Executive Summary : | Quantum information and quantum computation and communication have potential applications in various fields, but their practical realization is hindered by noise inherent to all quantum devices, including gates, buffers, and communication channels. Advances in fault-tolerant techniques have reduced the required redundancy from poly-logarithmic to a constant, prompting the question of the minimum required redundancy and the noise threshold. To ensure fair evaluation of quantum systems, it is essential to answer these questions. This project aims to obtain efficient bounds on the minimum required redundancy and noise threshold using information theoretic techniques developed for noisy Boolean circuits. The few existing bounds are asymptotic and applicable to large systems, while tighter bounds are also applicable at moderate scales, such as NISQ systems. Techniques from non-asymptotic quantum information theory will be utilized to achieve these bounds. Recently, noise can increase in quantum computation systems due to sharing limited resources and increased exposure to the environment. The project proposes suitable models for resource constraint-induced noise and studies the performance of specific fault-tolerant techniques like concatenation. The project also aims to address the impact of resource constraint-induced noise on fundamental bounds on redundancy and noise threshold. Encoders, decoders, and buffers used for quantum communication are made of quantum circuits, resulting in noise, potentially non-i.i.d., before transmission and after reception, resulting in lower effective channel capacity. |