Summary form only given. Quantum computers are expected to increase the efficiency of solving problems such as factoring large integers. However an experimental implementation of even relatively simple quantum information processing with a few to a dozen qubits presents an enormous technological challenge. One of the earliest proposals for quantum computation is based on implementing a quantum bit with two optical modes containing one photon. The proposal is appealing due to the ease with which photon interference can be observed. However these early proposals required huge single photon optical nonlinearities. Unfortunately currently available optical nonlinearities are too weak and too noisy to be useful. Recently however we have discovered that efficient quantum computation is possible using only beam splitters, phase shifters, single photon sources and photodetectors. Our methods exploit feed forward from photo-detectors and are robust against errors from photon loss and detector inefficiency. In this tutorial I will outline this scheme, highlighting the technical challenges required to implement it. The tutorial will be relatively self contained with a brief introduction to quantum optics and quantum computation.
Summary form only given. Quantum computers are expected to increase the efficiency of solving problems such as factoring large integers. However an experimental implementation of even relatively simple quantum information processing with a few to a dozen qubits presents an enormous technological challenge. One of the earliest proposals for quantum computation is based on implementing a quantum bit with two optical modes containing one photon. The proposal is appealing due to the ease with which photon interference can be observed. However these early proposals required huge single photon optical nonlinearities. Unfortunately currently available optical nonlinearities are too weak and too noisy to be useful. Recently however we have discovered that efficient quantum computation is possible using only beam splitters, phase shifters, single photon sources and photodetectors. Our methods exploit feed forward from photo-detectors and are robust against errors from photon loss and detector inefficiency. In this tutorial I will outline this scheme, highlighting the technical challenges required to implement it. The tutorial will be relatively self contained with a brief introduction to quantum optics and quantum computation.
Quantum computers are expected to increase the efficiency of solving problems such as factoring large integers. However an experimental implementation of even relatively simple quantum information processing with a few to a dozen qubits presents an enormous technological challenge. One of the earliest proposals for quantum computation is based on implementing a quantum bit with two optical modes containing one photon[1]. The proposal is appealing due to the ease with which photon interference can be observed. However these early proposals required huge single photon optical nonlinearities. Unfortunately currently available optical nonlinearities are too weak and too noisy to be useful.
Two qubit gates for photons are generally thought to require exotic materials with huge optical nonlinearities. We show here that, if we accept two qubit gates that only work conditionally, single photon sources, passive linear optics and particle detectors are sufficient for implementing reliable quantum algorithms. The conditional nature of the gates requires feed-forward from the detectors to the optical elements. Without feed forward, non-deterministic quantum computation is possible. We discuss one proposed single photon source based on the surface acoustic wave guiding of single electrons.
One of the earliest proposals for implementing quantum computation was based on encoding each qubit in two optical modes, each containing exactly one photon. However, it is extremely difficult to unitarily couple two optical modes containing few photons. In 2001, Knill, Laflamme, and Milburn (KLM) found a way to circumvent this restriction and implement efficient quantum computation using only passive linear optics, photodetectors, and single photon sources. This efficient linear optical quantum computing (LOQC) is distinct from other linear optical schemes that are not efficiently scalable. The technological requirements for even the simplest gates in the KLM proposal initially seemed out of reach. However, Ralph, White, Munro and Milburn soon showed that, in principle, demonstrations of key gates and techniques could be achieved with current technology. The objective of the research undertaken in this project was to produce, in three years, a prototype two-qubit gate for photons using the KLM linear optics quantum computation approach, and to develop a blue-print for a multiple qubit device that might be implemented over a longer time scale. A non-deterministic two-qubit gate was demonstrated that operates with high fidelity. A number of key tasks were demonstrated using this gate, and several theoretical investigations of short, medium, and longer term issues for the LOQC approach were successfully completed.
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.
We investigate the computational power of passive and active linear optical elements and photo-detectors. We show that single photon sources, passive linear optics and photo-detectors are sufficient for implementing reliable quantum algorithms. Feedback from the detectors to the optical elements is required for this implementation. Without feedback, non-deterministic quantum computation is possible. A single photon source sufficient for quantum computation can be built with an active linear optical element (squeezer) and a photo-detector. The overheads associated with using only linear optics appear to be sufficiently low to make quantum computation based on our proposal a viable alternative.