As we begin to reach the limits of classical computing, quantum computing has emerged as a technology that has captured the imagination of the scientific world. While for many years, the ability to execute quantum algorithms was only a theoretical possibility, recent advances in hardware mean that quantum computing devices now exist that can carry out quantum computation on a limited scale. Thus, it is now a real possibility, and of central importance at this time, to assess the potential impact of quantum computers on real problems of interest. One of the earliest and most compelling applications for quantum computers is Feynman's idea of simulating quantum systems with many degrees of freedom. Such systems are found across chemistry, physics, and materials science. The particular way in which quantum computing extends classical computing means that one cannot expect arbitrary simulations to be sped up by a quantum computer, thus one must carefully identify areas where quantum advantage may be achieved. In this review, we briefly describe central problems in chemistry and materials science, in areas of electronic structure, quantum statistical mechanics, and quantum dynamics that are of potential interest for solution on a quantum computer. We then take a detailed snapshot of current progress in quantum algorithms for ground-state, dynamics, and thermal-state simulation and analyze their strengths and weaknesses for future developments.
Knowing the ground state energies of molecules and atoms gives scientists critical insight into these particles' behavior in reactions, thermodynamic and molecular properties, and excitation energies.However, due to the quantum mechanical nature of particles, finding the ground state of a system is intractable, both mathematically and experimentally.Computational methods are utilized to estimate the ground state energies.As we approach the limits of classical computers, quantum computers are viewed as promising alternatives that present a bright future for computational chemistry.In this paper, I review classical and quantum algorithms/methods for computational chemistry.Then, I discuss the current topics in using quantum computers for computational chemistry by analyzing the performance of the Variational Quantum Eigensolver (VQE) in different contexts on IBM's noisy quantum computer simulator, "QasmSimulator," and one of IBM's quantum computers, ibmq_belem.This review presents a theoretical and practical view of quantum computational chemistry.It allows the reader to learn the theory behind the algorithms and implement them with the guidance of the presented code and its detailed explanations.The purpose of this paper is to leave the reader with the necessary theory and adequate programming reference to implement the algorithms in various contexts.
Quantum computing offers the promise of revolutionizing quantum chemistry by enabling the solution of chemical problems for substantially less computational cost. While most demonstrations of quantum computation to date have focused on resolving the energies of the electronic ground states of small molecules, the field of quantum chemistry is far broader than ground-state chemistry; equally important to practicing chemists are chemical reaction dynamics and reaction mechanism prediction. Here, we review progress toward and the potential of quantum computation for understanding quantum chemistry beyond the ground state, including for reaction mechanisms, reaction dynamics, and finite-temperature quantum chemistry. We discuss algorithmic and other considerations these applications share, as well as differences that make them unique. We also highlight the potential speedups these applications may realize and challenges they may face. We hope that this discussion stimulates further research into how quantum computation may better inform experimental chemistry in the future.
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.
Computational quantum chemistry is a theoretical approach that utilizes the principles of quantum mechanics to perform computations on the electronic structure of molecules and atoms. This method enables the prediction of properties such as molecular structure, energy, electron orbitals, and electron density. In the field of the first principles, or ab initio, which relies solely on computation and not on experimental data, mathematical understanding allows even those without a background in chemistry to perform molecular orbital computations. The computation of quantum chemistry is computationally intensive, making them highly applicable in the field of high-performance computing. However, initiating quantum chemistry can be challenging for newcomers due to the numerous specialized terms and complex equations from quantum mechanics and chemistry. Therefore, this paper aims to provide a clear and accessible compilation of the fundamental and essential algorithm of the Hartree- Fock method, from theory to implementation. The goal is to offer the minimum required knowledge, in an approachable manner, serving as a starting point for those interested in computational quantum chemistry.
Applications in chemistry and material sciencePerhaps the most credible application of quantum computers is to study quantum physics itself.This deepens our understanding of microscopic systems like molecules, atoms, or even sub-atomic particles, ultimately leading to the discovery of new drugs, materials, and chemical production methods.At first sight, there seems to be a significant advantage compared to conventional computers, which struggle to store the complex quantum state of systems with many particles.As far back as 1981, physicist Richard Feynman ended a conference talk with a famous quote, hinting at the opportunities of quantum computing: 1 I'm not happy with all the analyses that go with just the classical theory, because nature isn't classical, dammit, and if you want to make a simulation of nature, you'd better make it quantum mechanical.Since then, scientists have become increasingly adept at accurately controlling quantum systems.Today, universities boast a wide spectrum of analogue quantum experiments that help us understand nature under exotic circumstances.We're now lining up our tools to take these simulations to the next level: studying nature with digital quantum machines.In this chapter, we will assess how quantum computers can impact the fields of chemistry and material science.That makes this chapter more technical, and we'll assume some (very) basic background in chemistry and physics.We discuss the most relevant algorithms, evaluate claims about quantum computing's benefits in the fight against climate change, and analyse why the nitrogenase enzyme receives such widespread attention.