Scalable Quantum Embedding
Low Scaling Quantum Embedding for Large Molecular Systems
Reliable simulations of large molecular systems require electronic structure methods that remain both accurate and computationally tractable as system size grows. In this case study, we develop a low scaling coupled cluster based quantum embedding framework using modern tensor decomposition techniques to reduce computational cost and memory requirements while preserving accuracy across challenging molecular environments.
Reliable Quantum Embedding for Transition Metal Chemistry
Consistent and reliable simulations of transition metal complexes are essential for many applications modern chemistry. In this case study, we develop develop a coupled cluster based quantum embedding framework that consistently and reliably reproduces the electronic structure of transition metal complexes at the accuracy of CCSDT, one of the most trusted standards in computational chemistry.
Exactness of Density Matrix Embedding Theory Near the Non Interacting Limit
Quantum embedding methods are an important strategy for extending high accuracy electronic structure simulations to strongly correlated molecular systems. In this case study, we analyze the behavior of density matrix embedding theory near the non interacting limit, providing new theoretical insight into the stability and exactness of embedding based electronic structure methods.
Differential Geometry Optimization for Quantum Embedding Simulations
Reliable quantum embedding simulations require robust optimization strategies capable of handling the complex mathematical structure of correlated electronic systems. In this case study, we develop and analyze a Grassmann manifold optimization framework arising from quantum embedding methods, providing new mathematical foundations and numerical strategies for stable and scalable electronic structure simulations.
Quantum Computing
From Promise to Practice: Benchmarking Quantum Chemistry on Quantum Hardware
Computational quantum chemistry is a cornerstone of modern R&D, used across reaction design, catalysis, and materials discovery. In this case study, we benchmark sample based quantum diagonalization on the W4-11 thermochemistry suite, presenting the largest high-throughput evaluation of a digital quantum device to date.
Theory Frontiers
Algebraic Geometry for Spin-Adapted Coupled Cluster Theory
Spin symmetry is an essential physical principle for both chemical fidelity and scalable electronic-structure simulation. We develop a mathematical framework based on algebraic-geometric for spin-adapted coupled-cluster theory, providing new insights that allow us to push the boundaries of modern high-accuracy electronic-structure simulations.
Algebraic Geometry of Coupled Cluster Doubles Theory
Coupled cluster doubles theory is the first major approximation in the hierarchy of coupled cluster methods and serves as an important starting point for understanding the mathematical structure of high accuracy electronic structure simulation. In this case study, we develop new algebraic geometric foundations for coupled cluster doubles theory, revealing geometric structure in coupled cluster solution spaces that provides insight into more advanced and computationally challenging coupled cluster methods.
Algebraic Varieties in Coupled Cluster Theory
Coupled cluster theory forms the foundation of many of the most accurate methods in electronic structure simulation, yet its underlying mathematical structure remains only partially understood. In this case study, we develop an algebraic geometric framework for coupled cluster theory by introducing truncation varieties that generalize Grassmannians, providing new mathematical foundations for understanding coupled cluster solution spaces and the nonlinear equations that govern high accuracy quantum chemistry.
Algebraic Geometric Foundations of Coupled Cluster Theory
Coupled cluster theory is one of the most successful high accuracy methods in electronic structure simulation, yet many aspects of its nonlinear structure remain mathematically unexplored. In this case study, we develop an algebraic geometric framework for coupled cluster theory using Newton polytopes and algebraic varieties to analyze the root structure of the coupled cluster equations, providing new mathematical insight into the geometry and solution landscape of coupled cluster methods.
