Hybrid spin-boson systems Quantum simulations, sensing and dynamics

The aim of this Thesis is to understand and harness hybrid spin-boson systems.
In Part One we investigate hybrid spin-boson systems can be harnessed to realize quantum advantage. For quantum simulations, we investigate the effects of expected experimental errors, including micromotion and local stress, on quantum simulations of spin models with trapped ions in optical tweezers. For quantum metrology, we propose many-body sensing protocols for optimal quantum-enhanced displacement sensing. Finally, for quantum state preparation, we use a global variational quantum circuit to efficiently prepare arbitrary symmetric spin states, with applications in quantum metrology and quantum error correction.
In Part Two, because spin-boson systems are generally not amenable to exact analytic or classical numerical treatments, we develop efficient approximate classical methods for simulating their dynamics. We employ a superposition of bosonic Gaussian states as a variational state ansatz and simulate both closed- and open-system quantum dynamics using the time-dependent variational principle. Applications of this simulation framework range from studies of impurity physics and polaritonic chemistry, to fast quantum state preparation.