Quantum Systems for Computation and Vice Versa

Abstract

The potential of quantum computing has captured the interest of the academic and industrial spheres alike. However, the implementation of quantum systems for advantageous computation requires a good deal of further research, much of which must leverage classical computation techniques. In particular, relatively coherent hardware architectures have been fashioned from a variety of quantum systems, and numerous algorithms that are resilient to the noise of near to moderate-term devices have been proposed. In this thesis, we address both of these critical research fronts, exploring the dynamics of optical quantum systems as quantum information platforms and developing variational quantum algorithms. We also discuss the power of efficient tensor network representations for simulating quantum processes. \vspace{0.4cm}

First, in the vein of quantum platforms, we develop physical models and operational protocols for both the Nitrogen-vacancy (NV) center in diamond and the dipole-dipole interactions in atomic arrays with subwavelength latice spacing. In the former, we demonstrate that electron-nuclear spin couplings can facilitate all-optical control of the nitrogen nuclear spin, including the manipulation of optical Rabi drives. As decoherent interactions dominate over coherent oscillations, we develop a Bayesian model comparison/parameter fitting framework to affirm the nature of these dynamics. In the later, we analytically characterize the interaction of multiple quantum emitters in a single array, highlighting the potential for long-lived quantum memory and tuneable quantum interactions. \vspace{0.4cm}

Then, in the vein of quantum algorithms, we provide a myriad of solutions for the famed ``barren plateau'' problem, as well as introduce two novel algorithms for the circumvention of local minima in nonconvex training landscapes. In the former, we analytically characterize barren plateaus in terms of the spread of entanglement throughout a quantum landscape, framing it in terms of Langevin noise and devising initialization, entanglement regularization, and alternative measurement basis techniques for its curtailment. In the later, 1) Multi-Basis Encoding techniques are devised to improve the performance of quantum optimization algorithms while requiring fewer qubits, as well as highlighting the key features and advantages of tensor-based quantum machine learning simulation, and 2) a Markov chain Monte Carlo protocol for ergodically exploring the quantum optimization landscape (and thus avoiding local minima) is developed.