We review the physical principles behind measurement-based quantum information processing with optical fields. The original Knill–Laflamme–Milburn (KLM) scheme, based on single-photon states, is explained, as well as extensions of the scheme inspired by the idea of cluster state quantum computing, which dramatically reduce the resources required for implementation. A careful analysis of the intrinsic error sources in optical cluster state methods indicates that fault-tolerant quantum gates are feasible given developments in current technology. The main impediment to progress is the lack of single-photon sources and we briefly review what kinds of sources are needed. We conclude with a discussion of phase-shift coherent state codes and discuss a possible implementation in circuit quantum electrodynamics.
We review the physical principles behind measurement-based quantum information processing with optical fields. The original Knill–Laflamme–Milburn (KLM) scheme, based on single-photon states, is explained, as well as extensions of the scheme inspired by the idea of cluster state quantum computing, which dramatically reduce the resources required for implementation. A careful analysis of the intrinsic error sources in optical cluster state methods indicates that fault-tolerant quantum gates are feasible given developments in current technology. The main impediment to progress is the lack of single-photon sources and we briefly review what kinds of sources are needed. We conclude with a discussion of phase-shift coherent state codes and discuss a possible implementation in circuit quantum electrodynamics.
In the previous chapter we developed some of the basic aspects of quantum information processing with single photons as qubits. Apart from noting the obvious benefit of using light for quantum communication, we identified some difficulties in manipulating quantum information that is encoded in photons. In particular, it is difficult to construct two-qubit gates for photonic qubits. In this chapter we will have to face this difficulty head-on in our discussion of quantum computation with single photons and linear-optical elements. The possibility of a quantum computer based on single photons, linear optics, and photon counting was demonstrated in a landmark paper by Knill, Laflamme, and Milburn in 2001. Their protocol is commonly referred to as the ‘ klm protocol’. In subsequent years, the klm protocol has been dramatically slimmed down in terms of complexity and the necessary resources to create the universal set of quantum gates. For pedagogical reasons we give the streamlined version here, and we briefly describe the original klm protocol in Appendix 2. We will make extensive use of the results in Section 1.4 about mode transformations, and Section 2.3 about cluster-state quantum computing. We start this chapter, however, with a description of linear-optical networks, and how they fail as deterministic quantum computers. In Section 6.2 we discuss the principle of post-selection, and how this can be used to create probabilistic gates with deterministic feed-forward control.
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.
Compared with other physical platforms for Quantum Information Processing (QIP), photons have the unique advantages of travelling over free-space links or optical fiber with relatively low decoherence and of propagating with minimal coupling to the environment, while also being easily coupled to existing telecommunications technology. The R&D of various single photon and entangled photon generation technologies and the linear-optical implementations of quantum computation and communication are now surveyed and analyzed in a structured manner. We discuss photonic qubit degrees of freedom (polarization, time-bin, path, frequency and Orbital angular momentum), determine sources such as deterministic quantum-dot based sources and probabilistic sources based on spontaneous parametric down conversion (SPDC), and review architectures for Linear Optical Quantum Computation (LOQC), such as the Knill–Laflamme–Milburn (KLM) protocol and measurement-based quantum computation. Building on the density-matrix treatment of biexciton–exciton coherent dynamics in semiconductor quantum dots, we recapitulate the development of two-pulse coherent control schemes for generation and readout of photonic qubits in these systems and how they have been stretched towards optical control of logic gates. A comparative performance framework is established along the lines of source brightness, entanglement fidelity, photon indistinguishability, channel loss and scalability, which is illustrated by simulated performance plots and tabulated against literature numbers. Remaining hurdles in the field regarding issues of photon loss, scalable multiplexing, deterministic two-qubit interaction, and its integration with a quantum memory are highlighted and a perspective is provided on hybrid photonic–matter architectures for fault-tolerant quantum networks.
Quantum technology is a fundamentally new way of harnessing Nature and it has potential for a truly revolutionary innovation and promise the next generation of products with exciting and astounding properties that will affect our lives profoundly. They will have a great influence in defence, aerospace, energy and telecommunications sectors. If this process is to continue in the future, new, quantum technology must replace or supplement what we have now. In particular, Quantum Information Technology can support entirely new modes of information processing based on so called quantum bits or qubits. Its eventual impact may be as great as or greater than that of its classical predecessor. There is almost daily progress in developing promising technologies for realizing quantum information processing with various advantages over its classical counterpart. Logic gates and wires are becoming smaller, and soon they will be made out of only a handful of atoms. Photons are unsurpassed as qubits in terms of decoherence times, mobility, and achievability of high-fidelity single-qubit operations. Thus far, entanglement experiments in optics have been very clean, and an optical quantum processor would obviously have an advantage in connecting to a quantum “network” (no need to convert between stationary and flying qubits). All-optical quantum computing became feasible when, in 2001, a breakthrough known as the KLM (Knill-Laflamme-Milburn) scheme showed that scalable quantum computing is possible using only single-photon sources, detectors, and linear optical circuits. This scheme relies on quantum interference with auxiliary photons at a beam splitter and single-photon detection to induce not-deterministic interactions. Nowadays, the limits of the original KLM linear optics quantum computing proposal, as well as the more recent cluster and graph-state approaches, in addition to various nonlinear optical approaches are explored, but several challenges must be overcome. The most important issues are the practical scalability of quantum circuits, the ability to perform quantum logic gates with error rates below the fault-tolerant threshold and their incorporation into large-scale quantum circuits with realistic physical resources and single-photon detectors packed on an optical chip. Optical integrated circuits offer great potential for realizing previously unfeasible large-scale quantum circuits. However, this architecture suffers not only of the overhead of multiple sources, detectors and ancillary qubits, but it needs to maintain the complete coherence between single photons in which qubits are encoded. The idea to reduce the overhead due to multiple single photon sources with very high degree of reciprocal coherence exploits the possibility to encode the whole state space in a complex optical circuit based on Multiple Rail (MR) Architecture: a particular state in input is encoded in the quantum superposition of a coherent light beam trough the different waveguides, so that it is possible to reproduce the mathematical and physical aspects of quantum entanglement in classical beams of light. Multiple Rail Architecture provides the realization of so called Classical or, better, Intra-System Entanglement. In practics a reconfigurable optical matrix of interconnected MachZehnder provides the representation of the complex Hilbert-Schmidt space where the quantum operation lives. This integrated system on chip can be both Photonics and/or Plasmonics. By exploiting this idea we are able to obtain all the universal quantum gates as SWAP, CNOT, CPHASE, TOFFOLI for two qubits and for multiqubits cases. The most important goal is the possibility to perform deterministic Bell measurements: in usual optical schemes the probability of success of Bell measurements is ½, while the novel architecture provides the possibility to discriminate all Bell states, so that the teleportation can become completely deterministic.
We propose an approach to optical quantum computation in which a deterministic entangling quantum gate may be performed using, on average, a few hundred coherently interacting optical elements (beam splitters, phase shifters, single photon sources, and photodetectors with feedforward). This scheme combines ideas from the optical quantum computing proposal of Knill, Laflamme, and Milburn [Nature (London) 409, 46 (2001)]], and the abstract cluster-state model of quantum computation proposed by Raussendorf and Briegel [Phys. Rev. Lett. 86, 5188 (2001)]].