Proposals for linear optical quantum computation (LOQC) rely on quantum interference between single photons which, when coupled with photon detection, provides a mechanism to generate photonic entanglement. However, ideal quantum interference between photons only occurs if the photons are completely indistinguishable in all degrees of freedom except the one being interfered. In practice, no photons will be perfectly indistinguishable and therefore it is important to understand how using partially-distinguishable photons will affect the quantum information within the linear optical quantum computer. Here we describe how states of partially-distinguishable photons are transformed by linear-optical networks and measured by photon-counting detectors. In addition we show how to calculate the logical content of a given photonic state containing partially-distinguishable photons. Using a realistic model of single photon sources, we then apply these tools to calculate the resulting logical error rates on recent proposals for universal LOQC. Understanding the connection between physical imperfections and logical errors is crucial in assessing the fault-tolerance prospects of a quantum computation platform. Our results will help inform error correction strategies and allow one to specify the necessary fabrication and operational tolerances required for scalability.
Proposals for linear optical quantum computation (LOQC) rely on quantum interference between single photons which, when coupled with photon detection, provides a mechanism to generate photonic entanglement. However, ideal quantum interference between photons only occurs if the photons are completely indistinguishable in all degrees of freedom except the one being interfered. In practice, no photons will be perfectly indistinguishable and therefore it is important to understand how using partially-distinguishable photons will affect the quantum information within the linear optical quantum computer. Here we describe how states of partially-distinguishable photons are transformed by linear-optical networks and measured by photon-counting detectors. In addition we show how to calculate the logical content of a given photonic state containing partially-distinguishable photons. Using a realistic model of single photon sources, we then apply these tools to calculate the resulting logical error rates on recent proposals for universal LOQC. Understanding the connection between physical imperfections and logical errors is crucial in assessing the fault-tolerance prospects of a quantum computation platform. Our results will help inform error correction strategies and allow one to specify the necessary fabrication and operational tolerances required for scalability.
It is believed that the exotic properties of quantum systems can be harnessed to perform certain computational tasks more efficiently than classical theories allow. The production, manipulation and detection of single photons constitutes a potential platform for performing such non-classical information processing. The development of integrated quantum photonics has provided a miniaturised, monolithic architecture that is promising for the realisation of near-term analog quantum devices as well as full-scale universal quantum computers. In this thesis we investigate the viability of these photonic quantum computational approaches from an experimental and theoretical perspective. We implement the first universally reconfigurable linear optical network; a key capability for the rapid prototyping of photonic quantum protocols. We propose and demonstrate the use of these devices as a new platform for the programmable quantum simulation of molecular vibrational dynamics. We then tackle an important outstanding problem in linear optical quantum computing; quantifying how partial-distinguishability amongst photons aff ects logical error rates. Finally, we propose a series of schemes aimed at counteracting these distinguishability errors in order to achieve practical quantum technologies with imperfect photonic components.
Quantum computing is an exciting field that promises great improvements to our ability to solve certain intractable classes of problem. Implementing a quantum computer will require a physical system in which quantum effects are strongly evident. Many different physical systems have been proposed for this task, including ion traps, quantum dots, neutral atoms and photons. This thesis focuses on optical implementations of a quantum computer, and specifically on single-photon designs, as opposed to those utilising coherent states. Photonic systems have shown a great deal of promise for quantum computing tasks since it was shown by Knill, Laflamme and Milburn (KLM) that scalable efficient quantum computing could be performed using only linear optical elements and measurement. This was made viable through the use of error-correcting codes. The work in this thesis covers the use of error-correcting codes in single-photon linear optics quantum computing (LOQC). The central feature of these schemes is the parity code introduced by KLM and used to overcome the gate errors that are inherent in this type of LOQC. First is a discussion of an improved scheme that incorporates the fusion gates used in Browne and Rudolph's cluster state proposal in order to simplify the encoding and gate procedures. This results in high-probability gates with a resource usage comparable to the cluster state schemes. The remainder of the thesis examines the application of further error correcting codes to handle other errors that may arise in any practical implementation of an optical quantum computer. The most significant type of error in any optical system is photon loss, and hence an extension of the parity code is presented that allows loss errors to be detected and corrected. Procedures for performing universal quantum computation whilst employing this encoding are also described. These enable the establishment of loss thresholds for parity-state based LOQC, revealing this code is capable of handling up to 10\% loss in all elements during general computation, or 17\% if it is used solely as an active memory. Although loss is the most common type of optical error, other types of error will also become an issue when attempting to produce large quantum computing systems. An analysis of the error thresholds and resource usage which can be expected when applying a general error correcting code such as the Steane code to this type of LOQC system is also presented. The error thresholds and resource requirements established are greater than those found for cat state optical quantum computing, but fall below those calculated for cluster states. However, the resource requirements of the scheme are significantly smaller than the cluster state requirements for an equivalent circuit. Finally, a new experiment is proposed, achievable with today's technology, for testing the loss-tolerant encoding described earlier. Expansions of the experiment that would demonstrate tolerance of actual experimental error are also discussed.
One of the most significant challenges facing the development of linear optics quantum computing (LOQC) is mode mismatch, whereby photon distinguishability is introduced within circuits, undermining quantum interference effects. We examine the effects of mode mismatch on the parity (or fusion) gate, the fundamental building block in several recent LOQC schemes. We derive simple error models for the effects of mode mismatch on its operation, and relate these error models to current fault-tolerant-threshold estimates.
We previously established that in principle, it is possible to quantum compute using passive linear optics with photo-detectors (quant-ph/0006088). Here we describe techniques based on error detection and correction that greatly improve the resource and device reliability requirements needed for scalability. The resource requirements are analyzed for ideal linear optics quantum computation (LOQC). The coding methods can be integrated both with loss detection and phase error-correction to deal with the primary relaxation processes in non-ideal optics, including detector inefficiencies. The main conclusion of our work is that the resource requirements for implementing quantum communication or computation with LOQC are reasonable. Furthermore, this work clearly demonstrates how special knowledge of the error behavior can be exploited for greatly improving the fault tolerance and overheads of a physical quantum computer.
Quantum photonic technologies have many exciting applications including secure commu- nication, quantum enhanced measurement and quantum computing. Linear optical quantum computing (LOQC) is a technology of particular interest - especially given that recent progress in on-chip waveguide technology removes the requirement for complex and costly bulk optics setups and state-of-the-art detectors have detection efficiencies of over 90%. Arguably the largest remaining technological hurdle for LOQC is the development of a suitable photon source. A suitable source would produce single, indistinguishable photons deterministically. Additionally, it would be beneficial if the generated photons were entangled, as this can significantly reduce the degree of multiplexing needed to implement LOQC. Quantum dots are a suitable candidate system for these photon sources as they exhibit bright single photon emission and can act as the interface between light and a trapped spin qubit. These properties have resulted in proposals to generate multi-photon entangled states suitable for use in LOQC. This thesis presents some of the progress we have made towards the creation of a suitable photon source. After introducing the background material, we demonstrate pulsed resonant excitation using a single-electron-charged quantum dot. Deterministic excitation is demonstrated by performing Rabi oscillations and Ramsey interference in the excitonic population. We also investigate Ramsey interference in a Faraday geometry magnetic field and observe a variety of beats and oscillations in the interferograms. We develop a model to explain our results and conclude that controlling the phase between the two Ramsey interference pulses allows a degree of control over the state of the trapped spin. We then also demonstrate the coherent optical manipulation of a trapped spin in a Voigt geometry magnetic field. Once we have presented the manipulation of the excitonic state and the state of the trapped spin, we proceed to investigate the properties of the light produced by the resonant excitation of a quantum dot. Hong Ou Mandel interference experiments allow us to probe the indistinguishability of the photons resulting from the resonant excitation of the negative trion transition. Repeating the measurement using light generated from a similar system (this time with a trapped hole rather than a trapped electron) that is embedded in a micropillar cavity, we find that the cavity enhancement of the transition results is higher indistinguishabilities. We make use of this bright source of indistinguishable photons to perform an on-chip quantum enhanced measurement and observe the phase superresolution associated with N00N states. In the final experimental chapter, we propose and implement a scheme to generate multi- qubit single photon states. We show that by repeatedly driving a micropillar-cavity-enhanced Raman transition of a single-hole-charged quantum dot in a Voigt geometry magnetic field it is possible to coherently superpose a photon across multiple time bins. The scheme is conceptually similar to proposed schemes for producing multi-photon entangled states. Lastly, we propose a scheme that makes use of the capabilities shown in the three experimental chapters to overcome several of the experimental difficulties associated with generating multi-photon entangled states.
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.