We extend a previous proposal for performing deterministic quantum computation using coherent states and linear optics by examining a new version of one of the gates which offers several advantages.
Quantum computing promises a new paradigm of computation where information is processed in a way that has no classical analogue. There are a number of physical platforms conducive to quantum computation, each with a number of advantages and challenges. Single photons, manipulated using integrated linear optics, constitute a promising platform for universal quantum computation. Their low decoherence rates make them particularly favourable, however the inability to perform deterministic two-qubit gates and the issue of photon loss are challenges that need to be overcome. In this thesis we explore the construction of a linear optical quantum computer based on the cluster state model. We identify the different necessary stages: state preparation, cluster state construction and implementation of quantum error correcting codes, and address the challenges that arise in each of these stages. For the state preparation, we propose a series of linear optical circuits for the generation of small entangled states, assessing their performance under different scenarios. For the cluster state construction, we introduce a ballistic scheme which not only consumes an order of magnitude fewer resources than previously proposed schemes, but also benefits from a natural loss tolerance. Based on this scheme, we propose a full architectural blueprint with fixed physical depth. We make investigations into the resource efficiency of this architecture and propose a new multiplexing scheme which optimises the use of resources. Finally, we study the integration of quantum error-correcting codes in the linear optical scheme proposed and suggest three ways in which the linear optical scheme can be made fault-tolerant.
The use of photons as qubits is a promising implementation for quantum computation. The inability of photons to interact, especially with the environment, makes them an ideal physical candidate. However, this also makes them a difficult system to perform two qubit gates on. Recent breakthroughs in photonic quantum computing have shown methods around the requirement of direct photon-photon interaction. In this thesis we study three recently discovered schemes for optical quantum computation. \n \n We first investigate the so called linear optical quantum computing (LOQC) scheme, exploring a method to improve the original proposal by constructing a photon-number QND detector that succeeds with a high probability. In doing this we present a new type of LOQC teleporter, one that can detect the presence of a single photon in an arbitrary polarisation state when the input state is a sum of vacuum and multi-photon terms. This new type of teleporter is an improvement on the original scheme in that the entangled states required can be made offline with fewer entangling operations. \n \n We next investigate the so called quantum bus (qubus) scheme for photonic quantum computing. We show a scheme to measure the party of n qubit states by using a single qubus mode, controlled rotations and displacements. This allows for the syndrome measurements of any stabilizer quantum error correcting code. We extend these results to a fault tolerant scheme to measure an arbitrary Pauli operator of weight n, incorporating so called single bit teleportations. We investigate the construction of a Toffoli gate by using a single qubus mode, controlled rotations and displacements that works with a success probability of at least 25%. We also investigate the use of single bit teleportations to construct a universal set of gates on coherent state type logic and in the construction of cluster states. \n \nWe finally investigate the optical Zeno gate, a gate that uses the Zeno effect in the form of two photon absorbers to induce a CSIGN. We model realistic two photon absorption and include realistic single photon loss for this gate, examining the use of encoding to overcome the single photon loss, showing that our results are competitive with the leading equivalent LOQC scheme.
We suggest an efficient scheme for quantum computation with linear optical elements, where the qubits are encoded in single photon states. The scheme reduces the resources required per logical gate by several orders of magnitude, compared to an earlier proposal of Knill, Laflamme, and Milburn, while the resource overhead per gate is independent of the length of the computation. A central feature of the scheme, enabling these improvements, is the prior construction of a "linked" photon state designed according to the particular quantum circuit one wishes to process. Once this state has been successfully prepared, the computation is pursued deterministically by a sequence of teleportation steps.