Classical and Quantum Simulation of Chemical and Physical Systems

Various quantum mechanics effects have been found and widely studied in different microscopic systems, such as quantum nuclear effects and electron correlation in molecular systems, electron-phonon coupling in crystal systems, and quantum Zeno effects in open quantum systems. However, exact numerical simulations require exponentially scaled classical resources. In this thesis, we study these quantum systems by a series of classical or quantum methods, which include semiclassical, ab initio, machine learning, and quantum computing approaches. In Chapter 2, we develop the molecular-orbital-based machine learning (MOB-ML) method as a general-purpose method to learn molecular electronic structure properties. By preserving physical constraints, including invariance conditions and size consistency, MOB-ML is shown to be able to capture both weak and strong interactions. Furthermore, the Gaussian Process framework is extended for learning both scalar properties such as energies, and linear-response properties like dipole moments with the rotationally equivariant derivative kernel. With these improvements, MOB-ML shows not only significantly higher learning rates for organic molecules, non-covalent interactions, and transition states but also excellent transferability from small systems to large systems. In Chapter 3, we develop a generalized class of integrators in the thermostatted ring-polymer molecular dynamics (T-RPMD) method, which is a semi-classical quantum dynamics method to capture various types of molecular nuclear quantum effects, including zero point energy, quantum tunneling, and kinetic isotopic effects. Such generalized integrators are carefully designed to be strong stable and dimension-free, which are essential for robust numerical computations. In particular, a so-called "BCOCB" integrator is proved to be superior in terms of accuracy and efficiency in the harmonic limit. Such superiority is further verified in strongly anharmonic systems featured by liquid water. In Chapter 4, we develop an ab initio-based semi-analytical model of electron-phonon scattering to describe the transport and noise behavior in GaAs, which is a widely-used semiconductor. Such a semi-analytical model lifts a few approximations in the standard ab initio calculation of intervalley scatterings, which were believed to be the origin of the failure to capture the nonmonotonic noise phenomena. We find qualitatively unchanged transport and noise properties and agreements on the scattering rates between the photoluminescence experiments. These results indicate the most probable origin of the nonmonotonic noise behavior is the formation of space-charge domains rather than the intervalley scattering. In Chapter 5, we simulate the challenging measurement-induced phase transitions (MIPT) behavior in quantum many-body systems on a superconducting quantum processor. Due to the intrinsic exponential scaling of the quantum state tomography and post-selection process, traditional simulations of MIPT were limited to a few qubits. With the recently introduced linear cross-entropy benchmarking, such exponential overhead is eliminated, and the correct critical behavior of MIPT is observed on a 22-qubit system. Our work paves the way for the studies of open quantum systems on large-scale near-term quantum devices.