<p>We studied two topics: i) how much physical resources are needed to store information and ii) decoherent histories theory applied to Grover search. Given a system consisting of <i>d</i> degrees of freedom each of mass <i>m</i> to store an amount <i>S</i> of information, we find that its average energy, &lang;<i>H</i>&rang;, or size, &lang;<i>r</i>²&rang;, can be made arbitrarily small individually, but its product &lang;P&rang; = &lang;<i>H</i>&rang;&lang;<i> r</i>²&rang; is bounded below by (exp{<i>S/d</i>} &minus; 1)²<i>d</i>²/<i>m.</i> This result is obtained in a nonrelativistic, quantum mechanical setting, and it is independent of earlier thermodynamical results such as the Bekenstein bound on the entropy of black holes. </p><p> The second topic is decoherent histories applied to the Grover search problem. The theory of decoherent histories is an attempt to derive classical physics from positing only quantum laws at the fundamental level without notions of a classical apparatus or collapse of the wave-function. Searching for a marked target in a list of <i>N</i> items requires &Omega;(<i> N</i>) oracle queries when using a classical computer, while a quantum computer can accomplish the same task in <i>O</i>([special characters omitted]) queries using Grover's quantum algorithm. We study a closed quantum system executing Grover algorithm in the framework of decoherent histories and find it to be an exactly solvable model, thus yielding an alternate derivation of Grover's famous result. We also subject the Grover-executing computer to a generic external influence without needing to know the specifics of the Hamiltonian insofar as the histories decohere. Depending on the amount of decoherence, which is captured in our model by a single parameter related to the amount of information obtained by the environment, the search time can range from quantum to classical. Thus, we identify a key effect induced by the environment that can adversely affect a quantum computer's performance and demonstrate exactly how classical computing can emerge from quantum laws. </p>

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<p> Bayesian networks and their accompanying graphical models are widely used for prediction and analysis across many disciplines. We will reformulate these in terms of linear maps. This reformulation will suggest a natural extension, which we will show is equivalent to standard textbook quantum mechanics. Therefore, this extension will be termed <i>quantum.</i> However, the term <i> quantum</i> should not be taken to imply this extension is necessarily only of utility in situations traditionally thought of as in the domain of quantum mechanics. In principle, it may be employed in any modelling situation, say forecasting the weather or the stock market&mdash;it is up to experiment to determine if this extension is useful in practice. Even restricting to the domain of quantum mechanics, with this new formulation the advantages of Bayesian networks can be maintained for models incorporating quantum and mixed classical-quantum behavior. The use of these will be illustrated by various basic examples. </p><p> Parrondo's paradox refers to the situation where two, multi-round games with a fixed winning criteria, both with probability greater than one-half for one player to win, are combined. Using a possibly biased coin to determine the rule to employ for each round, paradoxically, the previously losing player now wins the combined game with probabilitygreater than one-half. Using the extended Bayesian networks, we will formulate and analyze classical observed, classical hidden, and quantum versions of a game that displays this paradox, finding bounds for the discrepancy from naive expectations for the occurrence of the paradox. A quantum paradox inspired by Parrondo's paradox will also be analyzed. We will prove a bound for the discrepancy from naive expectations for this paradox as well. Games involving quantum walks that achieve this bound will be presented.</p>

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

<p>The trapped atomic ion qubits feature desirable properties for use in a quantum computer such as long coherence times, high qubit readout fidelity, and universal logic gates. While these essential properties have been demonstrated, the ability to scale a trapped ion quantum system has not yet been shown. The challenge of scaling the system calls for methods to realize high-fidelity logic gates in scalable trap structures. Surface electrode ion traps, that are microfabricated from a silicon substrate, provide a scalable platform for trapping ion qubits only if high-fidelity operations are achievable in these structures. Here, we present a system for trapping and manipulating ions in a scalable surface trap. Trapping times exceeding 20 minutes without laser cooling, and heating rates as low as 0.8 quanta/ms indicate stable trapping conditions in these microtraps. Coherence times of more than one second verify adequate qubit and control field stability. We demonstrate low-error single-qubit gates performed using stimulated Raman transitions driven by lasers that are tightly focused on the ion qubit. Digital feedback loops are implemented to control the driving field's amplitude and frequency. Gate errors are measured using a randomized benchmarking protocol for single qubit gates, where residual amplitude error in the control beam is compensated using various pulse sequence techniques. Using pulse compensation, we demonstrate single qubit gates with an average error per randomized Clifford group gate of $3.6(3)\times10^{-4}$, which is below the fault-tolerant threshold for some error-correction schemes.</p> / Dissertation

Um computador quântico universal é capaz de efetuar qualquer cálculo que qualquer máquina de Turing clássica possa efetuar. Porém, sistemas quânticos, em geral, são descritos como sistemas isolados. A interação do meio com as superposições de estados reduz a função de onda para um único estado bem definido. Contudo nenhum sistema na natureza é de fato isolado. Assim, ruídos, dissipações e erros são 'inevitáveis' para quaisquer procedimentos que manipulem informação com quaisquer recursos naturais (quânticos ou clássicos). O formalismo conhecido por Operação Quântica (OQ) é usado para descrever a maioria dos sistemas quânticos abertos num formato de tempo discreto. A partir desse formato pode-se evidenciar operações e ruídos característicos de processos computacionais. Para mostrar a eficiência de uma OQ aplicamos o formalismo no modelo quântico-biológico de Fröhlich. A partir dessa caracterização construímos uma ponte entre computação quântica e processos biofísicos. Essa ponte pode revelar propriedades desconhecidas ou ajudar na compreensão da dinâmica ainda difusa de sistemas biológicos; ou mesmo em novas técnicas na construção de computadores quânticos. / An universal quantum computer is capable to perform any calculation that any classical turing machine can perform. However, the orthodox quantum mechanics is described for isolated systems. Therefore, the description of quantum computers is made starting from linear and reversible transformations. The interaction with the environment tends to eliminate the quantum effects as the superposition of states. However, any natural system is not infact isolated. Hence, noises, dissipations and errors are inevitable for any procedures that manipulate information with any natural resources. The formalism known by Quantum Operation (QO) issued to describe most of the open quantum systems. Through this format we can display the characteristic noises of the computational processes. To show the effectiveness of the QOs we applied the formalism in the quantum biological model of Fröhlich. Starting from that characterization we build a bridge between Quantum Computation and biological processes. That bridge can reveal unknown properties or to help in understanding the microbiologic dynamics; or even new techniques in the construction of quantum computers.

Made available in DSpace on 2015-03-04T18:50:42Z (GMT). No. of bitstreams: 1 Capitulo 1 e 2.pdf: 236440 bytes, checksum: 0afb7e8e3c2b968e8c9a8921330a01b0 (MD5) Previous issue date: 2004-05-13 / Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior / An universal quantum computer is capable to perform any calculation that any classical turing machine can perform. However, the orthodox quantum mechanics is described for isolated systems. Therefore, the description of quantum computers is made starting from linear and reversible transformations. The interaction with the environment tends to eliminate the quantum effects as the superposition of states. However, any natural system is not infact isolated. Hence, noises, dissipations and errors are inevitable for any procedures that manipulate information with any natural resources. The formalism known by Quantum Operation (QO) issued to describe most of the open quantum systems. Through this format we can display the characteristic noises of the computational processes. To show the effectiveness of the QO s we applied the formalism in the quantum biological model of Fröhlich. Starting from that characterization we build a bridge between Quantum Computation and biological processes. That bridge can reveal unknown properties or to help in understanding the microbiologic dynamics; or even new techniques in the construction of quantum computers. / Um computador quântico universal é capaz de efetuar qualquer cálculo que qualquer máquina de Turing clássica possa efetuar. Porém, sistemas quânticos, em geral, são descritos como sistemas isolados. A interação do meio com as superposições de estados reduz a função de onda para um único estado bem definido. Contudo nenhum sistema na natureza é de fato isolado. Assim, ruídos, dissipações e erros são 'inevitáveis' para quaisquer procedimentos que manipulem informação com quaisquer recursos naturais (quânticos ou clássicos). O formalismo conhecido por Operação Quântica (OQ) é usado para descrever a maioria dos sistemas quânticos abertos num formato de tempo discreto. A partir desse formato pode-se evidenciar operações e ruídos característicos de processos computacionais. Para mostrar a eficiência de uma OQ aplicamos o formalismo no modelo quântico-biológico de Fröhlich. A partir dessa caracterização construímos uma ponte entre computação quântica e processos biofísicos. Essa ponte pode revelar propriedades desconhecidas ou ajudar na compreensão da dinâmica ainda difusa de sistemas biológicos; ou mesmo em novas técnicas na construção de computadores quânticos.

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