimate eigenvalues of many-body Hamiltonians. Unlike fully quantum approaches such as quantum phase estimation (QPE), VQE trades deep coherent circuits for repeated state preparation, measurement, and classical optimization, making it more compatible with limited qubit counts and finite coherence times. Recent developments have focused on reducing quantum resource requirements while retaining chemically meaningful wavefunction structure. In this paper, we examine recent progress in VQE methods for molecular electronic structure with an emphasis on three themes: (i) strategies for circuit and ansatz complexity reduction, including adaptive and selectively screened approaches, (ii) chemically motivated workflows that combine VQE with orbital optimization, fragmentation, and localized active-space ideas to better address strong correlation, and (iii) extensions of VQE to excited-state calculations. Throughout, we emphasize the tradeoffs among parameter count, gate depth, symmetry preservation, measurement overhead, and classical preprocessing, and discuss where these approaches may become most useful for chemically challenging active spaces. We also highlight benchmarking considerations for assessing both accuracy and resource requirements, and conclude with a perspective on regimes in which VQE may offer the greatest long-term value, particularly multireference active spaces and low-lying excited-state manifolds.
Quantum computing is emerging as a transformative approach in bioinformatics and quantum chemistry, addressing fundamental computational limitations of classical methods in molecular science. Many biological and chemical systems are inherently governed by quantum mechanics, making accurate simulation with classical algorithms computationally expensive or infeasible. This review examines how quantum computing, particularly in the Noisy Intermediate-Scale Quantum (NISQ) era, is advancing molecular modeling, reaction dynamics, and bioinformatics applications. Key quantum algorithms, including the Variational Quantum Eigensolver (VQE) and Quantum Phase Estimation (QPE), demonstrate increasing capability in approximating molecular energies and simulating quantum systems. In parallel, applications in bioinformatics—such as protein folding, genomic search, and combinatorial optimization—highlight the potential of quantum computing to address complex biological problems. Quantum machine learning further extends these capabilities by integrating quantum algorithms with data-driven modeling. However, current progress is constrained by NISQ-era limitations, including noise, limited qubit counts, and scalability challenges. These constraints highlight the need for hybrid quantum–classical approaches and improved error mitigation strategies. Overall, quantum computing represents a complementary computational paradigm that can enhance classical methods in bioinformatics and chemistry. Continued advances in quantum algorithms, hardware, and hybrid modeling frameworks are expected to expand its role in molecular science and computational biology.