This thesis develops stochastic many-body methodologies for the electronic structure description of chemically relevant systems with strong electron correlation and nonequilibrium dynamics. Many phenomena of interest in chemistry and materials science, including excited-state processes, charge transfer at catalytic interfaces, and plasmon-mediated photocatalysis, require an accurate treatment of interacting electrons beyond mean-field theory. However, direct solutions of the many-body Schrodinger equation remain computationally intractable for realistic systems due to the exponential growth of the configurational Hilbert space with system size. This challenge motivates the development of reduced representations and embedding strategies capable of retaining essential correlation effects at lower computational cost. The work presented here focuses on stochastic matrix compression and downfolding techniques for many-body electronic structure theory. In particular, new stochastic compression approaches are introduced for the efficient representation of many-body Hamiltonians and correlated wavefunctions within reduced active subspaces. These methods extend stochastic electronic structure techniques beyond their traditional applications in many-body perturbation theory and provide a framework for treating correlated subsystems embedded within large chemical environments. Applications of these approaches are demonstrated across several classes of problems. First, stochastic downfolding methodologies are developed for the computation of charged excitations and Dyson orbitals relevant to catalytic interfaces and molecular spectroscopy. These techniques enable the treatment of large orbital spaces while maintaining accurate descriptions of electron correlation in the active region. Second, stochastic compression methods are applied to the computation of total energies in large solvated and reactive systems, where conventional correlated approaches become prohibitively expensive. Finally, the thesis explores nonequilibrium electronic dynamics at driven catalytic interfaces, including plasmon-assisted charge transfer processes. In this context, time-dependent many-body simulations reveal that transient driving fields can dynamically modify molecular spectral structure, opening additional resonant pathways for hot-carrier injection that are absent in equilibrium descriptions. Taken together, the methods developed in this thesis provide new strategies for reducing the computational complexity of correlated electronic structure calculations while preserving the essential physics of many-body interactions. These results broaden the applicability of stochastic and embedding-based approaches to large-scale equilibrium and nonequilibrium problems in chemistry, condensed matter physics, and materials science.
This thesis develops stochastic many-body methodologies for the electronic structure description of chemically relevant systems with strong electron correlation and nonequilibrium dynamics. Many phenomena of interest in chemistry and materials science, including excited-state processes, charge transfer at catalytic interfaces, and plasmon-mediated photocatalysis, require an accurate treatment of interacting electrons beyond mean-field theory. However, direct solutions of the many-body Schrodinger equation remain computationally intractable for realistic systems due to the exponential growth of the configurational Hilbert space with system size. This challenge motivates the development of reduced representations and embedding strategies capable of retaining essential correlation effects at lower computational cost. The work presented here focuses on stochastic matrix compression and downfolding techniques for many-body electronic structure theory. In particular, new stochastic compression approaches are introduced for the efficient representation of many-body Hamiltonians and correlated wavefunctions within reduced active subspaces. These methods extend stochastic electronic structure techniques beyond their traditional applications in many-body perturbation theory and provide a framework for treating correlated subsystems embedded within large chemical environments. Applications of these approaches are demonstrated across several classes of problems. First, stochastic downfolding methodologies are developed for the computation of charged excitations and Dyson orbitals relevant to catalytic interfaces and molecular spectroscopy. These techniques enable the treatment of large orbital spaces while maintaining accurate descriptions of electron correlation in the active region. Second, stochastic compression methods are applied to the computation of total energies in large solvated and reactive systems, where conventional correlated approaches become prohibitively expensive. Finally, the thesis explores nonequilibrium electronic dynamics at driven catalytic interfaces, including plasmon-assisted charge transfer processes. In this context, time-dependent many-body simulations reveal that transient driving fields can dynamically modify molecular spectral structure, opening additional resonant pathways for hot-carrier injection that are absent in equilibrium descriptions. Taken together, the methods developed in this thesis provide new strategies for reducing the computational complexity of correlated electronic structure calculations while preserving the essential physics of many-body interactions. These results broaden the applicability of stochastic and embedding-based approaches to large-scale equilibrium and nonequilibrium problems in chemistry, condensed matter physics, and materials science.
Strongly correlated electronic systems underpin a wide range of emerging quantum technologies, including solid-state defects for quantum information processing, molecular magnets, spin qubits, and quantum sensing platforms. Predictive computational design of these materials requires electronic structure methods capable of simultaneously describing strong electron correlation, excited-state phenomena, spin-dependent interactions, and environmental effects. While multireference wave function methods provide the necessary accuracy, their computational cost severely limits their application to realistic molecular and condensed-phase systems. This dissertation addresses this challenge through the development and application of quantum embedding and fragmentation methodologies that extend multireference electronic structure theory to increasingly complex quantum materials. The first part of this dissertation develops embedding-based approaches for describing optical properties of strongly correlated defects in extended solids. Complete Active Space Density Matrix Embedding Theory (CAS-DMET) and NEVPT2-DMET are applied to oxygen vacancy defects in magnesium oxide, where a systematic double-extrapolation protocol is introduced to approach both the non-embedding and thermodynamic limits. This framework enables quantitatively reliable calculations of absorption and emission energies while significantly reducing the computational cost of conventional multireference treatments of periodic systems. The second part extends embedding methodologies to the description of spin-dependent electronic structure. Density Matrix Embedding Pair-Density Functional Theory (DME-PDFT) is developed to recover dynamic electron correlation beyond the embedded active space, providing an efficient route for studying transition metal complexes and other strongly correlated molecular systems. Building upon these developments, CAS-DMET is further extended to investigate spin-phonon relaxation in molecular magnets and molecular crystals, demonstrating that quantum embedding can accurately describe spin dynamics and decoherence processes while substantially reducing computational cost. Beyond classical electronic structure calculations, this dissertation explores fragmentation strategies for hybrid quantum-classical algorithms through the development of efficient methodologies within the Localized Active Space Unitary Selective Coupled Cluster (LAS-USCC) framework. These developments improve the scalability of quantum chemistry algorithms for large active spaces and establish connections between embedding concepts and emerging quantum computing approaches. Finally, electronic structure calculations based on time-dependent density functional theory are employed to investigate fluorescent protein chromophores as potential biocompatible quantum sensors. These studies demonstrate how first-principles calculations can provide insight into spin-dependent properties in biologically relevant systems and expand the scope of computational approaches for quantum materials beyond traditional inorganic and molecular platforms. Collectively, the work presented in this dissertation establishes embedding and fragmentation as versatile frameworks for accurately describing the optical and spin properties of strongly correlated quantum systems across multiple length scales. By combining multireference electronic structure methods with physically motivated subsystem decompositions,these approaches bridge the gap between chemical accuracy and computational scalability, providing practical computational tools for the study and design of quantum materials relevant to quantum information science, molecular spintronics, and quantum sensing.
Achieving materials-specific predictions for large, realistic molecules and solids with strong electron correlations remains a long-standing challenge in quantum chemistry. This dissertation develops scalable ab initio quantum many-body methods for crystalline materials, demonstrating that rigorous optimization of theoretical approximations and numerical algorithms enables predictive computation even in strongly correlated systems. The work tackles three interconnected challenges, namely describing material-specific properties of strongly correlated superconductors, achieving linear scaling with k-points for large-scale periodic calculations, and establishing reliable methods for electron-phonon interactions. The following chapters address each challenge in turn. Chapter 2 demonstrates that ab initio density matrix embedding theory, combined with symmetry-breaking strategies for superconducting order parameters, reproduces experimental trends in cuprate superconductivity, including pressure and layer effects on transition temperatures. By directly solving the electronic Schrödinger equation from material structures, these calculations capture multi-orbital covalency effects that simplified model Hamiltonians neglect, revealing their essential role in the spin fluctuations driving pairing. This predictive capability establishes a foundation for efficient computational screening of superconducting materials. Extending these calculations to larger k-point meshes and broader phase diagram explorations, however, demands more efficient computational algorithms. To overcome this computational bottleneck, Chapter 3 introduces interpolative separable density fitting framework. This development enables thermodynamic limit calculations with up to 1000 k-points, as validated on diamond, carbon dioxide, nickel monoxide, and cuprate systems. Integration with density matrix embedding theory and local natural orbital methods further yields converged ground-state energies from accurate correlated wavefunction methods such as CCSD(T) for crystalline materials in the thermodynamic limit. With computational efficiency established, the remaining challenge lies in extending the theoretical framework beyond purely electronic degrees of freedom. Chapter 4 addresses this need by establishing exponential ansatz wavefunctions as competitive approaches for electron-phonon systems. Unlike previous treatments based on perturbation theory, systematic benchmarking of coupled cluster theory and variational Lang-Firsov methods on the Holstein model demonstrates, for the first time, that these approaches accurately describe polaron formation across coupling regimes when combined with appropriate reference state optimization. These results provide a foundation for incorporating phonon effects into ab initio studies of superconducting materials. In addition to these methodological advances, GPU acceleration and MPI parallelization enhance computational throughput, enabling efficient large-scale calculations. Together, these developments constitute a computational framework for predictive ab initio quantum many-body calculations in crystalline materials, opening new avenues for understanding and designing strongly correlated quantum materials.
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.
This dissertation develops quantum computing methods for two fundamental aspects of nature: electronic structure in molecules and materials, and the dynamics of open quantum systems. Framed by the theme of moving from structure to dynamics, the work explores how quantum computers can be utilized to compute both the stationary properties of many-body systems and their evolution in realistic environments. Throughout, the emphasis is on physically grounded algorithms that are compatible with noisy intermediate-scale quantum hardware.On the electronic-structure side, this dissertation develops hybrid quantum-classical workflows for chemistry and condensed-matter problems. Sample-based quantum diagonalization and its extended variant are used to recover low-energy molecular states from quantum samples, with application to a reactive molecular system. For materials, a quantum computing workflow is constructed for defect-containing LixCoO2 by combining first-principles electronic-structure calculations, Wannier downfolding, and quantum many-body solvers, including variational and neural-network-based approaches.On the dynamics side, this dissertation presents several complementary methods for simulating open quantum systems on quantum computers. A dilation-based framework is introduced to embed non-unitary reduced dynamics into enlarged unitary evolutions, first for Kraus-map dynamics and then for dynamics generated by the generalized quantum master equation. Two additional near-term strategies are also developed: an adaptive variational method for dissipative many-body dynamics, demonstrated for Dicke superradiance, and a stochastic Schr\"odinger equation approach based on quantum trajectories, applied to excitation transport in the Fenna-Matthews-Olson complex.Taken together, these results establish a set of quantum algorithmic tools that traverse scales and descriptions, from electronic structure to dynamical processes, and from molecular chemistry to complex quantum environments. In this way, the dissertation advances the use of quantum computers as a framework for probing the interconnected fabric of nature.
Accurate many-body treatments of condensed-phase systems are challenging because correlated solvers such as full configuration interaction (FCI) and the density matrix renormalization group (DMRG) scale exponentially with system size. Downfolding and embedding approaches mitigate this cost but typically require prior selection of a correlated subspace, which can be difficult to determine in heterogeneous or extended systems. Here, we introduce a stochastic cluster expansion framework for efficiently recovering the total correlation energy of large systems with near-DMRG accuracy, without the need to select an active space a priori. By combining correlation contributions from randomly sampled environment orbitals with an exactly treated subspace of interest, the method reproduces total energies for non-reacting and reactive systems while drastically reducing computational cost. The approach also provides a quantitative diagnostic for molecule-solvent correlation, guiding principled embedding decisions. This framework enables systematically improvable many-body calculations in extended systems, opening the door to high-accuracy studies of chemical processes in condensed phase environments.
Conspectus Ab initio modeling of matter has become a pillar of chemical research: with ever-increasing computational power, simulations can be used to accurately predict, for example, chemical reaction rates, electronic and mechanical properties of materials, and dynamical properties of liquids. Many competing quantum mechanical methods have been developed over the years that vary in computational cost, accuracy, and scalability: density functional theory (DFT), the workhorse of solid-state electronic structure calculations, features a good compromise between accuracy and speed. However, approximate exchange-correlation functionals limit DFT's ability to treat certain phenomena or states of matter, such as charge-transfer processes or strongly correlated materials. Furthermore, conventional DFT is purely a ground-state theory: electronic excitations are beyond its scope. Excitations in molecules are routinely calculated using time-dependent DFT linear response; however applications to condensed matter are still limited. By contrast, many-electron wavefunction methods aim for a very accurate treatment of electronic exchange and correlation. Unfortunately, the associated computational cost renders treatment of more than a handful of heavy atoms challenging. On the other side of the accuracy spectrum, parametrized approaches like tight-binding can treat millions of atoms. In view of the different (dis-)advantages of each method, the simulation of complex systems seems to force a compromise: one is limited to the most accurate method that can still handle the problem size. For many interesting problems, however, compromise proves insufficient. A possible solution is to break up the system into manageable subsystems that may be treated by different computational methods. The interaction between subsystems may be handled by an embedding formalism. In this Account, we review embedded correlated wavefunction (CW) approaches and some applications. We first discuss our density functional embedding theory, which is formally exact. We show how to determine the embedding potential, which replaces the interaction between subsystems, at the DFT level. CW calculations are performed using a fixed embedding potential, that is, a non-self-consistent embedding scheme. We demonstrate this embedding theory for two challenging electron transfer phenomena: (1) initial oxidation of an aluminum surface and (2) hot-electron-mediated dissociation of hydrogen molecules on a gold surface. In both cases, the interaction between gas molecules and metal surfaces were treated by sophisticated CW techniques, with the remainder of the extended metal surface being treated by DFT. Our embedding approach overcomes the limitations of conventional Kohn-Sham DFT in describing charge transfer, multiconfigurational character, and excited states. From these embedding simulations, we gained important insights into fundamental processes that are crucial aspects of fuel cell catalysis (i.e., O2 reduction at metal surfaces) and plasmon-mediated photocatalysis by metal nanoparticles. Moreover, our findings agree very well with experimental observations, while offering new views into the chemistry. We finally discuss our recently formulated potential-functional embedding theory that provides a seamless, first-principles way to include back-action onto the environment from the embedded region.