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Quantum information science has shown that computers which exploit the quantum nature of particles, namely quantum computers, can outperform contemporary computers in some computational tasks. The fundamental building blocks of a quantum computer are quantum logical gates and quantum bits (qubits). Previous research has shown that the optical approach to quantum computing is promising. However, linear optical quantum computing (LOQC) schemes require a huge amount of resource, which makes large scale LOQC impractical, and hence there have been renewed interests in nonlinear optical quantum computing schemes, where less resource is required. The performance of these quantum gates depends on the properties of the nonlinear media. However, requirements on some of the properties for high performance quantum gates are not fully known. This thesis intends to bridge this gap of knowledge and examines the necessary conditions on several types optical nonlinearities that are common in two-qubit quantum gates schemes. These types of nonlinearities are, namely two-photon absorption, $\chi^{(2)}$ nonlinearity and $\chi^{(3)}$ cross-Kerr nonlinearity. The two-photon absorption based quantum Zeno gate is modeled in this thesis. It is shown that for practical absorbers, the photon loss significantly lowers the quantum fidelity of the Zeno gate. Nevertheless, this thesis proposes to use the Zeno gate for fusing optical cluster states. With the best theoretical estimate of single photon loss in the absorbers, the Zeno gate can outperform linear optical schemes. This thesis also proposes to embed the Zeno gate in the teleportation-type of two-qubit gate, namely GC-Zeno gate, such that the success rate of the gate can be traded off for higher gate fidelity. The effect of some mode matching error and detector inefficiency on the GC-Zeno gate are also considered here. It is shown that the photon loss requirement as well as the mode matching requirement are both stringent for having a fault tolerant GC-Zeno gate. This thesis models some of the properties of a $\chi^{(3)}$ optical medium and explores how they affect the fidelity of the cross-Kerr nonlinearity based quantum gate. This thesis shows that for a cross-Kerr medium with fast time response but negligible wave dispersion, the medium would induce spectral entanglement between the input photons and this significantly lowers the fidelity of the quantum gate. Nevertheless, when the dispersion has a stronger effect than the time response, and if phase noise is negligible, it is possible to achieve a quantum gate with high fidelity. However, the noise is actually significant, and this thesis suggests that spectral filtering can be applied to prohibit the occurrence of the noise. The requirements on employing optical $\chi^{(2)}$ nonlinearity for quantum computing are also examined. This study models the spectral effects of a $\chi^{(2)}$ medium on its efficiency. It is shown in this thesis that since the Hamiltonian of the medium does not commute at different times, the unitary operation should be modeled by a Dyson series, which leads to undesired spectral entanglement that lowers the efficiency of the medium. However, in the case of periodical poling, the unitary operation can be modeled by a Taylor series, where under some phase matching conditions, the medium can have a high efficiency. Furthermore, this thesis proposes a Bell measurement scheme and a quantum gate scheme based on $\chi^{(2)}$ nonlinearity that can always outperform linear optics even when the nonlinearity strength is weak. In the case of sufficiently strong nonlinearity, a quantum gate with high success rate can be achieved. In summary, this thesis models some of the properties of two-photon absorbers, $\chi^{(2)}$ nonlinearity and $\chi^{(3)}$ nonlinearity, and shows that it is possible to achieve the conditions required for high performance quantum gates, however these conditions are experimentally challenging to meet.

This thesis investigates several different aspects of the physics of few state quantum systems and their use in information processing applications. The main focus is performing high precision computations or experiments using imperfect quantum systems. Specifically looking at methods to calibrate a quantum system once it has been manufactured or performing useful tasks, using a quantum system with only limited spatial or temporal coherence. / A novel method for characterising an unknown two-state Hamiltonian is presented which is based on the measurement of coherent oscillations. The method is subsequently extended to include the effects of decoherence and enable the estimation of uncertainties. Using the uncertainty estimates, the achievable precision for a given number of measurements is computed. This method is tested experimentally using the nitrogen-vacancy defect in diamond as an example of a two-state quantum system of interest for quantum information processing. The method of characterisation is extended to higher dimensional systems and this is illustrated using the Heisenberg interaction between spins as an example. / The use of buried donors in silicon is investigated as an architecture for realising quantum-dot cellular automata as an example of quantum systems used for classical information processing. The interaction strengths and time scales are calculated and both coherent and incoherent evolution are assessed as possible switching mechanisms. The effects of decoherence on the operation of a single cell and the scaling behaviour of a line of cells is investigated. / The use of type-II quantum computers for simulating classical systems is studied as an application of small scale quantum computing. An algorithm is developed for simulating the classical Ising model using Metropolis Monte-Carlo where random number generation is incorporated using quantum superposition. This suggests that several new algorithms could be developed for a type-II quantum computer based on probabilistic cellular automata.

This thesis identifies problems with the current operation proposals for Si:P based solid-state quantum computing architectures and outlines realistic alternatives as an effective fix. The focus is qubit read-out and robust two-qubit control of the exchange interaction in the presence of both systematic and environmental errors. We develop a theoretical model of the doubly occupied D- read-out state found in Si:P based nuclear spin architectures. We test our theory by using it to determine the binding energy of the D- state, comparing to known results. Our model can be used in detailed calculations of the adiabatic read-out protocol proposed for these devices. Regarding this protocol, preliminary calculations suggest the small binding energy of the doubly occupied read-out state will result in a state dwell-time less than that required for measurement using a single electron transistor (SET). We propose and analyse an alternative approach to single-spin read-out using optically induced spin to charge transduction, showing that the top gate biases required for qubit selection are significantly less than those demanded by the adiabatic scheme, thereby increasing the D+D- lifetime. Implications for singlet-triplet discrimination for electron spin qubits are also discussed.

Quantum information science has shown that computers which exploit the quantum nature of particles, namely quantum computers, can outperform contemporary computers in some computational tasks. The fundamental building blocks of a quantum computer are quantum logical gates and quantum bits (qubits). Previous research has shown that the optical approach to quantum computing is promising. However, linear optical quantum computing (LOQC) schemes require a huge amount of resource, which makes large scale LOQC impractical, and hence there have been renewed interests in nonlinear optical quantum computing schemes, where less resource is required. The performance of these quantum gates depends on the properties of the nonlinear media. However, requirements on some of the properties for high performance quantum gates are not fully known. This thesis intends to bridge this gap of knowledge and examines the necessary conditions on several types optical nonlinearities that are common in two-qubit quantum gates schemes. These types of nonlinearities are, namely two-photon absorption, $\chi^{(2)}$ nonlinearity and $\chi^{(3)}$ cross-Kerr nonlinearity. The two-photon absorption based quantum Zeno gate is modeled in this thesis. It is shown that for practical absorbers, the photon loss significantly lowers the quantum fidelity of the Zeno gate. Nevertheless, this thesis proposes to use the Zeno gate for fusing optical cluster states. With the best theoretical estimate of single photon loss in the absorbers, the Zeno gate can outperform linear optical schemes. This thesis also proposes to embed the Zeno gate in the teleportation-type of two-qubit gate, namely GC-Zeno gate, such that the success rate of the gate can be traded off for higher gate fidelity. The effect of some mode matching error and detector inefficiency on the GC-Zeno gate are also considered here. It is shown that the photon loss requirement as well as the mode matching requirement are both stringent for having a fault tolerant GC-Zeno gate. This thesis models some of the properties of a $\chi^{(3)}$ optical medium and explores how they affect the fidelity of the cross-Kerr nonlinearity based quantum gate. This thesis shows that for a cross-Kerr medium with fast time response but negligible wave dispersion, the medium would induce spectral entanglement between the input photons and this significantly lowers the fidelity of the quantum gate. Nevertheless, when the dispersion has a stronger effect than the time response, and if phase noise is negligible, it is possible to achieve a quantum gate with high fidelity. However, the noise is actually significant, and this thesis suggests that spectral filtering can be applied to prohibit the occurrence of the noise. The requirements on employing optical $\chi^{(2)}$ nonlinearity for quantum computing are also examined. This study models the spectral effects of a $\chi^{(2)}$ medium on its efficiency. It is shown in this thesis that since the Hamiltonian of the medium does not commute at different times, the unitary operation should be modeled by a Dyson series, which leads to undesired spectral entanglement that lowers the efficiency of the medium. However, in the case of periodical poling, the unitary operation can be modeled by a Taylor series, where under some phase matching conditions, the medium can have a high efficiency. Furthermore, this thesis proposes a Bell measurement scheme and a quantum gate scheme based on $\chi^{(2)}$ nonlinearity that can always outperform linear optics even when the nonlinearity strength is weak. In the case of sufficiently strong nonlinearity, a quantum gate with high success rate can be achieved. In summary, this thesis models some of the properties of two-photon absorbers, $\chi^{(2)}$ nonlinearity and $\chi^{(3)}$ nonlinearity, and shows that it is possible to achieve the conditions required for high performance quantum gates, however these conditions are experimentally challenging to meet.

Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro / A demanda crescente por poder computacional estimulou a pesquisa e desenvolvimento de processadores digitais cada vez mais densos em termos de transistores e com clock mais rápido, porém não podendo desconsiderar aspectos limitantes como consumo, dissipação de calor, complexidade fabril e valor comercial. Em outra linha de tratamento da informação, está a computação quântica, que tem como repositório elementar de armazenamento a versão quântica do bit, o q-bit ou quantum bit, guardando a superposição de dois estados, diferentemente do bit clássico, o qual registra apenas um dos estados. Simuladores quânticos, executáveis em computadores convencionais, possibilitam a execução de algoritmos quânticos mas, devido ao fato de serem produtos de software, estão sujeitos à redução de desempenho em razão do modelo computacional e limitações de memória. Esta Dissertação trata de uma versão implementável em hardware de um coprocessador para simulação de operações quânticas, utilizando uma arquitetura dedicada à aplicação, com possibilidade de explorar o paralelismo por replicação de componentes e pipeline. A arquitetura inclui uma memória de estado quântico, na qual são armazenados os estados individuais e grupais dos q-bits; uma memória de rascunho, onde serão armazenados os operadores quânticos para dois ou mais q-bits construídos em tempo de execução; uma unidade de cálculo, responsável pela execução de produtos de números complexos, base dos produtos tensoriais e matriciais necessários à execução das operações quânticas; uma unidade de medição, necessária à determinação do estado quântico da máquina; e, uma unidade de controle, que permite controlar a operação correta dos componente da via de dados, utilizando um microprograma e alguns outros componentes auxiliares. / The growing demand for computational power has pushed the research and development of digital processors that are even more dense in terms of transistor number and faster clock rate, without ignoring concerning constraints such as energy consumption, heat dissipation, manufacturing complexity and final market costs. Another approach to deal with digital information is quantum computation, that relies on a basic storage entity that keeps a superposition of the two possible states, in contrast with of a bit of a conventional computer, that stores only one of these two states. Simulators for quantum computation can run quantum algorithms on conventional computers. However, since these are developed using a software implementation, performance limitation occur due to the classical computational model used. This dissertation presents an implementable hardware architecture of a specialized coprocessor that simulates quantum operations, employing an application-specific design that allows parallel processing based on component replication and pipelining. The proposed architecture includes a quantum state memory, where individual and joined states of q-bits are stored; a scratch memory, dedicated to storing quantum operators that are built at runtime; the arithmetic unit, that performs complex numbers multiplications, to allow the full computation of tensorial and scalar products of matrices, required to implement quantum operators; the measurement unit, that is required to perform quantum state observation; and the control unit, that controls proper operation of the datapath components using a microprogram and some other auxiliary components.

The prospect of a universal quantum computer is alluring, yet formidable. Smaller scale quantum information processing, however, has been demonstrated. Quantum networks, interlinking flying and stationary qubits, and linear optical quantum computing (LOQC) are both good candidates for scaling up such computations. A strongly coupled atom-cavity system is a promising approach for applications in these fields, both as a node in a quantum network, and as a source of photons for LOQC. This thesis demonstrates the versatile capabilities of an atom-cavity system comprising a single ⁸⁷Rb atom within a macroscopic high-finesse Fabry-P&eacute;rot cavity. It operates intermittently for periods of up to 100 &mu;s, with single-photon repetition rates of 1 MHz and an intra-cavity production efficiency of up to 85%. Exploiting the long coherence time of around 500 ns, the photons are subdivided into d time bins, with arbitrary amplitudes and phases, thus encoding arbitrary qudits. High fidelity quantum logic is shown, operating a controlled-NOT gate integrated into a photonic chip with a classical fidelity of 95.9^+1.4<sub style='position: relative; left: -1.6em;'>-1.7</sub> %. Additionally, the generation of entanglement is verified and non-classical correlations between events separated by periods exceeding the travel time across the chip by three orders of magnitude are observed. Photonic quantum simulation is performed, using temporally encoded qudits to mimic the correlation statistics of both fermions and anyons, in addition to bosons. Finally measurement-based quantum feedback is demonstrated and used to actively control the routing of temporal qubits.

The development of a quantum computer presents one of the greatest challenges in science and engineering to date. The promise of more efficient computing based on entangled quantum states and the superposition principle has led to a worldwide explosion of interest in the fields of quantum information and computation. Among the number of hurdles which must first be cleared before we witness a physical realization are problems associated with environment-induced decoherence and noise more generally. However, the discovery of quantum error correction and the establishment of the accuracy threshold theorem provide us with the hope of someday harnessing the potential power a functioning fault-tolerant quantum information processor has to offer. This dissertation contributes to this effort by investigating a particular class of quantum error correcting codes, namely noiseless subsystem encodings. The passive approach to error correction taken by these encodings provides an efficient means of protection from symmetrically coupled system-environment interactions. Here I will present methods for determining the subsystem-preserving evolutions for noiseless subsystem encodings supported by arbitrary-dimensional physical quantum systems. Implications for universal, collective decoherence-free quantum computation using the derived operations are discussed. Moreover, I will present a proposal for an optical device which is capable of preparing a variety of these noiseless subsystem encodings through a postselection strategy.

Within the field of Quantum Information Processing, we study two subjects: For quantum state tomography, one common assumption is that the experimentalist possesses a stationary source of identical states. We challenge this assumption and propose a method to detect and characterize the drift of nonstationary quantum sources. We distinguish diffusive and systematic drifts and examine how quickly one can determine that a source is drifting. Finally, we give an implementation of this proposed measurement for single photons. For quantum computing, fault-tolerant protocols assume that errors are of certain types. But how do we detect errors of the wrong type? The problem is that for large quantum states, a full state description is impossible to analyze, and so one cannot detect all types of errors. We show through a quantum state estimation example (on up to 25 qubits) how to attack this problem using model selection. We use, in particular, the Akaike Information Criterion. Our example indicates that the number of measurements that one has to perform before noticing errors of the wrong type scales polynomially both with the number of qubits and with the error size. This dissertation includes previously published co-authored material.

Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro / A demanda crescente por poder computacional estimulou a pesquisa e desenvolvimento de processadores digitais cada vez mais densos em termos de transistores e com clock mais rápido, porém não podendo desconsiderar aspectos limitantes como consumo, dissipação de calor, complexidade fabril e valor comercial. Em outra linha de tratamento da informação, está a computação quântica, que tem como repositório elementar de armazenamento a versão quântica do bit, o q-bit ou quantum bit, guardando a superposição de dois estados, diferentemente do bit clássico, o qual registra apenas um dos estados. Simuladores quânticos, executáveis em computadores convencionais, possibilitam a execução de algoritmos quânticos mas, devido ao fato de serem produtos de software, estão sujeitos à redução de desempenho em razão do modelo computacional e limitações de memória. Esta Dissertação trata de uma versão implementável em hardware de um coprocessador para simulação de operações quânticas, utilizando uma arquitetura dedicada à aplicação, com possibilidade de explorar o paralelismo por replicação de componentes e pipeline. A arquitetura inclui uma memória de estado quântico, na qual são armazenados os estados individuais e grupais dos q-bits; uma memória de rascunho, onde serão armazenados os operadores quânticos para dois ou mais q-bits construídos em tempo de execução; uma unidade de cálculo, responsável pela execução de produtos de números complexos, base dos produtos tensoriais e matriciais necessários à execução das operações quânticas; uma unidade de medição, necessária à determinação do estado quântico da máquina; e, uma unidade de controle, que permite controlar a operação correta dos componente da via de dados, utilizando um microprograma e alguns outros componentes auxiliares. / The growing demand for computational power has pushed the research and development of digital processors that are even more dense in terms of transistor number and faster clock rate, without ignoring concerning constraints such as energy consumption, heat dissipation, manufacturing complexity and final market costs. Another approach to deal with digital information is quantum computation, that relies on a basic storage entity that keeps a superposition of the two possible states, in contrast with of a bit of a conventional computer, that stores only one of these two states. Simulators for quantum computation can run quantum algorithms on conventional computers. However, since these are developed using a software implementation, performance limitation occur due to the classical computational model used. This dissertation presents an implementable hardware architecture of a specialized coprocessor that simulates quantum operations, employing an application-specific design that allows parallel processing based on component replication and pipelining. The proposed architecture includes a quantum state memory, where individual and joined states of q-bits are stored; a scratch memory, dedicated to storing quantum operators that are built at runtime; the arithmetic unit, that performs complex numbers multiplications, to allow the full computation of tensorial and scalar products of matrices, required to implement quantum operators; the measurement unit, that is required to perform quantum state observation; and the control unit, that controls proper operation of the datapath components using a microprogram and some other auxiliary components.