TOPICS IN LINEAR OPTICAL QUANTUM COMPUTATION

This thesis covers several topics in optical quantum computation. A quantum computer is a computational device which is able to manipulate information by performing unitary operations on some physical system whose state can be described as a vector (or mixture of vectors) in a Hilbert space. The basic unit of information, called the qubit, is considered to be a system with two orthogonal states, which are assigned logical values of 0 and 1. Photons make excellent candidates to serve as qubits. They have little interactions with the environment. Many operations can be performed using very simple linear optical devices such as beam splitters and phase shifters. Photons can easily be processed through circuit-like networks. Operations can be performed in very short times. Photons are ideally suited for the long-distance communication of quantum information. The great difficulty in constructing an optical quantum computer is that photons naturally interact weakly with one another. This thesis first gives a brief review of two early approaches to optical quantum computation. It will describe how any discrete unitary operation can be performed using a single photon and a network of beam splitters, and how the Kerr effect can be used to construct a two photon logic gate. Second, this work provides a thorough introduction to the linear optical quantum computer developed by Knill, Laflamme, and Milburn. It then presents this author's results on the reliability of this scheme when implemented using imperfect photon detectors. This author finds that quantum computers of this sort cannot be built using current technology. Third, this dissertation describes a method for constructing a linear optical quantum computer using nearly orthogonal coherent states of light as the qubits. It shows how a universal set of logic operations can be performed, including calculations of the fidelity with which these operations may be accomplished. It discusses methods for reducing and correcting errors and recovering from failed operations. Lastly it describes an analysis of the long distance transmission of the coherent state qubits and shows how transmission errors can be corrected.