Quantum computers, if available, could substantially accelerate quantum simulations. We extend this result to show that the computation of molecular properties (energy derivatives) could also be sped up using quantum computers. We provide a quantum algorithm for the numerical evaluation of molecular properties, whose time cost is a constant multiple of the time needed to compute the molecular energy, regardless of the size of the system. Molecular properties computed with the proposed approach could also be used for the optimization of molecular geometries or other properties. For that purpose, we discuss the benefits of quantum techniques for Newton's method and Householder methods. Finally, global minima for the proposed optimizations can be found using the quantum basin hopper algorithm, which offers an additional quadratic reduction in cost over classical multi-start techniques.
Quantum computers, if available, could substantially accelerate quantum simulations. We extend this result to show that the computation of molecular properties (energy derivatives) could also be sped up using quantum computers. We provide a quantum algorithm for the numerical evaluation of molecular properties, whose time cost is a constant multiple of the time needed to compute the molecular energy, regardless of the size of the system. Molecular properties computed with the proposed approach could also be used for the optimization of molecular geometries or other properties. For that purpose, we discuss the benefits of quantum techniques for Newton's method and Householder methods. Finally, global minima for the proposed optimizations can be found using the quantum basin hopper algorithm, which offers an additional quadratic reduction in cost over classical multi-start techniques.
While most work on the quantum simulation of chemistry has focused on computing energy surfaces, a similarly important application requiring subtly different algorithms is the computation of energy derivatives. Almost all molecular properties can be expressed an energy derivative, including molecular forces, which are essential for applications such as molecular dynamics simulations. Here, we introduce new quantum algorithms for computing molecular energy derivatives with significantly lower complexity than prior methods. Under cost models appropriate for noisy-intermediate scale quantum devices, we demonstrate how low-rank factorization and other tomography schemes can be optimized for energy derivative calculations. We numerically demonstrate that our techniques reduce the number of circuit repetitions required by many orders of magnitude for even modest systems, and that the cost of estimating an entire force vector may in some systems be lower than the cost of estimating the energy. In the context of fault-tolerant algorithms, we develop new methods of estimating energy derivatives with Heisenberg limited scaling, incorporating state-of-the-art techniques for block encoding fermionic operators. In contrast to our near-term results, we find that the cost of estimating forces with any of our Heisenberg-limited methods is bounded by the cost of estimating energies, due to inner loops requiring either energy estimation or reflections around the ground state. This implies that applications such as geometry optimization, coupling parameter estimation, and spectral prediction may be practical on fault-tolerant quantum devices, but tractable molecular dynamics simulations of large-scale systems requires further algorithmic advances.
Quantum computing has shown promise in chemical simulation and other fields where computationally hard problems must be tackled. This research focuses on optimizing molecule structures, which is an important step in understanding the properties and activities of chemical substances. It also studies the possibility of quantum computing in this domain. The system's many-body wave function is optimized using the imaginary time evolution approach, with nuclei and electrons both being considered quantum mechanical particles. Based on numerical experiments in two-dimensional H2+ and H-C-N systems, the authors find that their suggested method may have two benefits—it can find the best nuclear positions with few observations (quantum measurements), and it can find the global minimum structure of nuclei without starting from a complex initial structure and getting stuck in local minima. It is anticipated that this approach would function admirably with quantum computers, and its advancement will pave the road for its potential application as a potent tool.
This paper explores the application of quantum computing to enhance gradient descent algorithms for molecular simulation, aiming to significantly accelerate the search for optimal molecular conformations. The core claim is to extend gradient descent to leverage quantum-enhanced gradient calculations and error correction, thereby dramatically reducing the computational time required for simulating molecular systems. We analyze the potential benefits of this approach, considering both the theoretical advantages of quantum mechanics and the practical challenges of implementation. The research will detail the proposed quantum enhancement techniques, focusing on error mitigation and improved gradient estimation. The paper concludes with a discussion of the current state of research and future directions for this transformative technology.
methods for the exact simulation of quantum systems on classical computers presents a limitation of current computational approaches. We report, in detail, how a set of pre-computed molecular integrals can be used to explicitly create a quantum circuit, i.e. a sequence of elementary quantum operations, that, when run on a quantum computer, to obtain the energy of a molecular system with xed nuclear geometry using the quantum phase estimation algorithm. We extend several known results related to this idea and discuss the adia- batic state preparation procedure for preparing the input states used in the algorithm. With current and near future quantum devices in mind, we provide a complete example using the hydrogen molecule, of how a chemical Hamiltonian can be simulated using a quantum computer.
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.
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.