Linear optical quantum computing (LOQC) seems attractively simple: Information is borne entirely by light and processed by components such as beam splitters, phase shifters, and detectors.However, this very simplicity leads to limitations, such as the lack of deterministic entangling operations, which are compensated for by using substantial hardware overheads.Here, we quantify the resource costs for full-scale LOQC by proposing a specific protocol based on the surface code.With the caveat that our protocol can be further optimized, we report that the required number of physical components is at least 5 orders of magnitude greater than in comparable matter-based systems.Moreover, the resource requirements grow further if the per-component photon-loss rate is worse than 10 -3 or the per-component noise rate is worse than 10 -5 .We identify the performance of switches in the network as the single most influential factor influencing resource scaling.
Linear optical quantum computing (LOQC) seems attractively simple: Information is borne entirely by light and processed by components such as beam splitters, phase shifters, and detectors.However, this very simplicity leads to limitations, such as the lack of deterministic entangling operations, which are compensated for by using substantial hardware overheads.Here, we quantify the resource costs for full-scale LOQC by proposing a specific protocol based on the surface code.With the caveat that our protocol can be further optimized, we report that the required number of physical components is at least 5 orders of magnitude greater than in comparable matter-based systems.Moreover, the resource requirements grow further if the per-component photon-loss rate is worse than 10 -3 or the per-component noise rate is worse than 10 -5 .We identify the performance of switches in the network as the single most influential factor influencing resource scaling.
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.
In order to place an upper bound on the tolerable amount of photon loss at the detectors, we calculate the error threshold for the linear optics quantum computing proposal by Knill, Laflamme, and Milburn [Nature (London) 409, 46 (2001)] under an error model where photon detectors have efficiency <100 but all other components---such as single photon sources, beam splitters, and phase shifters---are perfect and introduce no errors. We make use of the fact that the error model induced by the lossy hardware is that of an erasure channel, i.e., the error locations are always known. Using a method based on a Markov chain description of the error correction procedure, our calculations show that, with the 7 qubit Calderbank--Shor--Steane quantum code, the gate error threshold for fault tolerant quantum computation is bounded below by a value between 1.78% and 11.5% depending on the construction of the entangling gates.
Linear Optical Quantum Computing (LOQC) is emerging as a promising technology in large-scale quantum computing. Corresponding devices, including linear optical circuits, are rapidly growing in size and fabrication precision. However, even with improved quality, the circuits still exhibit imperfections leading to photon loss or phase noise that vary across the circuit. Already small deficiencies can have a vast impact on both accuracy and efficiency. For computations that do not require the entire linear optical circuit, so-called subcircuits, one can choose where to perform the computation, opening optimization opportunities that are addressed by subcircuit compilation. Current compilers spread the subcircuit's computation across the entire circuit, connecting the same input and output ports, thereby failing to fully exploit the optimization opportunities. However, given the subcircuit's reduced size compared to the entire circuit, one can keep its implementation localized and intentionally route photons to connect good input and output ports. This, however, is a highly non-trivial task, as numerous options must be weighed against one another, and the quality of the solution is influenced by a wide range of hardware parameters. In particular, the reflectivities of imperfect beam splitters can lead to photon losses during routing, which must be traded off against losses at the input and output ports due to imperfect transmission rates. Since current compilers do not account for these effects, we propose the first efficient subcircuit compilation method that optimizes for the coincidence rate, the probability of successfully measuring all desired photons, by handling hardware imperfections. Our evaluations demonstrate significant improvement over existing methods in robustness against phase noise and significantly increased coincidence rates across all benchmarks of up to plus 33.2%.
The realisation of a fault-tolerant universal quantum computer requires the ability to implement and control large scale quantum systems while maintaining physical noise levels sufficiently low to avoid errors in the computation. Fusion-Based Quantum Computation (FBQC) – a framework in which entangling fusion measurements are performed between constant-size entangled resource states – has emerged as a promising approach to achieve this, especially in the context of Linear Optical Quantum Computing (LOQC). Most FBQC schemes proposed so far use physical fusions between two qubits. In this thesis, we study the impact of using multi-way fusions, which act on more physical qubits simultaneously, on the error tolerance and resource overhead of linear optical FBQC architectures. The main challenge of LOQC is that entangling operations are inherently non-deterministic, leading to large resource overheads. The success probability is known to decrease exponentially with the number of input qubits. We introduce novel fusion circuits which succeed at higher rates and/or entangle subsets of inputs upon failure. We present a framework to analyse the impact of noise on these circuits and describe the resulting errors as effective Pauli error channels on the input qubits. We also examine the application of multi-way fusion circuits within a linear optical FBQC architecture. We find that they can be used to generate resource states with significantly reduced Pauli error rates and footprint compared to two-way fusions alone, in turn resulting in linear optical FBQC architectures with higher error tolerance and lower resource overheads. We also investigate their use as primitives of the computation, applied between different resource states, and find evidence that two-way fusions remain preferable in this context due to their lower erasure rate.
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.
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.