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Making spintronic devices is a hot topic for future technical development. In this work the non-equilibrium dynamics of a single spin in a tunnel junction is analyzed and numerically simulated. This is done in order to understand the dynamics of e.g. a magnetic molecule between two metal contacts for future spintronic devices. The work starts with looking at the system in a many-body theory picture in order to derive the interesting properties of the system. An initial solution for the system is analytically calculated as well as for the dynamic case. The dynamic has then been numerically simulated in order to get the time evolution of the system. The results showed that the dynamics of the molecular spin induced a spin dependent charge and spin currents in the system and that the currents could be used to control the molecular spin. It showed qualitatively how different parameters, for example coupling strength, effect the system and what to consider when designing a system similar to this.

Thesis (Ph.D.) - University of Queensland, 2005. / Includes bibliography.

Trapped atomic ions are one of the most promising systems for building a quantum computer -- all of the fundamental operations needed to build a quantum computer have been demonstrated in such systems. The challenge now is to understand and reduce the operation errors to below the 'fault-tolerant threshold' (the level below which quantum error correction works), and to scale up the current few-qubit experiments to many qubits. This thesis describes experimental work concentrated primarily on the first of these challenges. We demonstrate high-fidelity single-qubit and two-qubit (entangling) gates with errors at or below the fault-tolerant threshold. We also implement an entangling gate between two different species of ions, a tool which may be useful for certain scalable architectures. We study the speed/fidelity trade-off for a two-qubit phase gate implemented in ⁴³Ca^+ hyperfine trapped-ion qubits. We develop an error model which describes the fundamental and technical imperfections / limitations that contribute to the measured gate error. We characterize and minimise various error sources contributing to the measured fidelity, allowing us to account for errors due to the single-qubit operations and state readout (each at the 0.1% level), and to identify the leading sources of error in the two-qubit entangling operation. We achieve gate fidelities ranging between 97.1(2)% (for a gate time t_g = 3.8 μs) and 99.9(1)% (for t_g = 100 μs), representing respectively the fastest and lowest-error two-qubit gates reported between trapped-ion qubits by nearly an order of magnitude in each case. We also characterise single-qubit gates with average errors below 10^-4 per operation, over an order of magnitude better than previously achieved with laser-driven operations. Additionally, we present work on a mixed-species entangling gate. We entangle of a single ⁴⁰Ca^+ ion and a single ⁴³Ca^+ ion with a fidelity of 99.8(5)%, and perform full tomography of the resulting entangled state. We describe how this mixed-species gate mechanism could be used to entangle ⁴³Ca^+ and ⁸⁸Sr^+, a promising combination of ions for future experiments.

In this thesis, I investigate quantum walks in quantum computing from three aspects: the insights, the implementation, and the applications. Quantum walks are the quantum analogue of classical random walks. For the insights of quantum walks, I list and explain the required components for quantizing a classical random walk into a quantum walk. The components are, for instance, Markov chains, quantum phase estimation, and quantum spectrum theorem. I then demonstrate how the product of two reflections in the walk operator provides a quadratic speed-up, in comparison to the classical counterpart. For the implementation of quantum walks, I show the construction of an efficient circuit for realizing one single step of the quantum walk operator. Furthermore, I devise a more succinct circuit to approximately implement quantum phase estimation with constant precision controlled phase shift operators. From an implementation perspective, efficient circuits are always desirable because the realization of a phase shift operator with high precision would be a costly task and a critical obstacle. For the applications of quantum walks, I apply the quantum walk technique along with other fundamental quantum techniques, such as phase estimation, to solve the partition function problem. However, there might be some scenario in which the speed-up of spectral gap is insignificant. In a situation like that that, I provide an amplitude amplification-based iii approach to prepare the thermal Gibbs state. Such an approach is useful when the spectral gap is extremely small. Finally, I further investigate and explore the effect of noise (perturbation) on the performance of quantum walks

Made available in DSpace on 2015-03-04T18:58:01Z (GMT). No. of bitstreams: 1 daniel_msc_final.pdf: 1791948 bytes, checksum: 1e3d1d81251eb6cff151799519eef3f9 (MD5) Previous issue date: 2014-06-23 / Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior / Classical random walks and quantum walks are studied in a whole variety of graphs in order to obtain some of its physical properties. In this work we analyze these walks over the SierpiŃski Carpet, obtaining two physical quantities: the standard deviation and the mixing time. Using simulations and fitting the points obtained over a curve, we found analytical expressions to describe the behaviour of both the standard deviation and the mixing time. When studying the quantum walk we used the QWalk software to run the simulations and generate statistics. We compare the results presenting the advantages and disadvantages of the quantum walk over the classical random one. / Passeios aleatorios classicos e passeios quanticos sao estudados em diversos grafos com o objetivo de se obter suas propriedades fisicas. Neste trabalho analisamos estes passeios no Tapete de Sierpinski com o foco em duas grandezas fisicas: o desvio padrao e o tempo de mistura. Atraves de simulacoes e usando regressao dos pontos sobre uma curva, encontramos expressoes analiticas para descrever o comportamento do desvio padrao e do tempo de mistura. No caso quantico usamos o programa QWalk para fazer as simulacoes e gerar as estatisticas. Comparamos os resultados apresentando as vantagens e desvantagens do passeio quantico sobre o classico.

Hu, Jianliang. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 88-105). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

One of the newer and rapidly developing approaches in quantum computing is based on "quantum walks," which are quantum processes on discrete space that evolve in either discrete or continuous time and are characterized by mixing of components at each step. The idea emerged in analogy with the classical random walks and stochastic techniques, but these unitary processes are very different even as they have intriguing similarities. This thesis is concerned with study of discrete-time quantum walks. The original motivation from classical Markov chains required for discrete-time quantum walks that one adds an auxiliary Hilbert space, unrelated to the one in which the system evolves, in order to be able to mix components in that space and then take the evolution steps accordingly (based on the state in that space). This additional, "coin," space is very often an internal degree of freedom like spin. We have introduced a general framework for construction of discrete-time quantum walks in a close analogy with the classical random walks with memory that is rather different from the standard "coin" approach. In this method there is no need to bring in a different degree of freedom, while the full state of the system is still described in the direct product of spaces (of states). The state can be thought of as an arrow pointing from the previous to the current site in the evolution, representing the one-step memory. The next step is then controlled by a single local operator assigned to each site in the space, acting quite like a scattering operator. This allows us to probe and solve some problems of interest that have not had successful approaches with "coined" walks. We construct and solve a walk on the binary tree, a structure of great interest but until our result without an explicit discrete time quantum walk, due to difficulties in managing coin spaces necessary in the standard approach. Beyond algorithmic interests, the model based on memory allows one to explore effects of history on the quantum evolution and the subtle emergence of classical features as "memory" is explicitly kept for additional steps. We construct and solve a walk with an additional correlation step, finding interesting new features. On the other hand, the fact that the evolution is driven entirely by a local operator, not involving additional spaces, enables us to choose the Fourier transform as an operator completely controlling the evolution. This in turn allows us to combine the quantum walk approach with Fourier transform based techniques, something decidedly not possible in classical computational physics. We are developing a formalism for building networks manageable by walks constructed with this framework, based on the surprising efficiency of our framework in discovering internals of a simple network that we so far solved. Finally, in line with our expectation that the field of quantum walks can take cues from the rich history of development of the classical stochastic techniques, we establish starting points for the work on non-Abelian quantum walks, with a particular quantum walk analog of the classical "card shuffling," the walk on the permutation group. In summary, this thesis presents a new framework for construction of discrete time quantum walks, employing and exploring memoried nature of unitary evolution. It is applied to fully solving the problems of: A walk on the binary tree and exploration of the quantum-to-classical transition with increased correlation length (history). It is then used for simple network discovery, and to lay the groundwork for analysis of complex networks, based on combined power of efficient exploration of the Hilbert space (as a walk mixing components) and Fourier transformation (since we can choose this for the evolution operator). We hope to establish this as a general technique as its power would be unmatched by any approaches available in the classical computing. We also looked at the promising and challenging prospect of walks on non-Abelian structures by setting up the problem of "quantum card shuffling," a quantum walk on the permutation group. Relation to other work is thoroughly discussed throughout, along with examination of the context of our work and overviews of our current and future work. / Graduation date: 2012

The fullerene cage provides an ideal, isolated environment for trapping spin active atoms such as nitrogen or phosphorous. Alignment of these endohedral fullerenes in linear arrays would have applications in quantum computing as the interactions between spin-active molecules can be easily controlled. Self-assembled molecular networks such as block copolymers, Langmuir-Blodgett films, and self-assembled monolayers are ideal for this purpose as the spacing and geometry can be easily tuned. This dissertation will discuss using each of these methods to achieve alignment or orientation of fullerenes for application in quantum information processing.

Although mathematical cryptography has been widely used, its security has only been proven under certain assumptions such as the computational power of opponents. As an alternative, quantum communication, in particular quantum key distribution (QKD) can get around unproven assumptions and achieve unconditional security. However, the key generation rate of practical QKD systems is limited by device imperfections, excess noise from the quantum channel, limited rate of true random-number generation, quantum entanglement preparation, and/or post-processing efficiency. This dissertation contributes to improving the performance of quantum communication systems. First, it proposes a new continuous-variable QKD (CVQKD) protocol that loosens the efficiency requirement on post-processing, a bottleneck for long-distance CVQKD systems. It also demonstrates an experimental implementation of the proposed protocol. To achieve high rates, the CVQKD experiment uses a continuous-wave local oscillator (CWLO). The excess noise caused by guided acoustic-wave Brillioun scattering (GAWBS) is avoided by a frequency-shift scheme, resulting in a 32 dB noise reduction. The statistical distribution of the GAWBS noise is characterized by quantum tomography. Measurements show Gaussian statistics upto 55 dB of dynamical range, which validates the security calculations in the proposed CVQKD protocol. True random numbers are required in quantum and classical cryptography. A second contribution of this thesis is that it experimentally demonstrates an ultrafast quantum random-number generator (QRNG) based on amplified spontaneous emission (ASE). Random numbers are produced by a multi-mode photon counting measurement on ASE light. The performance of the QRNG is analyzed with quantum information theory and verified with NIST standard random-number test. The QRNG experiment demonstrates a random-number generation rate at 20 Gbits/s. Theoretical studies show fundamental limits for such QRNGs. Quantum entanglement produced in nonlinear optical processes can help to increase quantum communication distance. A third contribution is the research on nonlinear optics of graphene, a novel 2D material with unconventional physical properties. Based on a quantum-dynamical model, optical responses of graphene are derived, showing for the first time a link between the complex linear optical conductivity and the quantum decoherence. Nonlinear optical responses, in particular four-wave mixing, is studied for the first time. The theory predicts saturation effects in graphene and relates the saturation threshold to the ultrafast quantum decoherence and carrier relaxation in graphene. For the experimental part, four-wave mixing in graphene is demonstrated. Twin-photon production in graphene is under investigation.