Reversible logic is an emerging area of research. With the rapid growth of markets such as mobile computing, power dissipation has become an increasing concern for designers (temperature range limitations, generating smaller transistors) as well as customers (battery life, overheating). The main benefit of utilizing reversible logic is that there exists, theoretically, zero power dissipation. The synthesis of circuits is an important part of any design cycle. The circuit used to realize any specification must meet detailed requirements for both layout and manufacturing. Quantum cost is the main metric used in reversible logic. Many algorithms have been proposed thus far which result in both low gate count and quantum cost. In this thesis the AP algorithm is introduced. The goal of the algorithm is to drive quantum cost down by using multiple non-blocking orders, a breadth first search, and a quantum cost reduction transformation. The results shown by the AP algorithm demonstrate that the resulting quantum cost for well-known benchmarks are improved by at least 9% and up to 49%.

The computing power in terms of speed and capacity of today's digital computers has improved tremendously in the last decade. This improvement came mainly due to a revolution in manufacturing technology by developing the ability to manufacture smaller devices and by integrating more devices on a single die. Further development of the current technology will be restricted by physical limits since it won't be possible to shrink devices beyond a certain size. Eventually, classical electrical circuits will encounter the barrier of quantum mechanics. The laws of quantum mechanics can be used for building computing systems that work on the principles of quantum mechanics. Thus quantum computing has drawn the interest of many top scientists in the world. Ion Trap technology is one of the most promising prospective technologies for building quantum computers. This technology allows the placement of qubits - ions in 1-, 2- and 3-dimensional regular structures. Development of efficient algorithms and methodologies for designing reversible quantum circuits is one of the most rapidly growing areas of research. All existing algorithms for synthesizing quantum circuits use multi-input Toffoli gates that have very high quantum cost in terms of electromagnetic pulses. They also do not use the opportunity of regular structures provided by the Ion Trap technology. In this thesis I present a completely new methodology for synthesizing quantum circuits that use only small (3x3) Toffoli gates and new gate families that have similar properties and use regular structures. These methods are for both binary and multiple valued quantum circuits. All my methods require adding some limited number of ancilla qudits [sic] but dramatically decrease the quantum cost of the synthesized circuits. I also present a new family of gates called "D-gates" that allows synthesis of quantum and reversible logic functions using structures called layered diagrams. The designed circuits can be directly mapped to a Quantum Logic Array implemented using the Ion Trap technology.

This dissertation is devoted to efficient automated logic synthesis of reversible circuits using various gate types and initial specifications. These Reversible circuits are of interest to several modern technologies, including Nanotechnology, Quantum computing, Quantum Dot Cellular Automata, Optical computing and low power adiabatic CMOS, but so far the most important practical application of reversible circuits is in quantum computing. Logic synthesis methodologies for reversible circuits are very different than those for classical CMOS or other technologies. The focus of this dissertation is on synthesis of reversible (permutative) binary circuits. It is not related to general unitary circuits that are used in quantum computing and which exhibit quantum mechanical phenomena such as superposition and entanglement. The interest in this dissertation is only in logic synthesis aspects and not in physical (technological) design aspects of reversible circuits. Permutative quantum circuits are important because they include the class of oracles and blocks that are parts of oracles, such as comparators or arithmetic blocks, counters of ones, etc. Every practical quantum algorithm, such as the Grover Algorithm, has many permutative circuits. These circuits are also used in Shor Algorithm (integer factorization), simulation of quantum systems, communication and many other quantum algorithms. Designing permutative circuits is therefore the major engineering task that must be solved to practically realize a quantum algorithm. The dissertation presents the theory that leads to MP (Multi-Path) algorithm, which is currently the top minimizer of reversible circuits with no ancilla bits. Comparison of MP with other 2 leading software tools is done. This software allows to minimize functions of more variables and with smaller quantum cost that other CAD tools. Other software developed in this dissertation allows to synthesize reversible circuits for functions with "don't cares" in their initial specifications. Theory to realize functions from relational representations is also given. Our yet other software tool allows to synthesize reversible circuits for new types of reversible logic, for which no algorithm was ever created, using the so-called "pseudo-reversible" gates called Y-switches.

Made available in DSpace on 2015-03-04T18:57:46Z (GMT). No. of bitstreams: 1 TeseSantiago.pdf: 606719 bytes, checksum: 38e30569276229fb74710b61a35a4dad (MD5) Previous issue date: 2013-02-21 / Like a classical computer, a quantum computer would be affected by errors. Those need to be identified and corrected, so we need quantum error correcting codes. In this work, we study the Codeword Stabilized Quantum Codes (CWS codes) a generalization of the stabilizers quantum codes. First, we make a detailed description, with a new approach of the results about CWS codes on systems with more than one level (qudits). We make clear what results are correct in general and what results are correct only for qubits, qupits (prime number of levels) or what are correct for graph-states. We also show a new result that relates CWS codes with stabilizer codes generalizing the results found in the literature. After that, but only for qubits and CWS codes in a standard form, we also show new results on the kind of observables we may use to identify the errors in a CWS code. We create than a procedure to find these observables. Those observables not always suffices to identify the error, but when they do, the procedure to identify the errors is made in an efficient way. / Em um computador quântico, da mesma forma que em um computador clássico, a informação está sujeita a erros que precisam ser detectados e corrigidos, de onde surge a necessidade dos códigos quânticos de correção de erros. Neste trabalho estudamos os códigos CWS (Codeword Stabilized quantum codes) que generalizam os códigos estabilizadores. Primeiramente, descrevemos detalhadamente os códigos CWS sobre sistemas quânticos de mais de um nível (qudits) a partir de uma nova abordagem. Deixamos claro quais resultados valem em geral e quais valem apenas para qubits, qupits (sistemas com número primo de níveis) e quais valem no caso do código CWS ser baseado em um estado-grafo. Apresentamos também um novo resultado que relaciona códigos CWS com códigos estabilizadores generalizando os resultados presentes na literatura. Posteriormente, caracterizamos um tipo de operador de medida para códigos CWS para qubits. Criamos então um procedimento para buscar estes operadores, que nem sempre são suficientes para identificar o erro ocorrido, mas quando são, o fazem de forma eficiente.

Made available in DSpace on 2015-03-04T18:57:54Z (GMT). No. of bitstreams: 1 Tese_de_Doutorad--Jalil_Khatibi_Moqadam.pdf: 1436910 bytes, checksum: b9b764cc6fff54e55232108ba8b66c73 (MD5) Previous issue date: 2013-08-30 / Conselho Nacional de Desenvolvimento Cientifico e Tecnologico / In this thesis, the performance of the Toffoli gate under the influence of imperfections is studied. After giving a brief introduction to quantum computing and quantum control theory, superconducting charge qubits and their couplings to the transmission line resonator are discussed. Then, the implementation of the Toffoli gate in a chain of three superconducting transmon qubits, using quantum control methods, is reviewed. Having established the gate, the noise is introduced in the interqubits interactions. The coupling constants are then no longer fixed, instead, they fluctuate around average values obeying some given probability density functions characterizing the dynamical-imperfection case. The static-imperfection case in which the values of the coupling constants are not exactly known is also considered. Finally, a more robust gate is designed by modifying the quantum optimization problem using some weighted average fidelity as the objective functional. / Neste trabalho, o desempenho da porta Toffoli sob a influência de imperfeições é estudada. Depois de dar uma breve introdução a computação quântica e teoria de controle quântico, os qubits supercondutores de tipo de carga e seus acoplamentos a um ressonador da linha de transmissão são discutidos. Em seguida, a execução da porta Toffoli numa cadeia de três qubits supercondutores de tipo transmon, utilizando métodos de controle quântico, é revisada. Tendo estabelecido a porta, o ruído e introduzido nas interações entre os qubits. As constantes de acoplamento, então, não ficam fixas, flutuam em torno de valores médios e obedecem a algumas funções de densidade de probabilidade conhecidas que caracterizam o caso da imperfeição dinâmica. O caso da imperfeição estática no qual os valores das constantes de acoplamento não são conhecidas com precisão é também considerado. Finalmente, uma porta mais robusta e projetada com uma modificação do problema de otimização quântico usando uma fidelidade media ponderada como funcional objetivo.

Made available in DSpace on 2015-03-04T18:57:57Z (GMT). No. of bitstreams: 1 thesis_final_raqueline.pdf: 1818351 bytes, checksum: 040ff54327a69213f7a1ff0da4a7fd7a (MD5) Previous issue date: 2014-03-14 / Quantum Markov chains or quantum walks have been playing an important role in the development of efficient quantum algorithms. Therefore, studying its properties, analyzing its behavior in different topologies, and seeing the impact of decoherence on these walks and its algorithms is fundamental to the development of the area. In this context, we contribute through the analysis of the following issues. For Szegedy's quantum walk, we analytically study its behavior in the cycle; we describe how to calculate the limit distribution by providing examples for the two-dimensional grid, cycle and complete graph; we study a model of decoherence inspired by percolation, where we define the decoherent quantum hitting time and we establish a intensity range of decoherence where the decoherent quantum hitting time is quadratically smaller than the classic; the detection algorithm has a quadratic gain for the same range, under the action of decoherence. For the coined quantum walk, we present simulations of the algorithm for evaluating boolean formulas, also considering a faulty oracle model. / As cadeias de Markov quânticas ou passeios quânticos tem desempenhado um papel importante no desenvolvimento de algoritmos quânticos eficientes. Dessa forma, estudar suas propriedades, analisar o seu comportamento em diferentes topologias, e ver o impacto da descoerência sob esses passeios e seus algoritmos e fundamental para o desenvolvimento da area. Nesse contexto, contribuímos com a analise das seguintes questões. Para o passeio quântico de Szegedy, estudamos analiticamente o seu comportamento no ciclo; descrevemos como calcular a distribuição limite apresentando exemplos para a malha bidimensional, grafo completo e ciclo; estudamos um modelo de descoerência inspirado em percolação, em que definimos o tempo de alcance quântico descoerente e estabelecemos um intervalo da intensidade de descoerência em que o tempo de alcance quântico descoerente e quadraticamente menor que o clássico; o algoritmo de detecção sob ação da descoerência continua com ganho quadrático para o mesmo intervalo. Para o passeio quântico com moeda, presentamos simulações do algoritmo para avaliar fórmulas booleanas, também considerando um modelo de oráculo defeituoso.

The application of Moore's Law would not be feasible by using the computing systems fabrication principles that are prevalent today. Fundamental changes in the field of computing are needed to keep Moore's Law operational. Different quantum technologies are available to take the advancement of computing into the future. Logic in quantum technology uses gates that are very different from those used in contemporary technology. Limiting itself to reversible operations, this thesis presents different methods to realize these logic gates. Two methods using Generalized Ternary Gates and Muthukrishnan Stroud Gates are presented for synthesis of ternary logic gates. Realizations of well-known quantum gates like the Feynman gate, Toffoli Gate, 2-qudit and 3-qudit SW AP gates are shown. In addition a new gate, the Inverse SW AP gate, is proposed and its realization is also presented.

A study has been made of a few different freely available Quantum Computer simulators.All the simulators tested are available online on their respective websites. A number oftests have been performed to compare the different simulators against each other. Someuntested simulators of various programming languages are included to show the diversityof the quantum computer simulator applications. The conclusion of the review is that LibQuantum is the best of the simulatorstested because of ease of coding, a great amount of pre-defined functionimplementations and decoherence simulation support among other reasons.

A study has been made of a few different freely available Quantum Computer simulators. All the simulators tested are available online on their respective websites. A number of tests have been performed to compare the different simulators against each other. Some untested simulators of various programming languages are included to show the diversity of the quantum computer simulator applications. The conclusion of the review is that LibQuantum is the best of the simulators tested because of ease of coding, a great amount of pre-defined function implementations and decoherence simulation support among other reasons. / ICG QC

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