Reduced Density Matrix Approaches for Quantum Sensing, Computation, and Simulation

Theoretical chemistry uses the laws of physics to provide explanations for chemical observations, including molecular structure, bonding, and reactivity, in close connection with experiment. Although many answers in chemistry and materials science have been elucidated by accurate first-principles quantum-chemical calculations, their applicability is limited by high computational costs. This motivates the use of reduced descriptions of quantum many-body systems that retain core physical information at a lower computational cost. This thesis explores the development of reduced density matrix (RDM) techniques at the interface of chemistry, physics, and quantum information that address challenges in quantum technologies, including decoherence and scalability. The first part explores how minimal single-particle information can be used to detect environmental interactions in many-body quantum systems, aiding in the development of novel quantum sensing techniques and error mitigation strategies for quantum computation. The second part presents a framework for accelerating quantum state characterization for practical molecular simulation on quantum devices. The final part elucidates properties of entanglement in systems with mixed particle statistics, offering insight into quantum communication and the design of hybrid quantum platforms. Together, these results demonstrate how RDM-based approaches can improve the efficiency, interpretability, and robustness of quantum sensing, computation, and simulation.