Quantum optics is an extremely fruitful area of research in that it allows the probing of fundamental and basic science, as well as the opportunity to investigate potential applications that exploit these exotic phenomena. Entanglement is a uniquely quantum phenomenon that is a key feature of quantum mechanics. In this thesis we investigate the scalability of entangled states of light, as well as modest demonstrations of one-way quantum computations, based on a resource that exploits entanglement. Scalability has been a bottleneck of entanglement experiments since the first demonstrations began surfacing a few decades ago. In Part II of this thesis we investigate different methods of multiplexing quantum light modes in order to achieve a scalable architecture. 2 experiments are presented in spatial multiplexing, that lead to programmable linear optics networks that can produce up to 8 entangled modes. Building on this, and shifting domains we then demonstrate temporal multiplexing, where we entangle tens of thousands of quantum modes together in a highly entangled state called a cluster state. This is several orders of magnitude larger than any entangled state created to date, in any platform (be it atomic or electronic). The highly entangled cluster state is a universal resource for quantum computing, and we investigate a particular class of computations in Part III. We demonstrate that a cluster state consisting of only 4 highly entangled quantum modes is sufficient for universal 1-mode Gaussian quantum computing. Further, we demonstrate a tuneable entanglement gate that can be retrofitted to cluster states of arbitrary size or shape. Although the experiments in Part II and Part III are conceptually quite different, they employ very similar optical and electronic equipment. These experimental techniques as well as a survey of relevant quantum optics theory is presented in Part I.
Quantum optics is an extremely fruitful area of research in that it allows the probing of fundamental and basic science, as well as the opportunity to investigate potential applications that exploit these exotic phenomena. Entanglement is a uniquely quantum phenomenon that is a key feature of quantum mechanics. In this thesis we investigate the scalability of entangled states of light, as well as modest demonstrations of one-way quantum computations, based on a resource that exploits entanglement. Scalability has been a bottleneck of entanglement experiments since the first demonstrations began surfacing a few decades ago. In Part II of this thesis we investigate different methods of multiplexing quantum light modes in order to achieve a scalable architecture. 2 experiments are presented in spatial multiplexing, that lead to programmable linear optics networks that can produce up to 8 entangled modes. Building on this, and shifting domains we then demonstrate temporal multiplexing, where we entangle tens of thousands of quantum modes together in a highly entangled state called a cluster state. This is several orders of magnitude larger than any entangled state created to date, in any platform (be it atomic or electronic). The highly entangled cluster state is a universal resource for quantum computing, and we investigate a particular class of computations in Part III. We demonstrate that a cluster state consisting of only 4 highly entangled quantum modes is sufficient for universal 1-mode Gaussian quantum computing. Further, we demonstrate a tuneable entanglement gate that can be retrofitted to cluster states of arbitrary size or shape. Although the experiments in Part II and Part III are conceptually quite different, they employ very similar optical and electronic equipment. These experimental techniques as well as a survey of relevant quantum optics theory is presented in Part I.
Ever since its discovery, quantum mechanics has remained an intensely active field, and its real-world applications continue to unfold rapidly. In 1982, Richard Feynman proposed a new type of computer operating directly under quantum mechanics laws: – the quantum computer \cite{Feynman1982}. Compared with the classical computer, whose information is encoded in “bits”, the quantum computer, whose information is encoded in “quantum bits”, or “qubits”, will be able to perform calculations exponentially faster for such problems as factoring large integers into primes and simulating complicated quantum systems. Due to their extremely powerful calculation speeds and abilities, quantum computers have been the long-pursued dreams for both experimentalists and theorists in many research groups, government agencies, industrial companies, etc., and the fast-paced developments in their architecture and speed continue to make them more and more attractive. There are two principal models of quantum computing: the circuit model and the measurement-based model. The circuit model is similar to a traditional computer where there are inputs, gates and outputs. The measurement-based model is different, as it is crucially based on the cluster state, a type of highly entangled quantum state. In this new model, quantum computing begins with an initial cluster state and then carries out calculations by physical measurements of the cluster state itself along with feedforward. Thus, the cluster state serves as the material and resource for the entire set of calculations, and it is an extremely important part of measurement-based quantum computing. This thesis will discuss an experimental and theoretical work that holds the world record for the largest entangled cluster state ever created whose 60 qumodes (optical versions of qubits) are all available simultaneously. Moreover, the entangled state we created is not random, and it is a cluster state which meets the specific requirements for implementing quantum computing. In the race to build a practical quantum computer, the ability to create such a large cluster state is paramount. Also, our creative optical method to generate massive entanglement advances many other methods due to its high efficiency, super-compactness and large scalability. The entanglement proceeds from interfering multiple EPR entangled pairs, which are generated from the down-converting process of a nonlinear crystal in an optical parametric oscillator, into a very long dual-rail wire cluster state. Moreover, many copies of the same state can easily be obtained by merely adjusting the frequencies of the pump lasers. These cluster states serve as building blocks of the universal quantum computer, and also are, in their own right, important resources for studying and exploring quantum mechanics in large systems.
One-way quantum computation is a promising scheme for realizing large-scale quantum computation, where computation is done via measurements on a universal multi-mode entangled resource called cluster state. The capability of this method is determined by the size and the dimension of the cluster state; the size is roughly equivalent to the number of input modes times number of operation steps, while the dimension determines universality and fault tolerance of the computation. To achieve universality, two-dimensional cluster state is required. Among many approaches, time-domain multiplexing using optical system [1, 2] is a promising method where quantum state is encoded in a temporal wave packet. Although universality is still lacking, one-million-mode one-dimensional cluster state has been demonstrated with this approach [3].
Quantum computing promises exponential speedup for particular computational tasks, such as integer factoring, which bears importance for encryption technology, and quantum simulation, which holds vast scientific potential. Comparing with the traditional circuit-based quantum computers, one-way quantum computers are experimentally appealing because it requires only local measurements on an entangled resource called a cluster state. In this thesis, I first review the fundamental theory of one-way quantum computing and its experimental implementation using the quantum optical frequency comb. After that, I present two novel schemes for generating ultra-scalable cluster states with rich structures that can be used for universal quantum computing.
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.
Enabling large-scale and high-speed quantum computation is a key to practical quantum computation. Continuous-variable approach in optical systems offer advantages in scalability and speed by leveraging their temporal degree of freedom and inherent large carrier frequency. In this paper, we investigate the generation and manipulation of quantum entanglement through a time-domain multiplexing approach. By employing time-domain multiplexing, we generate a two-dimensional cluster state—a universal resource for large-scale quantum computation—and perform quantum operations in the time domain with cluster state. Additionally, our ongoing research focuses on the generation and measurement of broadband optical quantum entanglement through an optical parametric oscillator, which holds potential as a foundation for high-speed quantum computing surpassing limitations of existing systems. By further engineering the quantum entanglement, we have also theoretically formulated a practical teleportation-based architectures for quantum computation in time domain. These advancements form the groundwork for the development of practical optical quantum computation.
A quantum computer promises efficient processing of certain computational tasks that are intractable with classical computer technology. While basic principles of a quantum computer have been demonstrated in the laboratory, scalability of these systems to a large number of qubits, essential for practical applications such as the Shor algorithm, represents a formidable challenge. Most of the current experiments are designed to implement sequences of highly controlled interactions between selected particles (qubits), thereby following models of a quantum computer as a (sequential) network of quantum logic gates. Here we propose a different model of a scalable quantum computer. In our model, the entire resource for the quantum computation is provided initially in form of a specific entangled state (a so-called cluster state) of a large number of qubits. Information is then written onto the cluster, processed, and read out form the cluster by one-particle measurements only. The entangled state of the cluster thus serves as a universal substrate for any quantum computation. Cluster states can be created efficiently in any system with a quantum Ising-type interaction (at very low temperatures) between two-state particles in a lattice configuration.