A reliable large-scale quantum computer, if built, can solve many real-life problems exponentially faster than the existing digital devices. The biggest obstacle to building one is that they are extremely sensitive and error-prone regardless of the selection of physical implementation. Both data storage and data manipulation require careful implementation and precise control due to its quantum mechanical nature. For the development of a practical and scalable computer, it is essential to identify possible quantum errors and reduce them throughout every layer of the hierarchy of quantum computation.\n\nIn this dissertation, we present our investigation into new methods to reduce errors in quantum computers from three different directions: quantum memory, quantum control, and quantum error correcting codes. For quantum memory, we pursue the potential of the quantum equivalent of a magnetic hard drive using two-body-interaction structures in fractal dimensions. With regard to quantum control, we show that it is possible to arbitrarily reduce error when manipulating multiple quantum bits using a technique popular in nuclear magnetic resonance. Finally, we introduce an efficient tool to study quantum error correcting codes and present analysis of the codes' performance on model quantum architectures.
Quantum information processing requires efficient storage and manipulation of photonic states. In this work, we harness pre-created macroscopic spin coherence as an additional degree of freedom to control a cavity-assisted quantum memory. We derive equations of motion for such a memory that predict efficient emission and absorption of two-color fields under a generalized nonlocal spectral impedance-matching condition, which reduces to the well-known condition in the single-mode case. These equations reveal a new operating mechanism of cavity-assisted quantum memory wherein the controlled spin coherence couples the emitted spectral modes. As a result, our memory deterministically synthesizes arbitrary frequency-bin photonic qubits using simple radio-frequency rotations, while the temporal reversibility of the protocol provides perfect transformation of the qubit states. Our findings establish a unified platform bridging quantum storage with elementary signal processing for quantum networks based on spectral encoding of photonic qubits.