Orientadores: Gilberto Medeiros Ribeiro e Jose Antonio Brum / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-08-11T11:01:49Z (GMT). No. of bitstreams: 1 Alegre_ThiagoPedroMayer_D.pdf: 15787837 bytes, checksum: a41c0877b93a156734db9d614610e2f4 (MD5) Previous issue date: 2008 / Resumo: Esta tese consistiu na proposição e implementação de um sistema para processamento de informação quântica, focando a instrumentação necessária. Os aspectos físicos da computação, como a energia associada, entropia de Shannon, entre outros conceitos básicos observados na perspectiva de física, foram revistos. Pontos quânticos semicondutores de InAs:GaAs foram eleitos como candidatos para a implementação física do sistema; em particular, focou-se no grau de liberdade de spin do elétron. Conseqüentemente, investigaram-se as propriedades de tensor-g dos elétrons aprisionados em pontos quânticos e o grau de polarização de spin, como função do campo magnético e da temperatura. Naturalmente, as propriedades eletrônicas, como o potencial de confinamento e as transições ópticas, foram caracterizadas e modeladas através da teoria de massa efetiva, assumindo-se um potencial de confinamento lateral parabólico. Dado que o grau de liberdade de spin foi eleito, construiu-se um sistema de medidas de ressonância paramagnética de spins. Optou-se por não se utilizar sistemas comerciais padrão. Em lugar disto, foi projetada uma montagem conectorizada, onde o material semicondutor se encontra dentro de umchip desenhado para concentrar o campo magnético de microonda sobre o dispositivo, campo este necessário para a realização de ressonância paramagnética. O chip consistiu basicamente de uma cavidade de microfita de meia onda. Foi construída também uma cavidade com duas entradas, permitindo o controle arbitrário da polarização aplicada à amostra. Finalmente, a leitura de estados quânticos de spin em centros paramagnéticos é demonstrada através de detecção óptica. A alta sensibilidade desse tipo de detecção permite que um único defeito seja mapeado. A seletividade, tanto do ponto de vista das transições ópticas quanto das transições de spin, é estudada e manipulada, utilizando-se da montagem experimental de cavidades ressonantes. Adicionalmente, perspectivas de experimentos sobre a integração e utilidade do sistema são apresentados / Abstract: This thesis proposes and implements a system for quantum information processing, focusing primarily on the associated instrumentation. The basic physical aspects for computation, such as the associated energy and Shannon's entropy, were revisited. InAs:GaAs quantum dots were elected as the physical system of choice for this implementation; in particular, the spin degree of freedom of the trapped electrons was utilized. Therefore, the electronic properties of the quantum dots, as well the g-tensor and the polarization degree, were investigated as a function of the temperature and magnetic field. It was possible to describe the electronic properties within the effective mass formalism, assuming a parabolic lateral confinement. Since the spin degree of freedom was elected as the basis for the quantum computation, a system for spin paramagnetic resonance was devised. The choice for not using a commercial system was made. Instead, a connectorized setup was designed, permitting the semiconductor material to be within a chip, and additionally allowing for focusing the microwave magnetic field above the device. Basically, this chip consisted of a half-wavelength microstrip cavity. A second microstrip cavity with two input ports was also designed to allow the arbitrary control of microwave polarization delivered to the sample. Finally, the quantum state read-out was demonstrated through an optical technique on Nitrogen-Vacancy complexes in diamond. The high sensitivity of the system allows for single spin detection. The selectivity for the optical and spin transitions was characterized and manipulated, using the resonant cavity experimental setup. As a perspective, experiments exploring integration issues on the system are shown / Doutorado / Física da Matéria Condensada / Doutor em Ciências

Cette thèse a pour première vocation d’être un état de l’art sur le calcul quantique, sinon exhaustif, simple d’accès (chapitres 1, 2 et 3). La partie originale de cet essai consiste en deux approches mathématiques du calcul quantique concernant quelques systèmes quantiques : la première est de nature algébrique et fait intervenir des structures particulières : les corps et les anneaux de Galois (chapitre 4), la deuxième fait appel à la géométrie dite projective (chapitre 5). Cette étude a été motivée par le théorème de Kochen et Specker et par les travaux de Peres et Mermin qui en ont découlé / The first vocation of this thesis would be a state of the art on the field of quantum computation, if not exhaustive, simple access (chapters 1, 2 and 3). The original (interesting) part of this treatise consists of two mathematical approaches of quantum computation concerning some quantum systems : the first one is an algebraic nature and utilizes some particular structures : Galois fields and rings (chapter 4), the second one calls to a peculiar geometry, known as projective one (chapter 5). These two approaches were motivated by the theorem of Kochen and Specker and by work of Peres and Mermin which rose from it

Dans la classe de complexité QMA – la généralisation quantique de la classe NP – un état quantique est fourni comme preuve à un algorithme de vérification pour l’aider à résoudre un problème. Cette classe de complexité a un problème complet naturel, le problème des Hamiltoniens locaux. Inspiré par la Physique de la matière condensée, ce problème concerne l’énergie de l’état fondamental d’un système quantique. Dans le cadre de cette thèse, nous étudions quelques problèmes liés à la classe QMA et au problème des Hamiltoniens locaux. Premièrement, nous étudions la différence de puissance si au lieu d’une preuve quantique, l’algorithme de vérification quantique reçoit une preuve classique. Nous proposons un cadre intermédiaire à ces deux cas, où la preuve consiste en un état quantique “plus simple” et nous arrivons à démontrer que ces états plus simples sont suffisants pour résoudre tous les problèmes dans QMA. À partir de ce résultat, nous obtenons un nouveau problème QMA-complet et nous étudions aussi la version de notre nouvelle classe de complexité avec erreur unilatérale. Ensuite, nous proposons le premier schéma de délégation vérifiable relativiste de calcul quantique. Dans ce cadre, un client classique délègue son calcul quantique à deux serveurs quantiques intriqués. Ces serveurs peuvent communiquer entre eux en respectant l’hypothèse que l’information ne peut pas être propagé plus vite que la vitesse de la lumière. Ce protocole a été conçu à partir d’un jeu non-local pour le problème des Hamiltoniens locaux avec deux prouveurs et un tour de communication. Dans ce jeu, les prouveurs exécutent des calculs quantiques de temps polynomiaux sur des copies de l’état fondamental du Hamiltonien. Finalement, nous étudions la conjecture PCP quantique, où l’on demande si tous les problèmes dans la classe QMA acceptent un système de preuves où l’algorithme de vérification a accès à un nombre constant de qubits de la preuve quantique. Notre première contribution consiste à étendre le modèle QPCP avec une preuve auxiliaire classique. Pour attaquer le problème, nous avons proposé une version plus faible de la conjecture QPCP pour ce nouveau système de preuves. Nous avons alors montré que cette nouvelle conjecture peut également être exprimée dans le contexte des problèmes des Hamiltoniens locaux et ainsi que dans lecadre de la maximisation de la probabilité de acceptation des jeux quantiques. Notre résultat montre la première équivalence entre un jeu multi-prouveur et une conjecture QPCP. / In QMA, the quantum generalization of the complexity class NP, a quantum state is provided as a proof of a mathematical statement, and this quantum proof can be verified by a quantum algorithm. This complexity class has a very natural complete problem, the Local Hamiltonian problem. Inspired by Condensed Matters Physics, this problem concerns the groundstate energy of quantum systems. In this thesis, we study some problems related to QMA and to the Local Hamiltonian problem. First, we study the difference of power when classical or quantum proofs are provided to quantum verification algorithms. We propose an intermediate setting where the proof is a “simpler” quantum state, and we manage to prove that these simpler states are enough to solve all problems in QMA. From this result, we are able to present a new QMA-complete problem and we also study the one-sided error version of our new complexity class. Secondly, we propose the first relativistic verifiable delegation scheme for quantum computation. In this setting, a classical client delegates her quantumcomputation to two entangled servers who are allowed to communicate, but respecting the assumption that information cannot be propagated faster than speed of light. This protocol is achieved through a one-round two-prover game for the Local Hamiltonian problem where provers only need polynomial time quantum computation and access to copies of the groundstate of the Hamiltonian. Finally, we study the quantumPCP conjecture, which asks if all problems in QMA accept aproof systemwhere only a fewqubits of the proof are checked. Our result consists in proposing an extension of QPCP proof systems where the verifier is also provided an auxiliary classical proof. Based on this proof system, we propose a weaker version of QPCP conjecture. We then show that this new conjecture can be formulated as a Local Hamiltonian problem and also as a problem involving the maximum acceptance probability of multi-prover games. This is the first equivalence of a multi-prover game and some QPCP statement.

Orientador: Felipe Fernandes Fanchini / Resumo: Na presente Tese realizou-se um estudo acerca das relações monogâmicas entre emaranhamento de formação (EF) e discórdia quântica (DQ) para sistemas quânticos multipartidos, bem como um estudo acerca da dinâmica dissipativa de operações lógicas de 1 (portas NOT e Z) e 2 (porta CNOT) qubits para uma computação quântica baseada em medidas projetivas (MBQC). Como resultado, expressões as quais generalizam relações de conservação entre EF e DQ puderam ser deduzidas, bem como relações de distribuição de DQ para sistemas de n partes. Ademais, ampliando os estudos referentes a sistemas multipartidos, uma pesquisa a respeito da influência dos canais amplitude damping (AD) e phase damping (PD) em uma MBQC considerando ambientes altamente não-Markovianos pôde ser desenvolvida. Nesse sentido, uma medida denominada fidelidade média (Fm) foi então proposta, a partir da qual expressões analíticas puderam ser deduzidas para os canais em questão, e sendo demonstrado que Fm resulta em valores idênticos para as portas X e Z. Além do mais, também foi possível realizar um estudo acerca dos tempos ótimos das medidas, segundo o qual pôde-se concluir que sua rápida execução não necessariamente implica em melhores resultados, tampouco sua lenta execução não necessariamente implica em piores. Nesse contexto, pôde-se também demonstrar que para o canal AD o conhecimento do mapa dissipativo já é o suficiente para intuitivamente determinar os melhores tempos de medidas, sendo que o mesmo não necessariamen... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: In this work a study about the monogamous relations between entanglement of formation (EF) and quantum discord (QD) for multipartite quantum systems, as well the dissipative dynamics of 1 (NOT and Z gates) and 2 (CNOT gate) qubits for a measurement-based quantum computation (MBQC) could be developed. As a result, expressions which generalize conservation laws between EF and DQ could be deduced, as well as DQ distribution laws for n part quantum systems. In addition, expanding the multipartite systems studies, a research about the influence of the amplitude damping (AD) and phase damping (PD) channels in an MBQC considering highly non-Markovian environments also could be developed. In this sense, a measure called average gate fidelity (Fm) was proposed, from which we deduce analytical expressions for the channels and show that it is identical for the X and Z gates. In addition, we conducted a study of the optimal measurement times, where we conclude that neither fast application of the projective measurements necessarily implies better results, nor slow application necessarily implies worse results. Furthermore, it was also possible to demonstrate that while for the AD the knowledge of the dissipative map is sufficient to determine the best measurement times, the same is not necessarily true for the PD, where the time of the set of measures becomes crucial since a phase error in one qubit can fix the phase error that takes place in another. Finally, a study was carried out on ... (Complete abstract click electronic access below) / Doutor

<p dir="ltr">InSbAs is a promising platform for exploring topological superconductivity and spin-based device applications, thanks to its strong spin-orbit coupling (SOC) and high effective <i>g</i>-factor. This thesis investigates low-temperature transport of electrons confined in InSb_1-xAs_x quantum wells. Specifically, we study the properties of electrons confined in 2D and 0D by fabricating gated Hall bars and gate-defined quantum dots. Theoretical considerations suggest that InSbAs will have stronger SOC and a larger effective <i>g</i>-factor compared to InAs and InSb. Both the SOC and effective <i>g</i>-factor change as a function of arsenic mole fraction, but much remains to be understood in real material systems. Here, we study the dominant scattering mechanisms, effective mass, spin-orbit coupling strength, and the <i>g</i>-factor in InSb_1-xAs_x quantum wells grown by molecular beam epitaxy. </p><p dir="ltr">We explore 30 nm InSb_1-xAs_x quantum wells with arsenic mole fractions of <i>x</i> = 0.05, 0.13, and 0.19. The 2DEG properties were studied by fabricating gated Hall bars and placing them in a perpendicular magnetic field at low temperatures (T = 10 - 300 mK). All samples showed high-quality transport with mobility greater than 100,000 cm²/Vs. For the <i>x</i> = 0.05 sample, the 2DEG displays a peak mobility μ = 2.4 x 10⁵ cm²/Vs at a density of <i>n</i> = 2.5 x 10¹¹ cm^-². We investigated the evolution of mobility as a function of arsenic mole fraction and 2DEG density for all samples. As the arsenic mole fraction increases, peak mobility decreases, and the dependence of mobility on density becomes weaker, suggesting that short-range scattering becomes the dominant scattering mechanism. We extracted an alloy scattering rate of τ_alloy = 45 ns^-1 per % As, an important parameter for understanding the impact of disorder on induced superconductivity. The high mobility, strong spin-orbit coupling, and low effective mass in this material system resulted in a beating pattern in the Shubnikov de Haas oscillations, allowing for the extraction of the Rashba parameter as a function of density and arsenic mole fraction. We observed a gate tunable spin-orbit coupling and, as predicted by theory, an increase in spin-orbit coupling with increasing arsenic mole fraction. For the sample with x = 0.19, the highest Rashba parameter is α_R ~ 300 meVÅ, which is significantly higher than in InSb. </p><p dir="ltr">In addition, we explored 0D confinement by fabricating a gate-defined quantum dot in an InSb₀_.87As_0.13 quantum well. By studying the evolution of Coulomb blockade peaks and differential conductance peaks as a function of magnetic field, a nearly isotropic in-plane effective <i>g</i>-factor in the [1-10] and [110] crystallographic directions was extracted, ranging from 49-58. The values extracted are 1.8 times higher than in a quantum dot fabricated in pure InSb. Furthermore, this study produced the first demonstration of a tunable spin-orbit coupling in this material system. This was achieved by measuring the avoided crossing gap, mediated by spin-orbit coupling, between the ground state and excited state in a magnetic field. The avoided crossing gap indicates the strength of the spin-orbit coupling; the maximum energy separation extracted is Δ_SO ~100 μeV. </p><p dir="ltr">Our work should stimulate further investigation of InSbAs quantum wells as a promising platform for applications requiring strong spin-orbit coupling, such as topological superconductivity or spin-based devices.</p>

Quantum information technologies include secure quantum communications and ultra precise quantum sensing that are significantly more efficient than their classical counterparts. To enable such technologies, we need a scalable quantum platform in which qubits are con trollable. Color centers provide controllable optically-active spin qubits within the coherence time limit. Moreover, the nearby nuclear spins have long coherence times suitable for quantum memories. In this thesis, I present a theoretical understanding of and control protocols for various color centers. Using group theory, I explore the wave functions and laser pumping-induced dynamics of VSi color centers in silicon carbide. I also provide dynamical decoupling-based high-fidelity control of nuclear spins around the color center. I also present a control technique that combines holonomic control and dynamically corrected control to tolerate simultaneous errors from various sources. The work described here includes a theoretical understanding and control techniques of color center spin qubits and nuclear spin quantum memories, as well as a new platform-independent control formalism towards robust qubit control. / Doctor of Philosophy / Quantum information technologies promise to offer efficient computations of certain algorithms and secure communications beyond the reach of their classical counterparts. To achieve such technologies, we must find a suitable quantum platform to manipulate the quantum information units (qubits). Color centers host spin qubits that can enable such technologies. However, it is challenging due to our incomplete understanding of their physical properties and, more importantly, the controllability and scalability of such spin qubits. In this thesis, I present a theoretical understanding of and control protocols for various color centers. By using group theory that describes the symmetry of color centers, I give a phenomenological model of spin qubit dynamics under optical control of VSi color centers in silicon carbide. I also provide an improved technique for controlling nuclear spin qubits with higher precision. Moreover, I propose a new qubit control technique that combines two methods - holonomic control and dynamical corrected control - to provide further robust qubit control in the presence of multiple noise sources. The works in this thesis provide knowledge of color center spin qubits and concrete control methods towards quantum information technologies with color center spin qubits.

In this project a qutrit tripod system is studied to implement quantum gates using non-Abelian geometric phases, allowing for holonomic quantum computation which in turn results in more robust computations. First, a general foundation of the theory is presented. This includes the relevant theory of matrices in Hilbert space, as well as theory of the quantum mechanics used in the report. The method is then described in depth, showing how the pulse area is fixed. Using properties of the Hamiltonian as well as the time-evolution operator of the tripod system the computational subspace can be derived. These findings are combined to show how the computational subspace evolves in time, resulting in the unitary matrix used to form quantum gates. Using educated guesses to find the necessary parameters or utilizing iterative methods to find the parameters are the two main approaches used for constructing the considered gates. Three of the suggested quantum gates are successfully implemented through educated guesses, namely X, T and Z using an angle parametrization of the phase and amplitude of the pulses. The last desired gate is the Hadamard-gate, but the implementation of said gate required numerical approximation. The reasons as to why this is the case, are later discussed.

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal.

Made available in DSpace on 2015-03-04T18:50:57Z (GMT). No. of bitstreams: 1 Tese-Carlos-Magno1.pdf: 616333 bytes, checksum: 65e51c95902afd18d11a1d7366653fc0 (MD5) Previous issue date: 2008-03-13 / Conselho Nacional de Desenvolvimento Cientifico e Tecnologico / We present an efficient quantum algorithm for the Hidden Subgroup Problem (HSP) on the semidirect product of the cyclic groups and , where is any odd prime number, and are positives integers and the homomorphism which defines the group is given by the root such that . As a consequence we can solve efficiently de HSP on the semidirect product of the groups by , where has a special prime factorization. / Neste trabalho apresentamos um algoritmo quântico eficiente para o Problema do Subgrupos Oculto (PSO) no produto semidireto dos grupos cíclicos e , onde é qualquer número primo ímpar, e são inteiros positivos e o homomorfismo que define o grupo é dado por uma raiz para a qual . Como conseqüência, podemos resolver eficientemente o PSO também no produto semidireto dos grupos por , onde o inteiro possui uma especial fatoração prima.

The progess in NMRQIP can be outlined in to four parts.1) Implementation of theoretical protocols on small number of qubits. 2) Demonstration of QIP on various NMR systems. 3) Designing and implementing the algorithms for mixed initial states. 4) Developing the techniques for coherent and decoherent control on higher number(up to 15) of qubits. This thesis contains some efforts in the direction of first three points. Quantum-state discrimination has important applications in the context of quantum communication and quantum cryptography. One of the characteristic features of quantum mechanics is that it is impossible to devise a measurement that can distinguish nonorthogonal states perfectly. However, one can distinguish them with a finite probability by an appropriate measurement strategy. In Chapter 2, we describe the implementation of a theoretical protocol of programmable quantum-state discriminator, on a two-qubit NMR System. The projective measurement is simulated by adding two experiments. This device does the unambiguous discrimination of a pair of states of the data qubit that are symmetrically located about a fixed state. The device is used to discriminate both linearly polarized states and eillipitically polarized states. The maximum probability of successful discrimination is achieved by suitably preparing the ancilla quubit. The last step of any QIP protocol is the readout. In NMR-QIP the readout is done by using density matrix tomography. It was first proposed by Ernst and co-workers that a two-dimensional method can be used to correlate input and output states. This method uses an extra (aniclla) qubit, whose transitions indicate the quantum states of the remaining qubits. The 2D spectrum of ancilla qubit represent the input and output states along F1 and F2 dimensions respectively. However the 2D method requires several t1 increments to achieve the required spectral width and resolution in the indirect dimension, hence leads to large experimental time. In chapter 3, the conventional 2D NMRQIP method is speeded-up by using Hadamard spectroscopy. The Hadamard method is used to implement various two-, three-qubit gates and qutrit gates. We also use Hadamard spectroscopy for information storage under spatial encoding and to implement a parallel search algorithm. Various slices of water sample can be spatially encoded by using a multi-frequency pulse under the field gradient. Thus the information of each slice is projected to the frequency space. Each slice represents a classical bit, where excitation and no excitation corresponds to the binary values 0 and 1 respectively. However one has to do the experiment for each binary information, by synthesizing a suitable multi-frequency pulse. In this work we show that by recording the data obtained by various Hadamard encoded multi-frequency pulses, one can suitably decode it to obtain any birnary information, without doing further experiments. Geometric phases depend only on the geometry of the path executed in the projective Hilbert space, and are therefore resilient to certain types of errors. This leads to the possibility of an intrinsically fault-tolerant quantum computation. In liquid state NMRQIP. Controlled phase shift gates are achieved by using qubit selective pulses and J evolutions, and also by using geometir phases. In order to achieve higher number of qubits in NMR, one explores dipolar couplings which are larger in magnitude, yielding strongly coupled spectra. In such systems since the Hamiltonian consists of terms, it is difficult to apply qubit selective pulses. However such systems have been used for NMRQIP by considering 2n eigen states as basis states of an n-qubit system. In chapter 4, it is shown that non-adiabatic geometric phases can be used to implement controlled phase shift gates in strongly dipolar coupled systems. A detailed theoretical explanation of non-adiabatic geometric phases in NMR is given, by using single transition operators. Using such controlled phase shift gates, the implementation of Deutsch-Jozsa and parity algorithms are demonstrated. Search algorithms play an important role in the filed of information processing. Grovers quantum search algorithm achieves polynomial speed-up over the classical search algorithm. Bruschweiler proposed a Liouville space search algorithm which achieve polymonial speed-up. This algorithm requires a weakly coupled system with a mixed initial state. In chapter 5 we modified the Bruschweiler’s algorithm, so that it can be implemented on a weakly as well as strongly coupled system. The experiments are performed on a strongly dipolar coupled four-qubit system. The experiments from four spin-1/2 nuclei of a molecule oriented in a liquid crystal matrix. Chapter 6 describes the implementation of controlled phase shift gates on a quadrupolar spin-7/2 nucleus, using non-adiabatic geometric phases. The eight energy levels of spin-7/2 nucleus, form a three qubit system. A general procedure is given, for implementing a controlled phase shift gate on a system consisting of any number of energy levels. Finally Collin’s version of three-qubit DJ algorithm using multi-frequency pulses, is implemented in the spin-7/2 system.