Quantum computing has the potential to solve problems that are intractable for classical computers. In practice, physical qubits are coupled to their environments and are open quantum systems. To mitigate and correct environmental noises or utilize environmental degrees of freedom, one needs to carefully study the qubit properties in a open quantum system setting. In this thesis, we will first provide an overview of environmental couplings that are relevant to the quantum hardware of interest in the following chapters.

We begin the main body of this thesis by introducing a robust control method for the implementation of quantum logic gates in superconducting devices. By switching between two time-constant Hamiltonians, single and two-qubit gates can be implemented with fidelity exceeding the threshold of most quantum error corrections codes in the presence of TLS bath and Markovian bath. This method is inspired by variational quantum algorithms (VQA), and we continue to study quantum machine learning (QML), which is a specific type of VQA, in the following chapter. We investigate the impact of dephasing on QML and show dephasing significantly lower image classification accuracy of QML models. However, we also reveal that increasing virtual bond dimension of QML networks by adding ancilla can improve the accuracy and adding two ancilla can mostly compensate for the accuracy loss due to dephasing.

We then investigate qubits in open quantum system for quantum emulation. Specifically, we focus on the emulation of energy transfer between chromosomes in natural light-harvesting complexes using ion-trap quantum devices. This uphill energy transfer is assisted by vibrational modes in the molecules and is named vibration assisted energy transfer (VAET). We start with the study of VAET between two sites (qubits) coupled to one vibrational mode in the presence of classical white noise, which has the effect of dephasing. We show that in the weak noise regime, energy transfer is enhanced by VAET and harmed by the classical noise. In strong noise regime, the VAET signature is wiped out and the energy transfer efficiency will first increase with noise strength and then decrease to a quantum Zeno regime, a phenomenon termed as environment-assisted quantum transport (ENAQT). This is followed by the study of an expanded system with three sites coupled to two vibrational modes. We present a rich array of energy transfer processes. Among them, two phonon process associated to the mode coupled to the bridging site is found to have the greatest contribution to the energy transfer process. We also investigate the model in different scenarios, including varying coupling strength and temperature, presence of dephasing and coupled nodes, finding similar patterns but different relative energy transfer efficiencies. We then conclude with the impact of these studies on the application of near-term quantum devices.

Topologically ordered phases of matter are quantum liquids with a non-local quantum order. Because of their unique properties due to the non-local quantum entanglement present in these phases, topological phases have been proposed as the basis of a physically fault-tolerant quantum computer. The formation of such topological order is well understood in terms of the mechanism of loop condensation in systems with loop-like degrees of freedom. Certain quantum dimer models posses topologically ordered dimer liquid ground states and can be mapped to loop models. In this dissertation we present a study of the geometric properties of the loop condensates of quantum dimer models and related models using classical Monte Carlo as well as ground state quantum Monte Carlo calculations. Additionally, we present an approach for the robust experimental generation of a topologically ordered phase in a system of neutral atoms trapped in an optical lattice.