Each year, the gap between theoretical proposals and experimental endeavours to create quantum computers gets smaller, driven by the promise of fundamentally faster algorithms and quantum simulations. This occurs by the combination of experimental ingenuity and ever simpler theoretical schemes. This thesis comes from the latter perspective, aiming to find new, simpler ways in which components of a quantum computer could be built. We first search for ways to create quantum gates, the primitive building blocks of a quantum computer. We find a novel, low-control way of performing a two-qubit gate on qubits encoded in a decoherence-free subspace, making use of many-body interactions that may already be present. This includes an analysis of the effect of control errors and magnetic field fluctuations on the gate. We then present novel ways to create three-qubit Toffoli and Fredkin gates in a single step using linear arrays of qubits, including an assessment of how well these gates could perform, for quantum or classical computation, using state-of-the-art ion trap and silicon donor technology. We then focus on a very different model from the normal circuit model, combining ideas from measurement-based quantum computation (MBQC) and holonomic quantum computation. We generalise an earlier model to show that all MBQC patterns with a property called gflow can be converted into a holonomic computation. The manifestation of the properties of MBQC in this adiabatically driven model is then explored. Finally, we investigate ways in which quantum information can be communicated between distant parties, using minimally engineered spin chains. The viability of using 1D Wigner crystals as a quantum channel is analysed, as well as schemes using ideal uniform spin chains with nextneighbour interactions, and edge-locking effects.
Each year, the gap between theoretical proposals and experimental endeavours to create quantum computers gets smaller, driven by the promise of fundamentally faster algorithms and quantum simulations. This occurs by the combination of experimental ingenuity and ever simpler theoretical schemes. This thesis comes from the latter perspective, aiming to find new, simpler ways in which components of a quantum computer could be built. We first search for ways to create quantum gates, the primitive building blocks of a quantum computer. We find a novel, low-control way of performing a two-qubit gate on qubits encoded in a decoherence-free subspace, making use of many-body interactions that may already be present. This includes an analysis of the effect of control errors and magnetic field fluctuations on the gate. We then present novel ways to create three-qubit Toffoli and Fredkin gates in a single step using linear arrays of qubits, including an assessment of how well these gates could perform, for quantum or classical computation, using state-of-the-art ion trap and silicon donor technology. We then focus on a very different model from the normal circuit model, combining ideas from measurement-based quantum computation (MBQC) and holonomic quantum computation. We generalise an earlier model to show that all MBQC patterns with a property called gflow can be converted into a holonomic computation. The manifestation of the properties of MBQC in this adiabatically driven model is then explored. Finally, we investigate ways in which quantum information can be communicated between distant parties, using minimally engineered spin chains. The viability of using 1D Wigner crystals as a quantum channel is analysed, as well as schemes using ideal uniform spin chains with nextneighbour interactions, and edge-locking effects.
Each year, the gap between theoretical proposals and experimental endeavours to create quantum computers gets smaller, driven by the promise of fundamentally faster algorithms and quantum simulations. This occurs by the combination of experimental ingenuity and ever simpler theoretical schemes. This thesis comes from the latter perspective, aiming to find new, simpler ways in which components of a quantum computer could be built. We first search for ways to create quantum gates, the primitive building blocks of a quantum computer. We find a novel, low-control way of performing a two-qubit gate on qubits encoded in a decoherence-free subspace, making use of many-body interactions that may already be present. This includes an analysis of the effect of control errors and magnetic field fluctuations on the gate. We then present novel ways to create three-qubit Toffoli and Fredkin gates in a single step using linear arrays of qubits, including an assessment of how well these gates could perform, for quantum or classical computation, using state-of-the-art ion trap and silicon donor technology. We then focus on a very different model from the normal circuit model, combining ideas from measurement-based quantum computation (MBQC) and holonomic quantum computation, showing that all MBQC patterns with a property called \emph{gflow} can be converted into a holonomic computation. The manifestation of the properties of MBQC in this adiabatically driven model is then explored. Finally, we investigate ways in which quantum information can be communicated between distant parties, using minimally engineered spin chains. The viability of using 1D Wigner crystals as a quantum channel is analysed, as well as schemes using ideal uniform spin chains with next-neighbour interactions, and edge-locking effects.
The ability to manipulate individual quantum systems in a precise way has led to a new era of quantum technologies, including quantum computation and quantum simulation. In this thesis we present several new implementations of these quantum technologies. We first aim at addressing current experimental challenges for quantum dot based quantum computing. We propose a systematic way to study the dynamics of nuclear spin, which is responsible for the short electron spin coherence time. Our calculation is based on diffusion model and is consistent with experiments. We also invent a novel protocol to realize high-fidelity ultrafast universal quantum gate in recently-developed quantum dot molecule system. Experimental realization of our protocol requires only a simple time engineering of optical pulses. We then propose a new quantum state transfer scheme for Nitrogen-Vacancy center based quantum computer, which is applicable at room temperature. Our method accomplishes high fidelity robust quantum state transfer through uncontrolled thermal nitrogen spin chain between two remote NV registers. Our next study helps building a hybrid quantum computer by entangling disparate systems using photonic links. The photons emitted from two types of system need to be matched in both frequency and pulse shape. We propose a simple method to match the emitted pulse shape from two qubit systems with different transition linewidths. We then focus on quantum simulation with trapped ions. We show the possibility of observing a novel type of temperature driven structural phase transition in trapped ion chain, which originates from anharmonic interaction between different vibrational modes. Afterward, an experimental protocol to simulate a conceptually new state of matter, called time crystal, is proposed based on ions trapped in a ring trap. Finally, we propose two new applications based on the recently developed trapped ion quantum simulator of spin models: (1) simulation of Haldane-Shastry model, which opens the way of experimental study to a remarkable theoretical model involving spin liquid ground state and fractional excitations (2) observation of prethermalization and dynamical phase transition, which are poorly understood non-equilibrium phenomena in closed quantum many-body system.
Quantum computing and quantum information science are two recently discovered and rapidly growing fields of physics that show substantial promise in providing new and valuable technologies in the foreseeable future. Large-scale quantum computers, if ever realized experimentally, are likely to outperform their classical counterparts in a number of important computational tasks, the most important of which may be the accurate simulation of many-body quantum systems such as the ones encountered in physics, chemistry and life sciences. This thesis investigates the problem of controlling quantum systems for the purpose of performing quantum information processing tasks. The problem is approached from a theoretical and simulational viewpoint. The work contained here encompasses a range of levels of abstraction. Firstly, we discuss the decomposition of abstract multiqubit logic gates into sequences of simple elementary gates. Secondly, we study the local commutational properties of two-qubit gates using local gate invariants. Thirdly, we develop methods for the physical implementation of the elementary gates through the control of specific quantum systems, possibly in the presence of noise and decoherence. We present a new, almost optimal n-qubit gate decomposition based on the cosine-sine decomposition, which utilizes a likewise new intermediate quantum circuit structure we call a uniformly controlled gate. We then show how they can be used in constructing a general state transformation circuit. Both of the resulting circuits can be efficiently implemented using nearest-neighbor gates which makes their physical realization simpler. A local gate invariant is introduced which can be used to assess the suitability of two-qubit gates for serving as the entangling gate in elementary gate libraries. Finally, we develop numerical optimization methods for finding near-optimal control sequences for generating oneand two-qubit gates, both in closed quantum systems and in the presence of Markovian noise.
The last two decades have witnessed the rapid growth of quantum information processing as an active field of multidisciplinary science and technology. Tremendous theoretical and experimental progress has been made in quantum communication and quantum computation, and it seems clear that some of this progress will soon result in practical applications outside the laboratory. Quantum computation aims to build a quantum computer and to explore the origins and limits of quantum computing power. The original circuit model of a quantum computer, due to Deutsch, has a strong formal similarity with the circuit model of a classical computer. Both models depict a computation as processing via the wiring of a number of fiducial gates, each of which dynamically couples a small number of input (qu)bits in a controlled manner. In other words, unitary evolution is the basic mechanism of information processing in the circuit model of quantum computers. Starting with a given fixed state of many qubits, measurement based quantum computation (MBQC) processes information by applying a sequence of measurements to designated qubits in designated bases. This is remarkable, given the probabilistic nature of quantum measurement and the murky physical status of the dynamics of 'wavefunction collapse'. The final result of the computation is determined from the classical data of all the measurement outcomes. There exist two principle models: the teleportation based model and the 'one-way quantum computer' of 'cluster state computation'. The formalism of cluster states has proven to be a powerful way of describing the essential entanglement resources needed to perform quantum information processing. Unlike the circuit model, the MBQC models have no natural classical counterpart. There are a number of physical architectures for which measurements on the relevant systems are more easily performed than controlled unitary evolution. Moreover, it appears the MBQC models can offer novel computational benefits, especially regarding issues of fault-tolerance and parallelizability of algorithms. As a result, the theory of MBQC is now shaping the latest experimental proposals across the full spectrum of quantum information processing technologies. Naturally, understanding the scope of measurement based quantum computation is also yielding many insights into what is necessary (as opposed to merely sufficient) for us to harness the power of quantum computers. Quantum communication aims to offer efficient and secure ways of information exchange, directly based on quantum mechanics. Photons serve as natural information carriers, owing to their robustness against decoherence. A major problem for photonic communication systems is due to photon loss. It turns out that this difficulty can be overcome by the quantum repeater, a measurement-based technique. The basic idea is to divide the transmission channel into many segments and perform some quantum measurement on each segment. Additional measurement-based protocols and technologies have also been demonstrated to improve the quality of quantum communication, such as entanglement swapping and purification. The articles in this invited Focus Issue cover topics both in measurement-based quantum communication and computation, but the emphasis is given to quantum computation. A significant number of articles deal with the preparation of cluster states, the experimental realization of a one-way quantum computer, and the associated efficiency and benefits. We hope that you will find that some of these new results are of interest to you, and further hope that the issue will increase your interest in this interdisciplinary research field if you are a non-expert. Focus on Measurement-Based Quantum Information Processing Contents A proof-of-principle experiment of eliminating photon-loss errors in cluster states Wei-Bo Gao, Xiao-Qi Zhou, Jin Zhang, Tao Yang and Jian-Wei Pan Continuous variable multipartite entanglement and optical implementations of quantum communication networks Yimin Lian, Changde Xie and Kunchi Peng Generalized flow and determinism in measurement-based quantum computation Daniel E Browne, Elham Kashefi, Mehdi Mhalla and Simon Perdrix The entanglement of the four-photon cluster state C Schmid, N Kiesel, W Wieczorek and H Weinfurter Optical zeno gate: bounds for fault tolerant operation Patrick M Leung and Timothy C Ralph Towards experimental entanglement connection with atomic ensembles in the single excitation regime Julien Laurat, Chin-wen Chou, Hui Deng, Kyung Soo Choi, Daniel Felinto, Hugues de Riedmatten and H J Kimble Towards minimal resources of measurement-based quantum computation Simon Perdrix Experimental realization of a quantum game on a one-way quantum computer Robert Prevedel, Andre Stefanov, Philip Walther and Anton Zeilinger Fundamentals of universality in one-way quantum computation M Van den Nest, W Dur, A Miyake and H J Briegel Loss tolerant linear optical quantum memory by measurement-based quantum computing Michael Varnava, Daniel E Browne and Terry Rudolph Graph state generation with noisy mirror-inverting spin chains Stephen R Clark, Alexander Klein, Martin Bruderer and Dieter Jaksch One-way quantum computing in adecoherence-free subspace M S Tame, M Paternostro and M S Kim Cluster state preparation using gates operating at arbitrary success probabilities K Kieling, D Gross and J Eisert Topological fault-tolerance in cluster state quantum computation R Raussendorf, J Harrington and K Goyal Strategies for the preparation of large cluster states using non-deterministic gates Peter P Rohde and Sean D Barrett A repeat-until-success quantum computing scheme A Beige, Y L Lim and L C Kwek Efficient growth of complex graph states via imperfect path erasure Earl T Campbell, Joseph Fitzsimons, Simon C Benjamin and Pieter Kok Investigation of a single-photon source based on quantum interference T B Pittman, J D Franson and B C Jacobs Entanglement and local information access for graph states Damian Markham, Akimasa Miyake and Shashank Virmani The efficiencies of generating cluster states with weak nonlinearities Sebastien G R Louis, Kae Nemoto, W J Munro and T P Spiller A direct approach to fault-tolerance in measurement-based quantum computation via teleportation Marcus Silva, Vincent Danos, Elham Kashefi and Harold Ollivier Experimental ancilla-assisted qubit transmission against correlated noise T Yamamoto, R Nagase, J Shimamura, S K Ozdemir, M Koashi and N Imoto Terry Rudolph, Imperial College, London, UK Jian-Wei Pan, University of Science and Technology of China, Hefei, People's Republic of China and Universitat Heidelberg, Germany
Quantum information and quantum computation is an area of quantum mechanics which utilizes quantum properties of particles in schemes for computation. These quantum schemes have been shown to improve computational capabilities for some systems. In quantum computation, the decoherence problem is a limiting factor. Decoherence is the process of loss of quantum information due to interaction from the environment, which puts a limit to how long a quantum computation is valid. There are ways to limit the effect of decoherence. The idea of a noiseless subsystem is to encode the quantum information in a smaller subsystem of the physical system that is not affected by decoherence. Holonomic quantum computation encodes quantum information in holonomies, making it more robust and less affected by decoherence. In this report, these two concepts are combined by encoding one logical qubit in three physical spin-1 particles. The approach to combine these concepts is entirely analytical. A Hamiltonian acting on the physical system is derived. To achieve a result which is possible to implement experimentally, the analytical derivation utilizes permutation operators to derive the Hamiltonian, which is known to be implementable experimentally. A resulting Hamiltonian to implement the scheme is derived, using only permutaion operators. Both a one-qubit gate and a two-qubit gate is derived, which forms a universal set allowing all possible quantum computation. The resulting scheme seems to only use two-body interactions. The project has shown that holonomic quantum computation in a noiseless subsystem using threephysical spin-1 particles is possible. The resulting scheme only using two-body interactions is of a large interest since this simplifies the experimental implementation.
One of the most essential processes in classical computation is that related to the information manipulation; each component or register of a computer needs to communicate to others by exchanging information encoded in bits and transforming it through logical operations. Hence the theoretical study of methods for information transfer and processing in classical information theory is of fundamental importance for telecommunications and computer science, along with study of errors and robustness of such proposals. When adding the quantum ingredient, there arises a whole new set of paradigms and devices, based on manipulations of \\emph{qubits}, the quantum analogues of conventional data bits. Such systems can show enormous advantage against their classical analogues, but at the same time present a whole new set of technical and conceptual challenges to overcome. The full and detailed understanding of quantum processes and studies of theoretical models and devices therefore provide the first logical steps to the future technological exploitation of these new machines. In this line, this thesis focuses on spin chains as such theoretical models, formed by series of coupled qubits that can be applied to a wide range of physical systems, and its several potential applications as quantum devices. In this work spin chains are presented as reliable devices for quantum communication with high transfer fidelities, entanglement generation and distribution over distant parties and protected storage of quantum information. Methods to design these tools to have some robustness against errors and noise are provided, giving optimism for future quantum technologies.