Quantum embedding is an appealing route to fragment a large interacting quantum system into several smaller auxiliary ‘cluster’ problems to exploit the locality of the correlated physics. In this work we critically review approaches to recombine these fragmented solutions in order to compute non-local expectation values, including the total energy. Starting from the democratic partitioning of expectation values used in density matrix embedding theory, we motivate and develop a number of alternative approaches, numerically demonstrating their efficiency and improved accuracy as a function of increasing cluster size for both energetics and non-local two-body observables in molecular and solid state systems. These approaches consider the N-representability of the resulting expectation values via an implicit global wave function across the clusters, as well as the importance of including contributions to expectation values spanning multiple fragments simultaneously, thereby alleviating the fundamental locality approximation of the embedding. We clearly demonstrate the value of these introduced functionals for reliable extraction of observables and robust and systematic convergence as the cluster size increases, allowing for significantly smaller clusters to be used for a desired accuracy compared to traditional approaches in ab initio wave function quantum embedding.
Quantum embedding is an appealing route to fragment a large interacting quantum system into several smaller auxiliary ‘cluster’ problems to exploit the locality of the correlated physics. In this work we critically review approaches to recombine these fragmented solutions in order to compute non-local expectation values, including the total energy. Starting from the democratic partitioning of expectation values used in density matrix embedding theory, we motivate and develop a number of alternative approaches, numerically demonstrating their efficiency and improved accuracy as a function of increasing cluster size for both energetics and non-local two-body observables in molecular and solid state systems. These approaches consider the N-representability of the resulting expectation values via an implicit global wave function across the clusters, as well as the importance of including contributions to expectation values spanning multiple fragments simultaneously, thereby alleviating the fundamental locality approximation of the embedding. We clearly demonstrate the value of these introduced functionals for reliable extraction of observables and robust and systematic convergence as the cluster size increases, allowing for significantly smaller clusters to be used for a desired accuracy compared to traditional approaches in ab initio wave function quantum embedding.
Quantum embedding is an appealing route to fragment a large interacting quantum system into several smaller auxiliary `cluster' problems to exploit the locality of the correlated physics. In this work we critically review approaches to recombine these fragmented solutions in order to compute non-local expectation values, including the total energy. Starting from the democratic partitioning of expectation values used in density matrix embedding theory, we motivate and develop a number of alternative approaches, numerically demonstrating their efficiency and improved accuracy as a function of increasing cluster size for both energetics and non-local two-body observables in molecular and solid state systems. These approaches consider the N-representability of the resulting expectation values via an implicit global wave~function across the clusters, as well as the importance of including contributions to expectation values spanning multiple fragments simultaneously, thereby alleviating the fundamental locality approximation of the embedding. We clearly demonstrate the value of these introduced functionals for reliable extraction of observables and robust and systematic convergence as the cluster size increases, allowing for significantly smaller clusters to be used for a desired accuracy compared to traditional approaches in ab initio wave~function quantum embedding.
We present a multiscale approach to efficiently embed an ab initio correlated chemical fragment described by its energy-weighted density matrices and entangled with a wider mean-field many-electron system. This approach, first presented by Fertitta and Booth [Phys. Rev. B 98, 235132 (2018)], is here extended to account for realistic long-range interactions and broken symmetry states. The scheme allows for a systematically improvable description in the range of correlated fluctuations out of the fragment into the system, via a self-consistent optimization of a coupled auxiliary mean-field system. It is discussed that the method has rigorous limits equivalent to the existing quantum embedding approaches of both dynamical mean-field theory and density matrix embedding theory, to which this method is compared, and the importance of these correlated fluctuations is demonstrated. We derive a self-consistent local energy functional within the scheme and demonstrate the approach for hydrogen rings, where quantitative accuracy is achieved despite only a single atom being explicitly treated.
We describe an efficient quantum embedding framework for realistic ab initio density matrix embedding theory (DMET) calculations in solids. We discuss in detail the choice of orbitals and mapping to a lattice, treatment of the virtual space and bath truncation, and the lattice-to-embedded integral transformation. We apply DMET in this ab initio framework to a hexagonal boron nitride monolayer, crystalline silicon, and nickel monoxide in the antiferromagnetic phase, using large embedded clusters with up to 300 embedding orbitals. We demonstrate our formulation of ab initio DMET in the computation of ground-state properties such as the total energy, equation of state, magnetic moment, and correlation functions.
Abstract Quantum computing has shown great potential in various quantum chemical applications such as drug discovery, material design, and catalyst optimization. Although significant progress has been made in quantum simulation of simple molecules, ab initio simulation of solid-state materials on quantum computers is still in its early stage, mostly owing to the fact that the system size quickly becomes prohibitively large when approaching the thermodynamic limit. In this work, we introduce an orbital-based multi-fragment approach on top of the periodic density matrix embedding theory, resulting in a significantly smaller problem size for the current near-term quantum computer. We demonstrate the accuracy and efficiency of our method compared with the conventional methodologies and experiments on solid-state systems with complex electronic structures. These include spin polarized states of a hydrogen chain (1D-H), the equation of state of a boron nitride layer (h-BN) as well as the magnetic ordering in nickel oxide (NiO), a prototypical strongly correlated solid. Our results suggest that quantum embedding combined with a chemically intuitive fragmentation can greatly advance quantum simulation of realistic materials, thereby paving the way for solving important yet classically hard industrial problems on near-term quantum devices.
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.
The accuracy of large-scale ab initio calculations is always desired, but they are unfortunately not usually practical in many fields, such as studies of heterogeneous catalysis, photosynthesis, and functional mechanisms of biomolecules. DFT serves as a prevailing method for large calculations due to its compromise between cost and accuracy, but it has a number of failure cases, like bond breaking. On the other hand, the simple theoretical nature of force-field simulations, which often work well, reminds us that large systems are not necessarily exponentially complicated. A recurring theme in the electronic structure of large systems is therefore the use of fragment-based approaches. Existing fragment approaches typically treat the most powerful electron correlations perturbatively, on the same footing with dispersion forces (if at all). In our approach, electrons are not treated individually in the global calculation, but subunits will be chosen. (e.g., amino acid residues or individual water molecules). The most important local states are selected to account for inter-subunit interactions. Most familiar wavefunction methods (SCF, PT, coupled-cluster) can be applied directly to this internally correlated Hamiltonian, and the Hamiltonian itself is systematically improvable to exactitude. Furthermore, different parts of a system can be treated at different accuracy. Our initial investigations focus on the correlation structure of groups of harmonic oscillators, where the coupling inside of groups is stronger than between groups. This mimics discrete molecules while providing us with exact analytical solutions for comparison. Correlations between grouped oscillators will be characterized by both numerical and analytical methods, in order to shed light on building an algorithm for real molecules and systems.