Dissertations / Theses on the topic 'Quantum Logic'

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.

Since Quantum Computer is almost realizable on large scale and Quantum Technology is one of the main solutions to the Moore Limit, Quantum Logic Synthesis (QLS) has become a required theory and tool for designing Quantum Logic Circuits. However, despite its growth, there is no any unified aproach to QLS as Quantum Computing is still being discovered and novel applications are being identified. The intent of this study is to experimentally explore principles of Quantum Logic Synthesis and its applications to Inductive Machine Learning. Based on algorithmic approach, I first design a Genetic Algorithm for Quantum Logic Synthesis that is used to prove and verify the methods proposed in this work. Based on results obtained from the evolutionary experimentation, I propose a fast, structure and cost based exhaustive search that is used for the design of a novel, least expensive universal family of quantum gates. The results form both the evolutionary and heuristic search are used to formulate an Inductive Learning Approach based on Quantum Logic Synthesis with the intended application being the humanoid behavioral robotics. The presented approach illustrates a successful algorithmic approach, where the search algorithm was able to invent/discover novel quantum circuits as well as novel principles in Quantum Logic Synthesis.

This thesis describes research on the design of quantum logic circuits suitable for the experimental demonstration of a three-qubit quantum computation prototype. The design is based on a proposal for optically controlled, solid-state quantum logic gates. In this proposal, typically referred to as SFG model, the qubits are stored in the electron spin of donors in a solid-state substrate while the interactions between them are mediated through the optical excitation of control particles placed in their proximity. After a brief introduction to the area of quantum information processing, the basics of quantum information theory required for the understanding of the thesis work are introduced. Then, the literature on existing quantum computation proposals and experimental implementations of quantum computational systems is analysed to identify the main challenges of experimental quantum computation and typical system parameters of quantum computation prototypes. The details of the SFG model are subsequently described and the entangling characteristics of SFG two-qubit quantum gates are analysed by means of a geometrical approach, in order to understand what entangling gates would be available when designing circuits based on this proposal. Two numerical tools have been developed in the course of the research. These are a quantum logic simulator and an automated quantum circuit design algorithm based on a genetic programming approach. Both of these are used to design quantum logic circuits compatible with the SFG model for a three-qubit Deutsch-Jozsa algorithm. One of the design aims is to realise the shortest possible circuits in order to reduce the possibility of errors accumulating during computation, and different design procedures which have been tested are presented. The tolerance to perturbations of one of the designed circuits is then analysed by evaluating its performance under increasing fluctuations on some of the parameters relevant in the dynamics of SFG gates. Because interactions in SFG two-qubit quantum gates are mediated by the optical excitation of the control particles, the solutions for the generation of the optical control signal required for the proposed quantum circuits are discussed. Finally, the conclusions of this work are presented and areas for further research are identified.

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.

Quantum mechanics is basically a mathematical recipe on how to construct physical models. Historically its origin and main domain of application has been in the microscopic regime, although it strictly seen constitutes a general mathematical framework not limited to this regime. Since it is a statistical theory, the meaning and role of probabilities in it need to be defined and understood in order to gain an understanding of the predictions and validity of quantum mechanics. The interpretational problems of quantum mechanics are also connected with the interpretation of the concept of probability. In this thesis the use of probability theory as extended logic, in particular in the way it was presented by E. T. Jaynes, will be central. With this interpretation of probabilities they become a subjective notion, always dependent on one's state of knowledge or the context in which they are assigned, which has consequences on how things are to be viewed, understood and tackled in quantum mechanics. For instance, the statistical operator or density operator, is usually defined in terms of probabilities and therefore also needs to be updated when the probabilities are updated by acquisition of additional data. Furthermore, it is a context dependent notion, meaning, e.g., that two observers will in general assign different statistical operators to the same phenomenon, which is demonstrated in the papers of the thesis. It is also presented an alternative and conceptually clear approach to the problematic notion of "probabilities of probabilities", which is related to such things as probability distributions on statistical operators. In connection to this, we consider concrete numerical applications of Bayesian quantum state assignment methods to a three-level quantum system, where prior knowledge and various kinds of measurement data are encoded into a statistical operator, which can then be used for deriving probabilities of other measurements. The thesis also offers examples of an alternative quantum state assignment technique, using maximum entropy methods, which in some cases are compared with the Bayesian quantum state assignment methods. Finally, the interesting and important problem whether the statistical operator, or more generally quantum mechanics, gives a complete description of "objective physical reality" is considered. A related concern is here the possibility of finding a "local hidden-variable theory" underlying the quantum mechanical description. There have been attempts to prove that such a theory cannot be constructed, where the most well-known impossibility proof claiming to show this was given by J. S. Bell. In connection to this, the thesis presents an idea for an interpretation or alternative approach to quantum mechanics based on the concept of space-time.<br>QC 20100810

The logic Lq, introduced within this thesis, is a logic for quantum information. The purpose was, in fact, to describe logically the qubit structure (that is, the intrinsic quantum superposition of a two-level quantum state) and the maximal quantum entanglement of two qubits. The logic Lq is obtained via Sambin’s reflection principle of Basic logic, by which the metalinguistic links among assertions reflect (by solving a definitional equation) into logical connectives among propositions. However, while in Basic logic the metalanguage is classical, in our case it is quantum. In the quantum metalanguage each atomic assertion carries along an assertion degree, a complex number, which is interpreted as a probability amplitude. It is just the presence of assertion degrees that allows the introduction of the connective “quantum superposition” in Lq. This connective is a generalization of the logical conjunction “and”. It is labelled by complex numbers indicating the weight by which each proposition contributes to the compound proposition. The truth-values (or truth-degrees) are the squared modules of the assertion degrees, and their range is the real interval [0,1]. Then, the logic Lq is many-valued. Differently from fuzzy logics, however, the truth-degrees are interpreted here as quantum-mechanical probabilities. The logic Lq keeps the three main properties of Basic logic, namely symmetry, reflection and visibility. This choice has been dictated by the following considerations: 1) The no-cloning and no-erase theorems of quantum information do not allow the corresponding logic to have the structural rules of weakening and contraction, with which they disagree. This fact rules out, in the search of a logic for quantum information, every kind of structural logic. 2) Choosing Basic logic instead of Linear logic (the other main sub-structural logic) was due to the fact that without visibility the connective “quantum entanglement” cannot be introduced. Furthermore, we looked for a logic of quantum information which was endowed with a deductive calculus, (in particular a sequent calculus). The logic Lq appears, in so far, as the only one which can take into account all the above desiderata. The interpretation of the assertions of the quantum metalanguage is given in terms of quantum states (the quantum metalanguage “is” the Hilbert space). The interpretation of the propositions of Lq is given in terms of (non-hermitian) operators which are weak measurements. Then, the interpretation of Lq is based on a generalization of the concepts already proposed by Birkhoff and von Neumann in “orthodox” quantum logic. The difference stands in the fact that the interpretation of Lq is not given in terms of projectors, but in terms of weak measurements, which do not give rise to an abrupt collapse of quantum wave functions. This allows a logical description of quantum superposition, because the latter is not destroyed. The possibility of interpreting propositions as weak measurements is due to the fact that we introduced a quantum metalanguage. In fact, in the interpretation of propositions, the complex factors multiplying the projection operators are nothing else than the assertion degrees. Some results of this thesis are: a) The adoption of a new kind of metalanguage, the quantum metalanguage, where the metalinguistic links are quantum correlations, and assertions have a complex assertion-degree. b) The introduction, through the reflection principle, of new (quantum) connectives, like “quantum superposition”, and “quantum entanglement”. c) The introduction of a new dual operation (which is a generalization of Sambin-Girard logical duality) to take into account the dual Hilbert space occurring in the interpretation. d) A quantum cut rule, which is interpreted as a quantum projective measurement. As the cut is a meta-rule, it follows that a quantum machine cannot perform a self-measurement and destroy itself. e) A new meta-rule, not equivalent to the cut, named “EPR rule” (to remind the Einstein-Podolsky-Rosen paradox). This rule allows to prove simultaneously two entangled theorems. f) The formulation of the “qubit theorem”, which is the logical description of the preparation of the optical qubit state. g) The lattice of propositions of Lq is, in the case of two qubits, orthomodular and non-distributive. Then, Lq is a quantum logic. It should be noticed that Lq is the first logic which is sub-structural, many-valued and quantum at the same time.<br>La logica introdotta in questa tesi, detta Lq, è una logica dell’ informazione quantistica. Lo scopo, infatti, era quello di descrivere logicamente la struttura del qubit (cioè, la sovrapposizione quantistica intrinseca di uno stato quantico a due livelli) e l’intreccio (entanglement) quantistico massimale di due qubits. La logica Lq è ottenuta tramite il principio di riflessione di Sambin della logica di Base, secondo il quale i legami metalinguistici tra asserzioni si riflettono (risolvendo un’ equazione definitoria) in connettivi logici tra proposizioni. Comunque, mentre nella logica di Base il metalinguaggio è classico, nel nostro caso è quantistico. Nel metalinguaggio quantistico, ciascuna asserzione atomica è dotata di un grado di asserzione, un numero complesso che viene interpretato come un’ ampiezza di probabilità. E’ proprio la presenza dei gradi di asserzione che permette l’introduzione del connettivo logico di “sovrapposizione quantistica” in Lq. Quest’ultimo è una generalizzazione del connettivo di congiunzione “and” dotato di indici complessi indicanti con quale “peso” ciascuna proposizione contribuisce alla formazione della proposizione composta. I valori (o gradi) di verità sono i moduli quadrati dei gradi di asserzione, con un range che è l’intervallo reale [0,1]. Pertanto, la logica Lq è polivalente. I gradi di verità, differentemente dalle logiche fuzzy, sono qui interpretati come probabilità quantistiche. Nella logica Lq si mantengono le tre importanti proprietà della logica di Base, cioè simmetria, riflessione e visibilità. Questa scelta è stata dettata dalle seguenti considerazioni: 1) I teoremi di no-cloning e no-erase dell’informazione quantistica non permettono di avere, nella logica corrispondente, le regole strutturali di indebolimento e contrazione, che sono in antitesi con i suddetti teoremi. Pertanto, nella ricerca di una logica dell’ informazione quantistica, ogni logica strutturale deve essere esclusa a priori. 2) La scelta tra le due più importanti logiche sub-strutturali, cioè la logica di Base e la logica Lineare, in favore della prima, è dovuta al fatto che, in assenza di visibilità, il connettivo logico “quantum entanglement” non può essere introdotto. Inoltre, si è cercata una logica dell’ informazione quantistica che avesse un calcolo deduttivo (in particolare il calcolo dei sequenti). La logica Lq sembra essere, finora, l’ unica logica dell’ informazione quantistica che possa soddisfare questi desiderata. L’ interpretazione delle asserzioni del metalinguaggio quantistico è data in termini di stati quantistici (il metalinguaggio quantistico “è” lo spazio di Hilbert). L’ interpretazione delle proposizioni di Lq è data in termini di operatori non-hermitiani, che sono misure deboli. L’ interpretazione di Lq si basa su una generalizzazione dei concetti già proposti da Birkhoff e von Neumann nella logica quantistica “ortodossa”, dove le proposizioni sono interpretate come operatori di proiezione. La differenza consiste nel fatto che in Lq le proposizioni sono interpretate invece come misure deboli, che, diversamente dalle misure proiettive, non danno luogo ad un brusco collasso della funzione d’onda. Questo permette una descrizione logica della sovrapposizione quantistica, perché essa non viene distrutta. La possibilità di interpretare le proposizioni come misure deboli, è dovuta al fatto che abbiamo introdotto un metalinguaggio quantistico. Infatti, il grado di asserzione si riflette, nell’ interpretazione delle proposizioni, con la presenza un fattore moltiplicativo complesso sui proiettori. Alcuni risultati di questa tesi sono: a) L’ adozione di un nuovo tipo di metalinguaggio, il metalinguaggio quantistico, dove i legami metalinguistici sono correlazioni quantistiche, e le asserzioni hanno un grado di asserzione complesso. b) L’ introduzione, tramite il principio di riflessione, di nuovi connettivi logici “quantistici”, quali la “sovrapposizione quantistica” e l’ “entanglement”. c) L’ introduzione di una nuova operazione duale, che è una generalizzazione della dualità logica di Sambin-Girard, che tiene conto, nell’ interpretazione, dello spazio duale di Hilbert. d) Una regola del taglio quantistica, che viene interpretata come misura quantistica proiettiva. Poiché il taglio è una meta-regola, ne consegue che una macchina quantistica non può effettuare una auto-misura e quindi auto-distruggersi. e) Una nuova meta-regola, non equivalente al taglio, detta regola EPR (rifacentesi al paradosso di Einstein-Podolsky-Rosen). Questa regola permette di dimostrare simultaneamente due teoremi entanglati. f) La formulazione del “teorema del qubit”, che è la descrizione logica della preparazione dello stato quantistico del qubit ottico. g) Il fatto che il reticolo delle proposizioni di Lq nel caso di due qubits è orto-modulare non-distributivo. Quindi Lq è una logica quantistica. E’ da notare il fatto che Lq è la prima logica ad essere contemporaneamente sub-strutturale, a molti valori di verità, e quantistica.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2015.<br>This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.<br>Cataloged from student-submitted PDF version of thesis.<br>Includes bibliographical references (pages 151-161).<br>InGaAs is a promising candidate as an n-type channel material for future CMOS due to its superior electron transport properties. Great progress has taken place recently in demonstrating InGaAs MOSFETs for this goal. Among possible InGaAs MOSFET architectures, the recessed-gate design is an attractive option due to its scalability and simplicity. In this thesis, a novel self-aligned recessed-gate fabrication process for scaled InGaAs Quantum-Well MOSFETs (QW-MOSFETs) is developed. The device architectural design emphasizes scalability, performance and manufacturability by making extensive use of dry etching and Si-compatible materials. The fabrication sequence yields precise control of all critical transistor dimensions. This work achieved InGaAs MOSFETs with the shortest gate length (Lg=20 nm), and MOSFET arrays with the smallest contact size (Lc=40 nm) and smallest pitch size (Lp=150 nm), at the time when they were made. Using a wafer bonding technique, InGaAs MOSFETs were also integrated onto a silicon substrate. The fabricated transistors show the potential of InGaAs to yield devices with well-balanced electron transport, electrostatic integrity and parasitic resistance. A device design optimized for transport exhibits a transconductance of 3.1 mS/[mu]m, a value that matches the best III-V high-electron-mobility transistors (HEMTs). The precise fabrication technology developed in this work enables a detailed study of the impact of channel thickness scaling on device performance. The scaled III-V device architecture achieved in this work has also enabled new device physics studies relevant for the application of InGaAs transistors for future logic. A particularly important one is OFF-state leakage. For the first time, this work has unambiguously identified band-to-band tunneling (BTBT) amplified by a parasitic bipolar effect as the cause of excess OFF-state leakage current in these transistors. This finding has important implications for future device design<br>by Jianqiang Lin.<br>Ph. D.

Introduced by C.C. Chang in the 1950s, MV algebras are to many-valued (Łukasiewicz) logics what boolean algebras are to two-valued logic. More recently, effect algebras were introduced by physicists to describe quantum logic. In this thesis, we begin by investigating how these two structures, introduced decades apart for wildly different reasons, are intimately related in a mathematically precise way. We survey some connections between MV/effect algebras and more traditional algebraic structures. Then, we look at the categorical structure of effect algebras in depth, and in particular see how the partiality of their operations cause things to be vastly more complicated than their totally defined classical analogues. In the final chapter, we discuss coordinatization of MV algebras and prove some new theorems and construct some new concrete examples, connecting these structures up (requiring a detour through effect algebras!) to boolean inverse semigroups.

While classical accounts of identity (‘classical’ here pertaining to both logics and physics) are generally well understood, the advent of quantum theory, specifically quantum statistics, has cast shadow over these conceptions. Dealing with the consequently surfacing problems is a philosophically rich and interesting enterprise. I begin this thesis by providing an exegesis of the roles played by, and features of, identity in logics, classical physics, and quantum physics. Therein I consider how under a quantal description of reality, classical notions of identity and individuality break down. In the second chapter, I address how this problem has launched an arc of thought in analytic metaphysics and formal philosophy motivating the development of non-standard formal frameworks with which philosophical sense can be made of quantal objects. Among these, I explore and critically evaluate quaset theory, quasi-set theory, and non-reflexive Schr¨odinger logics, identifying some significant problems with quaset theory that arise in defining cardinality and later, pointing out a problem with Schr¨odinger logics in their modelling of the continuity between quantal and classical treatments of the world. The queer character of identity in the quantal regime motivates a turn to vagueness which I introduce in the third chapter, providing a brief outline of vagueness and the sorites paradox. Further, I reflect on the fundamental nature of vagueness, outlining and evaluating the semantic and ontic conceptions thereof. In the final chapter, I proceed to explicate and assess notions that identity and quantal objects can be vague. I shall discuss accounts according to which the vagueness of identity and quantum objects is posited as a feature of nature emerging in quantum systems — the ontic vagueness of identity — finding that these ideas are flawed and/or rely on misinterpretations of vagueness. Finally, I present an argument which suggests how the vagueness of identity can arise as an artifact of the differing treatments of identity in the quantal and classical regimes in which the vagueness involved can be semantic rather than ontic.

This thesis concerns the wide research area of logic. In particular, the first part is devoted to analyze different kinds of relational systems (orthogonal and residuated), by investigating the properties of the algebras associated to them. The second part is focused on algebras of logic, in particular, the relationship between prominent quantum and fuzzy structures with certain semirings is proved. The last chapter concerns an application of group theory to some well known mathematical puzzles.

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%.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2008.<br>Includes bibliographical references (p. 143-153).<br>In this thesis, I describe demonstration of various quantum information processing tasks using single-photon two-qubit (SPTQ) quantum logic. As an initial state of those tasks, I used various entangled photon pairs, and I describe development of a polarization entangled photon pair source based on a collinear spontaneous parametric down conversion (SPDC) process within a bidirectionally pumped periodically-poled potassium titanyl phosphate (PPKTP) crystal embedded in a polarization Sagnac interferometer and generation of hyper-entangled photon pairs that are simultaneously entangled in the polarization and momentum degrees of freedom. I also introduce deterministic quantum gates based on SPTQ quantum logic where the polarization and momentum degrees of freedom in a single photon are used as two qubits. By applying SPTQ quantum logic to different entangled states, I demonstrate several quantum information tasks such as transferring entanglement from the momentum qubits to the polarization qubits, SPTQ-based complete polarization Bell state measurements, entanglement distillation (Schmidt projection), and a physical simulation of the entangling-probe attack on the Bennett Brassard 1984 (BB84) quantum key distribution (QKD).<br>by Taehyun Kim.<br>Ph.D.

Thesis (M.S. in Computer Engineering)--S.M.U.<br>Title from PDF title page (viewed Mar. 16, 2009). Source: Masters Abstracts International, Volume: 46-05, page: 2734. Adviser: Mitchell A. Thornton. Includes bibliographical references.

The thesis aims to analyze the circuit model of quantum computation, from a fuzzy logico-algebraic perspective, by employing a technique of continuous t-norm based fuzzy polynomial residuation of some of the important building-blocks of quantum circuits involving qudits. The thesis builds upon the previous works on the framework of Quantum Computational Logic, representing the quantum computational operations in general in terms of the ‘Lukasiewicz sum’ (x ⊕ y = min{x + y, 1}), ‘Lukasiewicz negation’ (¬x = 1 − x), and a ‘product t-norm’ (x · y), forming what is known as a ‘product Mv-algebra’. The framework is extended here to the qudit based quantum computational schemes, as the qudits based schemes are yet more nontrivial than even the qubits based schemes – due to the well known non-trivialities of the (d>2) higher-dimensional Hilbert Spaces. Employing a novel unitary gate construction recipe in a qudits-based multi-valued logical setting, the work constructs and investigates generalized quantum versions of the logical-gate-operations of Negation (and its square-root), Hadamard, Swap, as well as those due to Toffoli and Fredkin. It is hoped that the work will be of utility in constructing and interpreting the quantum computational schemes further, –especially from (but not limited to) logico-algebraic perspectives.

In this dissertation we take in account the possibility to face the notion of quantum information from two different points of view: meanwhile in the first part we develop a concrete approach to the notion of quantum information, in the second part we proceed to a more abstract approach. The firts part explores what quantum mechanics forbids to do with information encoded in states of quantum systems. Many of the results of researches about what we can and what we can t do with the information encoded in quantum states are known as no-go theorems; in this dissertation we explore new limitations on the possibility to manipulate quantum information revealing that many easy tasks for classical information are impossible when the information is encoded in quantum states. As result of our analysis it arises that the nature of information encoded in quantum states restricts in a very structured way the possible manipulations or exact behaviour of the operations on the information itself. In the second part of dissertation we concentrate on logic-algebraich approach to quantum information. We relax the condition of a quantum circuit constitued by a fixed number of particles and we take in account a quantum system of variable and undeterminate number of particles. This approach is developed in the mathematical framework of Fock space which allows a more flexible treatment of information encoded in quantum register of variable lenght. As consequence, we proceed towards a possible logic-algebraic formalization of the behaviour of quantum information encoded in variable lenght registers during a computational process.

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 thesis is concerned with the development of an intermediate magnetic field "clock-qubit" in ⁴³Ca⁺ at 146G and techniques to manipulate this qubit using microwaves and lasers. While ⁴³Ca⁺ has previously been used as a qubit, its relatively complicated level structure - with a nuclear spin of 7/2 and low-lying D-states -- makes cooling it in the intermediate field an intimidating prospect. As a result, previous experiments have used small magnetic fields of a few gauss where coherence times are limited and off-resonant excitation is a significant source of experimental error. We demonstrate a simple scheme that allows ⁴³Ca⁺ to be cooled in the intermediate field without any additional experimental complexity compared with low fields. Using the clock-qubit, we achieve a coherence time of T^*<sub style='position:relative;left:-.5em;'>2</sub> = 50 (10)s - the longest demonstrated in any single qubit. We also demonstrate a combined state preparation and measurement error of 6.8(6)x 10^-4 - the lowest achieved for a hyperfine trapped ion qubit [NVG⁺13] - and single-qubit logic gates with average errors of 1.0(3) x 10^-6 - more than an order of magnitude better than the previous record [BWC⁺11]. These results represent the state-of-the-art in the field of single-qubit control. Moreover, we achieve them all in a single scalable room-temperature ion trap using experimentally robust techniques and without relying on the use of narrow-linewidth lasers, magnetic field screening or dynamical decoupling techniques. We also present work on a recent scheme [OWC⁺11] to drive two-qubit gates using microwaves. We have constructed an ion trap with integrated microwave circuitry to perform these gates. Using this trap, we have driven motional sideband transitions, demonstrating the spin-motion coupling that underlies the two-qubit gate. We present an analysis of likely sources of experimental error during a future two-qubit gate and the design and preliminary characterisation of apparatus to minimise the main error contributions. Using this apparatus, we hope to perform a two-qubit gate in the near future.

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.

The reversible logic has the promising applications in emerging computing paradigm such as quantum computing, quantum dot cellular automata, optical computing, etc. In reversible logic gates there is a unique one-to-one mapping between the inputs and outputs. To generate an useful gate function the reversible gates require some constant ancillary inputs called ancilla inputs. Also to maintain the reversibility of the circuits some additional unused outputs are required that are referred as the garbage outputs. The number of ancilla inputs, number of garbage outputs and quantum cost plays an important role in the evaluation of reversible circuits. Thus minimizing these parameters are important for designing an efficient reversible circuit. Barrel shifter is an integral component of many computing systems due to its useful property that it can shift and rotate multiple bits in a single cycle. The main contribution of this thesis is a set of design methodologies for the reversible realization of reversible barrel shifters where the designs are based on the Fredkin gate and the Feynman gate. The Fredkin gate can implement the 2:1 MUX with minimum quantum cost, minimum number of ancilla inputs and minimum number of garbage outputs and the Feynman gate can be used so as to avoid the fanout, as fanout is not allowed in reversible logic. The design methodologies considered in this work targets 1.) Reversible logical right- shifter, 2.) Reversible universal right shifter that supports logical right shift, arithmetic right shift and the right rotate, 3.) Reversible bidirectional logical shifter, 4.) Reversible bidirectional arithmetic and logical shifter, 5) Reversible universal bidirectional shifter that supports bidirectional logical and arithmetic shift and rotate operations. The proposed design methodologies are evaluated in terms of the number of the garbage outputs, the number of ancilla inputs and the quantum cost. The detailed architecture and the design of a (8,3) reversible logical right-shifter and the (8,3) reversible universal right shifter are presented for illustration of the proposed methodologies.

Semiconductor industry seems to approach a wall where physical geometry and power density issues could possibly render the device fabrication infeasible. Quantum-dot Cellular Automata (QCA) is a new nanotechnology that claims to offer the potential of manufacturing even denser integrated circuits, which can operate at high frequencies and low power consumption. In QCA technology, the signal propagation occurs as a result of electrostatic interaction among the electrons as opposed to flow to the electrons in a wire. The basic building block of QCA technology is a QCA cell which encodes binary information with the relative position of electrons in it. A QCA cell can be used either as a wire or as logic. In QCA, the directionality of the signal flow is controlled by phase-shifted electric field generated on a separate layer than QCA cell layer. This process is called clocking of QCA circuits. The logic realization using regular structures such as PLAs have played a significant role in the semiconductor field due to their manufacturability, behavioral predictability and the ease of logic mapping. Along with these benefits, regular structures in QCA's would allow for uniform QCA clocking structure. The clocking structure is important because the pioneers of QCA technology propose it to be fabricated in CMOS technology. This thesis presents a detailed design implementation and a comparative analysis of logic realization using regular structures, namely Shannon-Lattices and PLAs for QCAs. A software tool was developed as a part of this research, which automatically generates complete QCA-Shannon-Lattice and QCA-PLA layouts for single-output Boolean functions based on an input macro-cell library. The equations for latency and throughput for the new QCA-PLA and QCA-Shannon-Lattice design implementations were also formulated. The correctness of the equations was verified by performing simulations of the tool-generate layouts with QCADesigner. A brief design trade-off analysis between the tool-generated regular structure implementation and the unstructured custom layout in QCA is presented for the full-adder circuit.

A scheme for realizing arbitrary controlled-unitary operations in a two qubit system is presented here. If the 2 × 2 unitary matrix is special unitary (has unit determinant), the controlled-unitary gate operation can be realized in a single pulse operation. The pulse in this scheme constitutes varying one of the parameters of the system between an arbitrary maximum and a “calculated” minimum value. This parameter will constitute the variable parameter of the system while the other parameters, which include the coupling between the two qubits, will be treated as fixed parameters. The values of the parameters are what are solved for to realize an arbitrary controlled-unitary operation where the computational complexity of the operation is no greater than that required for a Controlled-NOT (CNOT) gate. Since conventional schemes realize a controlled-unitary operation by breaking it into a sequence of single-qubit and CNOT gate operations, the method presented here is an improvement because not only does it require lesser time duration, but also fewer control lines, to implement the same operation. Furthermore, the method can be applied to a wide range of coupling schemes and can be used to realize gate operations between two qubits coupled via Ising, Heisenberg and anisotropic interactions. Next, a general scheme for implementing bi-directional quantum state transfer in a linear architecture involving un-tunable nearest-neighbor interactions is presented. Unlike quantum spin networks, the scheme allows transmission of several quantum states at a time, requiring only a two qubit separation between quantum states. Moreover, it is shown that only eight control lines are required to achieve state transfer along a channel of arbitrary length, making the scheme efficient.<br>Thesis (Ph.D.)--Wichita State University, College of Engineering, Dept. of Electrical and Computer Engineering<br>"July 2007."

Submitted by Isaac Francisco de Souza Dias (isaac.souzadias@ufpe.br) on 2016-04-22T17:25:36Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) DISSERTAÇÃO Bruna Gabrielly Moraes Araujo.pdf: 1520286 bytes, checksum: 8710e7e722157c16863f72b3fa57f732 (MD5)<br>Made available in DSpace on 2016-04-22T17:25:36Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) DISSERTAÇÃO Bruna Gabrielly Moraes Araujo.pdf: 1520286 bytes, checksum: 8710e7e722157c16863f72b3fa57f732 (MD5) Previous issue date: 2015-08-04<br>CNPQ<br>Nesta dissertação, tratamos da computação quântica em variáveis contínuas empregando a armadilha de íons como plataforma física. A proposta central deste trabalho consiste na sistematização de uma toolbox com portas lógicas gaussianas a partir da manipulação coerente dos modos de vibração de um íon aprisionado. Através da irradiação de feixes de lasers clássicos monocromáticos e bicromáticos em um íon confinado, propomos portas lógicas gaussianas análogas às operações de ótica linear e não linear. Relacionamos essas portas lógicas a operações já bem conhecidas do caso discreto, tais como transformada de Fourier, gates CNOT e CPHASE. A execução de cada uma dessas operações lógicas é selecionada pela frequência do laser de interação e pelo parâmetro de Lamb-Dicke. Reunindo todas as operações obtidas, gaussianas e não gaussianas, mostramos ser possível com nosso sistema simular hamiltonianas descritas por um polinômio em cada coordenada do espaço de fase, permitindo com isso a realização de dinâmicas hamiltonianas polinomiais nesse espaço.<br>In this monography, we propose the realization of quantum computation over continuous variables using the ion trap as physical platform. The central idea of our work is to provide a toolbox of Gaussian logic gates from the coherent manipulation of the vibrational modes of a trapped ion. By irradiating monochromatic and bichromatic classical laser beams in a confined ion, we propose gaussian logic gates similar to the operations of linear and nonlinear optics. We connect these gates with operations already employed in the discrete case, such as Fourier, CNOT and CPHASE gates. The execution of each of these logical operations is selected by the frequency of the interacting laser and the Lamb-Dicke parameters. Bringing together all the proposed operations, Gaussian and non-Gaussian, we show the simulation of Hamiltonians with polynomial expansion in the phase space coordinates.

We investigate the geometric phase (GP) acquired by the states of a spin-1/2 nucleus which is subject to a static magnetic field. This nucleus as the carrier system of GP, is taken as coupled to a dissipative environment, so that it evolves non-unitarily. We study the effects of different characteristics of different environments on GP as nucleus evolves in time. We showed that magnetic field strength is the primary physical parameter that determines the stability of GP<br>its stability decreases as the magnetic field strength increases. (By decrease in stability what we mean is the increase in the time rate of change of GP.) We showed that this decrease can be very rapid, and so it could be impossible to make use of it as a quantum logic gate in quantum information theory (QIT). To see if these behaviors differ in different environments, we analyze the same system for a fixed temperature environment which is under the influence of an electromagnetic field in a squeezed state. We find that the general dependence of GP on magnetic field does not change, but this time the effects are smoother. Namely, increase in magnetic field decreases the stability of GP also for in this environment<br>but this decrease is slower in comparison with the former case, and furthermore it occurs gradually. As a second problem we examine the entanglement of two atoms, which can be used as a two-qubit system in QIT. The entanglement is induced by an external quantum system. Both two-level atoms are coupled to a third two-level system by dipole-dipole interaction. The two atoms are assumed to be in ordinary vacuum and the third system is taken as influenced by a certain environment. We examined different types of environments. We show that the steady-state bipartite entanglement can be achieved in case the environment is a strongly fluctuating, that is a squeezed-vacuum, while it is not possible for a thermalized environment.

Quantum computers offer great potential for significant speedup in executing certain algorithms compared to their classical counterparts. One of the most promising physical systems in which implementing such a device seems viable are trapped atomic ions. All of the fundamental operations needed for quantum information processing have already been experimentally demonstrated in trapped ion systems. Today, the remaining two obstacles are to improve the fidelities of these operations up to the point where quantum error correction techniques can be successfully applied, as well as to scale up the present systems to a higher number of quantum bits (qubits). This thesis addresses both issues. On the one hand, it decribes the experimental implementation of a high-fidelity two-qubit quantum logic gate, which is the most technically demanding fundamental operation to realise in practice. On the other hand, the presented work is carried out in a microfabricated surface ion trap - an architecture that holds the promise of scalability. The gate is applied directly to hyperfine "atomic clock" qubits in ⁴³Ca⁺ ions using the near-field microwave magnetic field gradient produced by an integrated trap electrode. To protect the gate against fluctuating energy shifts of the qubit states, as well as to avoid the need to null the microwave field at the position of the ions, a dynamically decoupled Mølmer-Sørensen scheme is employed. After accounting for state preparation and measurement errors, the achieved gate fidelity is 99.7(1)%. In previous work, the same apparatus has been used to demonstrate coherence times of T^&ast;₂ &asymp; 50 s and all single-qubit operations with fidelity > 99.95%. To gain access to the "atomic clock" qubit transition in ⁴³Ca⁺, a static magnetic field of 146G is applied. The resulting energy level Zeeman-structure is spread over many times the linewidth of the atomic transition used for Doppler cooling. This thesis presents a simple and robust method for Doppler cooling and obtaining high fluorescence from this qubit in spite of the complicated level structure. A temperature of 0.3mK, slightly below the Doppler limit, is reached.

This thesis describes experimental work towards the development of a trapped-ion quantum computer based on microchip ion traps and long-wavelength radiation, using magnetic field gradients. The relationship between experimental parameters and two-qubit gate fidelity is investigated for microchips with two different static magnetic field gradient generation methods. For current-carrying wires and under-chip permanent magnets, optimum ion heights of 110 μm and 200 μm are found respectively. Construction of an experiment capable of demonstrating high-fidelity gates is reported, including innovations for the use of microchip ion traps with permanent magnets. The development of a vacuum system for versatile microchip experiments is described, including new methods for impedance-matched RF delivery, in-vacuum filtering and liquid nitrogen microchip cooling. Protection of both the microchip surface from atomic flux and of ions from the charged imaging viewport are both investigated in detail. A new preparation framework for microchip ion traps before their use in experiments is developed. In order to remove unwanted deposited layers on the microchips, a process of multiple chemical treatments is used. In addition, these characterisation efforts lead to refinement of the microfabrication process for future microchips. The application of large currents to microchips is of fundamental importance to scalable trapped-ion quantum computing using static magnetic field gradients. As part of the characterisation process, currents of ≈ 10A are successfully applied to microfabricated current-carrying wires, demonstrating the viability of these structures for generation of local magnetic fields and gradients in a quantum computing device. The operation of a microchip ion trap experiment with under-chip permanent magnets for a high magnetic field gradient (≈ 140Tm−1) is described. The successful trapping of ytterbium-174 and -171 ions is reported, as well as their use to measure and optimise the ion trap parameters. The thesis concludes with consideration of the expected future results from the ongoing operation of the experiment.

A fundamental component of theoretical computer science is the application of logic. Logic provides the formalisms by which we can model and reason about computational questions, and novel computational features provide new directions for the development of logic. From this perspective, the unusual features of quantum computation present both challenges and opportunities for computer science. Our existing logical techniques must be extended and adapted to appropriately model quantum phenomena, stimulating many new theoretical developments. At the same time, tools developed with quantum applications in mind often prove effective in other areas of logic and computer science. In this thesis we explore logical aspects of this fruitful source of ideas, with category theory as our unifying framework. Inspired by the success of diagrammatic techniques in quantum foundations, we begin by demonstrating the effectiveness of string diagrams for practical calculations in category theory. We proceed by example, developing graphical formulations of the definitions and proofs of many topics in elementary category theory, such as adjunctions, monads, distributive laws, representable functors and limits and colimits. We contend that these tools are particularly suitable for calculations in the field of coalgebra, and continue to demonstrate the use of string diagrams in the remainder of the thesis. Our coalgebraic studies commence in chapter 3, in which we present an elementary formulation of a representation result for the unitary transformations, following work developed in a fibrational setting in [Abramsky, 2010]. That paper raises the question of what a suitable "fibred coalgebraic logic" would be. This question is the starting point for our work in chapter 5, in which we introduce a parameterized, duality based frame- work for coalgebraic logic. We show sufficient conditions under which dual adjunctions and equivalences can be lifted to fibrations of (co)algebras. We also prove that the semantics of these logics satisfy certain "institution conditions" providing harmony between syntactic and semantic transformations. We conclude by studying the impact of parameterization on another logical aspect of coalgebras, in which certain fibrations of predicates can be seen as generalized invariants. Our focus is on the lifting of coalgebra structure along a fibration from the base category to an associated total category of predicates. We show that given a suitable parameterized generalization of the usual liftings of signature functors, this induces a "fibration of fibrations" capturing the relationship between the two different axes of variation.

Some people believe that IC densities are approaching the fundamental limits inherent to semiconductor technologies. One alternative to semiconductors is Quantum-dot Cellular Automata (QCA); QCA is a nanotechnology that offers the potential to build denser IC's that switch at higher frequencies and run on lower power. QCA's most basic building block, the QCA cell, is inherently binary; digital circuits are implemented by arranging these QCA cells in pre-defined configurations on a two dimensional plane. This paper proposes a logic formulation that describes arranging QCA cells on a two dimensional plane; it is presented as a set of rules that can be implemented with basic Boolean variables and operators. This Boolean formulation is general and can be applied to any given specification. In addition, an optimization constraint is defined so that the logic formulation will only validate the most efficient QCA cell arrangements. The correctness of the logic formulation has been empirically verified by testing it with a SAT solver. The effectiveness of the minimization constraint in conjunction with the logic formulation has been tested with a Pseudo-Boolean ILP solver.

The successful era of CMOS technology is coming to an end. The limit on minimum fabrication dimensions of transistors and the increasing leakage power hinder the technological scaling that has characterized the last decades. In several different ways, this problem has been addressed changing the architectures implemented in CMOS, adopting parallel processors and thus increasing the throughput at the same operating frequency. However, architectural alternatives cannot be the definitive answer to a continuous increase in performance dictated by Moore’s law. This problem must be addressed from a technological point of view. Several alternative technologies that could substitute CMOS in next years are currently under study. Among them, magnetic technologies such as NanoMagnet Logic (NML) are interesting because they do not dissipate any leakage power. More- over, magnets have memory capability, so it is possible to merge logic and memory in the same device. However, magnetic circuits, and NML in this specific research, have also some important drawbacks that need to be addressed: first, the circuit clock frequency is limited to 100 MHz, to avoid errors in data propagation; second, there is a connection between circuit layout and timing, and in particular, longer wires will have longer latency. These drawbacks are intrinsic to the technology and for this reason they cannot be avoided. The only chance is to limit their impact from an architectural point of view. The first step followed in the research path of this thesis is indeed the choice and optimization of architectures able to deal with the problems of NML. Systolic Ar- rays are identified as an ideal solution for this technology, because they are regular structures with local interconnections that limit the long latency of wires; more- over they are composed of several Processing Elements that work in parallel, thus exploit parallelization to increase throughput (limiting the impact of the low clock frequency). Through the analysis of Systolic Arrays for NML, several possible im- provements have been identified and addressed: 1) it has been defined a rigorous way to increase throughput with interleaving, providing equations that allow to esti- mate the number of operations to be interleaved and the rules to provide inputs; 2) a latency insensitive circuit has been designed, that exploits a data communication protocol between processing elements to avoid data synchronization problems. This feature has been exploited to design a latency insensitive Systolic Array that is able to execute the Floyd-Steinberg dithering algorithm. All the improvements presented in this framework apply to Systolic Arrays implemented in any technology. So, they can also be exploited to increase performance of today’s CMOS parallel circuits. This research path is presented in Chapter 3. While Systolic Arrays are an interesting solution for NML, their usage could be quite limited because they are normally application-specific. The second re- search path addresses this problem. A Reconfigurable Systolic Array is presented, that can be programmed to execute several algorithms. This architecture has been tested implementing many algorithms, including FIR and IIR filters, Discrete Cosine Transform and Matrix Multiplication. This research path is presented in Chapter 4. In common Von Neumann architectures, the logic part of the circuit and the memory one are separated. Today bus communication between logic and memory represents the bottleneck of the system. This problem is addressed presenting Logic- In-Memory (LIM), an architecture where memory elements are merged in logic ones. This research path aims at defining a real LIM architectures. This has been done in two steps. The first step is represented by an architecture composed of three layers: memory, routing and logic. In the second step instead the routing plane is no more present, and its features are inherited by the memory plane. In this solution, a pyramidal memory model is used, where memories near logic elements contain the most probably used data, and other memory layers contain the remaining data and instruction set. This circuit has been tested with odd-even sort algorithms and it has been benchmarked against GPUs and ASIC. This research path is presented in Chapter 5. MagnetoElastic NML (ME-NML) is a technological improvement of the NML principle, proposed by researchers of Politecnico di Torino, where the clock system is based on the induced stretch of a piezoelectric substrate when a voltage is ap- plied to its boundaries. The main advantage of this solution is that it consumes much less power than the classic clock implementation. This technology has not yet been investigated from an architectural point of view and considering complex circuits. In this research field, a standard methodology for the design of ME-NML circuits has been proposed. It is based on a Standard Cell Library and an enhanced VHDL model. The effectiveness of this methodology has been proved designing a Galois Field Multiplier. Moreover the serial-parallel trade-off in ME-NML has been investigated, designing three different solutions for the Multiply and Accumulate structure. This research path is presented in Chapter 6. While ME-NML is an extremely interesting technology, it needs to be combined with other faster technologies to have a real competitive system. Signal interfaces between NML and other technologies (mainly CMOS) have been rarely presented in literature. A mixed-technology multiplexer is designed and presented as the basis for a CMOS to NML interface. The reverse interface (from ME-NML to CMOS) is instead based on a sensing circuit for the Faraday effect: a change in the polarization of a magnet induces an electric field that can be used to generate an input signal for a CMOS circuit. This research path is presented in Chapter 7. The research work presented in this thesis represents a fundamental milestone in the path towards nanotechnologies. The most important achievement is the de- sign and simulation of complex circuits with NML, benchmarking this technology with real application examples. The characterization of a technology considering complex functions is a major step to be performed and that has not yet been ad- dressed in literature for NML. Indeed, only in this way it is possible to intercept in advance any weakness of NanoMagnet Logic that cannot be discovered consid- ering only small circuits. Moreover, the architectural improvements introduced in this thesis, although technology-driven, can be actually applied to any technology. We have demonstrated the advantages that can derive applying them to CMOS cir- cuits. This thesis represents therefore a major step in two directions: the first is the enhancement of NML technology; the second is a general improvement of parallel architectures and the development of the new Logic-In-Memory paradigm.

In recent years ternary reversible logic has caught the attention of researchers because of its enormous potential in different fields, in particular quantum computing. It is desirable that any future reversible technology should be fault tolerant and have low power consumption; hence developing testing techniques in this area is of great importance. In this work we propose a design for an online testable ternary reversible circuit. The proposed design can implement almost all of the ternary logic operations and is also capable of testing the reversible ternary network in real time (online). The error detection unit is also constructed in a reversible manner, which results in an overall circuit which meets the requirements of reversible computing. We have also proposed an upgrade of the initial design to make the design more optimized. Several ternary benchmark circuits have been implemented using the proposed approaches. The number of gates required to implement the benchmarks for each approach have also been compared. To our knowledge this is the first such circuit in ternary with integrated online testability feature.<br>xii, 92 leaves : ill. ; 29 cm

The following dissertation addresses the study of nano-magnetic devices configured to produce logic machines through magnetostatic coupling interactions. The ability for single domain magnets to reliably couple through magnetostatic interactions is essential to the proper functionality of Magnetic Cellular Automata (MCA) devices (p. 36). It was significant to explore how fabrication defects affected the coupling reliability of MCA architectures. Both ferromagnetic and anti-ferromagnetic coupling architectures were found to be robust to common fabrication defects. Experiments also verified the functionality of the previously reported MCA majority gate [1] and a novel implementation of a ferromagnetic MCA majority gate is reported. From these results, the study of clocking Magnetic Cellular Automata (MCA) interconnect architectures was investigated (p. 54). The wire architectures were saturated under distinct directions of an external magnetic field. The experimental results suggested ferromagnetic coupled wires were able to mitigate magnetic frustrations better than anti-ferromagnetic coupled wires. Simulations were also implemented supporting the experimental results. Ferromagnetic wires were found to operate more reliably and will likely be the primary interconnects for MCA. The first design and implementation of a coplanar cross wire system for MCA was constructed which consisted of orthogonal ferromagnetic coupled wires (p. 68). Simulations were implemented of a simple crossing wire junction to analyze micro-magnetic dynamics, data propagation, and associated energy states. Furthermore, two systems were physically realized; the first system consisted of two coplanar crossing wires and the second was a more complex system consisting of over 120 nano-magnetic cells. By demonstrating the combination of all the possible logic states of the first system and the low ground state achieved by the second system, the data suggested coplanar cross wire systems would indeed be a viable architecture in MCA technology. Finally, ongoing research of an unconventional method for image processing using nano-magnetic field-based computation is presented (p. 79). In magnetic field-based computing (MFC), nano-disks were mapped to low level segments of an image, and the magnetostatic coupling of magnetic dipole moments was directly related to the saliency of a low level segment for grouping. A proof of concept model for two MFC systems was implemented. Details such as the importance of fabricating circular nano-magnetic cells to mitigate shape anisotropy, experimental coupling analysis via Magnetic Force Microscopy, and current results from a complex MFC system is outlined.

Since its inception, Moore's Law has been a reliable predictor of computational power. This steady increase in computational power has been due to the ability to fit increasing numbers of transistors in a single chip. A consequence of increasing the number of transistors is also increasing the power consumption. The physical properties of CMOS technologies will make this powerwall unavoidable and will result in severe restrictions to future progress and applications. A potential solution to the problem of rising power demands is to investigate alternative low power nanotechnologies for implementing logic circuits. The intrinsic properties of these emerging nanotechnologies result in them being low power in nature when compared to current CMOS technologies. This thesis specifically highlights quantum dot celluar automata (QCA) and nanomagnetic logic (NML) as just two possible technologies. Designs in NML and QCA are explored for simple arithmetic units such as full adders and subtractors. A new multilayer 5-input majority gate design is proposed for use in NML. Designs of reversible adders are proposed which are easily testable for unidirectional stuck at faults.

This thesis reports high-fidelity near-field spatial microwave addressing of long-lived ⁴³Ca⁺ "atomic clock" qubits performed in a two-zone single-layer surface-electrode ion trap. Addressing is implemented by using two of the trap's integrated microwave electrodes, one in each zone, to drive single-qubit rotations in the zone we choose to address whilst interferometrically cancelling the microwave field at the neighbour (non-addressed) zone. Using this field-nulling scheme, we measure a Rabi frequency ratio between addressed and non-addressed zones of up to 1400, from which we calculate an addressing error (or a spin-flip probability on the qubit transition) of 1e-6. Off-resonant excitation out of the qubit state is a more significant source of error in this experiment, but we also demonstrate polarisation control of the microwave field at an error level of 2e-5, which, if combined with individual-ion addressing, would be sufficient to suppress off-resonant excitation errors to the 1e-9 level. Further, this thesis presents preliminary results obtained with a micron-scale coupled-microstrip differential antenna probe that can be scanned over an ion-trap chip to map microwave magnetic near fields. The probe is designed to enable the measurement of fields at tens of microns above electrode surfaces and to act as an effective characterisation tool, speeding up design-fabrication-characterisation cycles in the production of new prototype microwave ion-trap chips. Finally, a new multi-layer design for an ion-trap chip which displays, in simulations, a 100-fold improvement in addressing performance, is presented. The chip electrode structure is designed to use the cancelling effect of microwave return currents to produce Rabi frequency ratios of order 1000 between trap zones using a single microwave electrode (i.e. without the need for nulling fields). If realised, this chip could be used to drive individually addressed single-qubit operations on arrays of memory qubits in parallel and with high fidelity.

Recently, researchers have been interested in reversible computing because of its ability to dissipate nearly zero heat and because of its applications in quantum computing and low power VLSI design. Synthesis and testing are two important areas of reversible logic. The thesis first presents an approach for the synthesis of reversible circuits from the exclusive- OR sum-of-products (ESOP) representation of functions, which makes better use of shared functionality among multiple outputs, resulting in up to 75% minimization of quantum cost compared to the previous approach. This thesis also investigates the previous work on constructing the online testable circuits and points out some design issues. A simple approach for online fault detection is proposed for a particular type of ESOP-based reversible circuit, which is also extended for any type of Toffoli circuits. The proposed online testable designs not only address the problems of the previous designs but also achieve significant improvements of up to 78% and 99% in terms of quantum cost and garbage outputs, respectively.<br>xii, 82 leaves : ill. ; 29 cm

This thesis studies the categorical formalisation of quantum computing, through the prism of type theory, in a three-tier process. The first stage of our investigation involves the creation of the dagger lambda calculus, a lambda calculus for dagger compact categories. Our second contribution lifts the expressive power of the dagger lambda calculus, to that of a quantum programming language, by adding classical control in the form of complementary classical structures and dualisers. Finally, our third contribution demonstrates how our lambda calculus can be applied to various well known problems in quantum computation: Quantum Key Distribution, the quantum Fourier transform, and the teleportation protocol.

In thinking about quantum causality one would like to approach rigorous QFT from outside the perspective of QFT, which one expects to recover only in a specific physical domain of quantum gravity. This thesis considers issues in causality using Category Theory, and their application to field theoretic observables. It appears that an abstract categorical Machian principle of duality for a ribbon graph calculus has the potential to incorporate the recent calculation of particle rest masses by Brannen, as well as the Bilson-Thompson characterisation of the particles of the Standard Model. This thesis shows how Veneziano n point functions may be recovered in such a framework, using cohomological techniques inspired by twistor theory and recent MHV techniques. This distinct approach fits into a rich framework of higher operads, leaving room for a generalisation to other physical amplitudes. The utility of operads raises the question of a categorical description for the underlying physical logic. We need to consider quantum analogues of a topos. Grothendieck's concept of a topos is a genuine extension of the notion of a space that incorporates a logic internal to itself. Conventional quantum logic has yet to be put into a form of equal utility, although its logic has been formulated in category theoretic terms. Axioms for a quantum topos are given in this thesis, in terms of braided monoidal categories. The associated logic is analysed and, in particular, elements of linear vector space logic are shown to be recovered. The usefulness of doing so for ordinary quantum computation was made apparent recently by Coecke et al. Vector spaces underly every notion of algebra, and a new perspective on it is therefore useful. The concept of state vector is also readdressed in the language of tricategories.

Thesis (Ph. D.)--Ohio State University, 2004.<br>Title from first page of PDF file. Document formatted into pages; contains xxv, 201 p.; also includes graphics Includes bibliographical references (p. 188-201). Available online via OhioLINK's ETD Center

Orientador: Jose Antonio Roversi<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin<br>Made available in DSpace on 2018-08-23T20:03:52Z (GMT). No. of bitstreams: 1 Yabu-uti_BrunoFerreiradeCamargo_D.pdf: 3039693 bytes, checksum: f0b083dd372cff54e492778d15824a5b (MD5) Previous issue date: 2013<br>Resumo: Na presente tese estudamos o processamento de informação quântica no sistema de átomos e cavidades acopladas. Em particular, a comunicação quântica estabelecida entre átomos remotos e a implementação de portas lógicas no sistema de cavidades acopladas. Iniciamos apresentando o sistema de cavidades acopladas, o Hamiltoniano que governa sua evolução, algumas promissoras implementações experimentais e a transferência de um estado de campo arbitrário de um fóton ao longo da cadeia. Incluindo um sistema massivo, propomos um novo protocolo para uma transferência perfeita, determinística e flexível de estados quânticos entre átomos remotos interagindo sucessivamente com o sistema de cavidades acopladas (atuando como quantum bus). Mesmo levando em conta efeitos dissipativos e erros de procedimento obtivemos uma alta fidelidade máxima de transmissão. Por fim, apresentamos uma proposta alternativa para a implementação de um porta R(rotação)- controlada de dois qubits. A proposta está baseada em operações de um qubit e fase geométrica não-convencional em átomos de três níveis idênticos fortemente bombeados por um campo clássico ressonante em cavidades ópticas distantes conectadas por uma fibra óptica. Nossa proposta resulta em um tempo operacional constante e, com um acoplamento qubit-bus ajustável (atomoressonador), pode-se especificar uma rotação R particular no qubit alvo<br>Abstract: In this thesis we study the quantum information processing in the system of atom-coupled cavity. In particular, the quantum communication between remote atoms and the implementation of logic gates in the coupled cavities system. We begin by presenting the system of coupled cavities, the Hamiltonian that governs its evolution, some promising experimental implementations and the transfer of an arbitrary one photon field state along the array. Including a massive system, we propose a new protocol for a perfect, deterministic and flexible quantum state transfer between remote atoms interacting successively with the system of coupled cavities (which act as a quantum bus). Even taking into account dissipative effects and error procedure we obtained a maximum high-fidelity transmission. We also present an alternative proposal for the implementation of a controlled-R gate of two qubits. The proposal is based on single qubit operations and unconventional geometric phases on two identical three-level atoms, strongly driven by a resonant classical field, trapped in distant cavities connected by an optical fiber. Our scheme results in a constant gating time and, with an adjustable qubit-bus coupling (atom-resonator), one can specify a particular rotation R on the target qubit<br>Doutorado<br>Física<br>Doutor em Ciências