| Two subjects in the area of quantum computation are considered here. In the first chapter I present a universal model for a quantum Robot. Chapters two, three, and four are dedicated to the problem of quantum error correction/protection.;A quantum robot is described as a quantum system that moves in, and interacts with, an external environment of quantum systems. Such environments consist of arbitrary numbers and types of particles in two or three dimensional space lattices. I find a set of universal operations that enables the quantum robot to simulate arbitrary quantum dynamics.;A computational approach to the quantum error correction problem is presented in chapters two and three. I develop a theory for finding quantum error correction (QEC) procedures which are optimized for given noise channels. This theory accounts for uncertainties in the noise channel, against which our QEC procedures are robust. I demonstrate via numerical examples that such optimized QEC procedures always achieve a higher channel fidelity than the standard error correction method, which is agnostic about the specifics of the channel. In the setting of a known noise channel the recovery ancillas are redundant for optimized quantum error correction. I show this using a general rank minimization heuristic and supporting numerical calculations. Therefore, one can further improve the fidelity by utilizing all the available ancillas in the encoding block.;However, this conclusion breaks down in the presence of an initial entanglement between the encoding and recovery ancillas. Such entanglement assisted error correction procedures are studied in chapter three. I show how entanglement can increase fidelity in the optimized setting by improving the function of the recovery ancillas.;In the last chapter quantum error protection methods, decoherence-free subspaces and subsystems, are studied in the framework of linear maps. This framework provides the most general description of open quantum system dynamics. |
