This dissertation studies two different aspects of two-player interaction in the model of quantum communication and quantum computation.First, we study two cryptographic primitives, that are used as basic blocks to construct sophisticated cryptographic protocols between two players, e.g. identification protocols. The first primitive is ''quantum bit commitment''. This primitive cannot be done in an unconditionally secure way. However, security can be obtained by restraining the power of the two players. We study this primitive when the two players can only create quantum Gaussian states and perform Gaussian operations. These operations are a subset of what is allowed by quantum physics, and plays a central role in quantum optics. Hence, it is an accurate model of communication through optical fibers. We show that unfortunately this restriction does not allow secure bit commitment. The proof of this result is based on the notion of ''intrinsic purification'' that we introduce to circumvent the use of Uhlman's theorem when the quantum states are Gaussian. We then examine a weaker primitive, ''quantum weak coin flipping'', in the standard model of quantum computation. Mochon has showed that there exists such a protocol with arbitrarily small bias. We give a clear and meaningful interpretation of his proof. That allows us to present a drastically shorter and simplified proof.The second part of the dissertation deals with different methods of proving lower bounds on the quantum query complexity. This is a very important model in quantum complexity in which numerous results have been proved. In this model, an algorithm has restricted access to the input: it can only query individual bits. We consider a generalization of the standard model, where an algorithm does not compute a classical function, but generates a quantum state. This generalization allows us to compare the strength of the different methods used to prove lower bounds in this model. We first prove that the ''multiplicative adversary method'' is stronger than the ''additive adversary method''. We then show a reduction from the ''polynomial method'' to the multiplicative adversary method. Hence, we prove that the multiplicative adversary method is the strongest one. Adversary methods are usually difficult to use since they involve the computation of norms of matrices with very large size. We show how studying the symmetries of a problem can largely simplify these computations. Last, using these principles we prove the tight lower bound of the INDEX-ERASURE problem. This a quantum state generation problem that has links with the famous GRAPH-ISOMORPHISM problem.

In this thesis we study quantum-like representation and simulation of quantum algorithms by using classical computers.The quantum--like representation algorithm (QLRA) was  introduced by A. Khrennikov (1997) to solve the ``inverse Born's rule problem'', i.e. to construct a representation of probabilistic data-- measured in any context of science-- and represent this data by a complex or more general probability amplitude which matches a generalization of Born's rule.The outcome from QLRA matches the formula of total probability with an additional trigonometric, hyperbolic or hyper-trigonometric interference term and this is in fact a generalization of the familiar formula of interference of probabilities. We study representation of statistical data (of any origin) by a probability amplitude in a complex algebra and a Clifford algebra (algebra of hyperbolic numbers). The statistical data is collected from measurements of two dichotomous and trichotomous observables respectively. We see that only special statistical data (satisfying a number of nonlinear constraints) have a quantum--like representation. We also study simulations of quantum computers on classical computers.Although it can not be denied that great progress have been made in quantum technologies, it is clear that there is still a huge gap between the creation of experimental quantum computers and realization of a quantum computer that can be used in applications. Therefore the simulation of quantum computations on classical computers became an important part in the attempt to cover this gap between the theoretical mathematical formulation of quantum mechanics and the realization of quantum computers. Of course, it can not be expected that quantum algorithms would help to solve NP problems for polynomial time on classical computers. However, this is not at all the aim of classical simulation.  The second part of this thesis is devoted to adaptation of the Mathematica symbolic language to known quantum algorithms and corresponding simulations on classical computers. Concretely we represent Simon's algorithm, Deutsch-Josza algorithm, Shor's algorithm, Grover's algorithm and quantum error-correcting codes in the Mathematica symbolic language. We see that the same framework can be used for all these algorithms. This framework will contain the characteristic property of the symbolic language representation of quantum computing and it will be a straightforward matter to include future algorithms in this framework.

Superconducting qubits are a promising technology for building a scalable quantum computer. An important architecture employed in the field is called Circuit Quantum Electrodynamics (circuit QED), where such qubits are combined with high quality microwave cavities to study the interaction between artificial atoms and single microwave photons. The ultra-strong coupling achieved in these systems allows for control and readout of the quantum state of qubits to perform quantum information processing. The work on circuit QED performed in this thesis consisted of realizing an experimental setup for qubit experiments in a new laboratory, investigating the coherence and decay of higher energy levels of superconducting transmon qubits and finally demonstrating a novel coaxial form of circuit QED. Designing and building a 3D circuit QED setup involved the following main accomplishments: producing high quality 3D cavities; designing and installing the cryogenic microwave setup as well as the room temperature amplification and data acquisition circuitry; successfully developing a recipe for the fabrication of Josephson junctions; controlling and measuring superconducting 3D transmon qubits at 10mK. Several qubits were fully characterised and have shown coherence times of several microseconds and relaxation times up to 25μs. Superconducting qubits in fact possess higher energy levels that can provide significant computational advantages in quantum information applications. In experiments performed at MIT, preparation and control of the five lowest states of a transmon qubit was demonstrated, followed by an investigation of the phase coherence and decay dynamics of these higher energy levels. The decay was found to proceed mainly sequentially with relaxation times in excess of 20μs for all transitions. A direct measurement of the charge dispersion of these levels was performed to explore their characteristics of dephasing. This experiment was also reproduced on a 3D transmon fabricated and measured in Oxford, where due to a higher effective qubit temperature a multi-level decay model including thermal excitations was developed to explain the observed relaxation dynamics. Finally, a coaxial transmon, which we name the coaxmon, is presented and measured with a coaxial LC readout resonator and input/output coupling ports placed inline along the third dimension. This novel coaxial circuit QED architecture holds great promise for developing a scalable planar grid of qubits to build a quantum computer.

Quantum memories are key components in photonics-based quantum information processing networks. Their ability to store and retrieve information on demand makes repeat-until-success strategies scalable. Warm alkali-metal vapours are interesting candidates for the implementation of such memories, thanks to their very long storage times as well as their experimental simplicity and versatility. Operation with the Raman memory protocol enables high time-bandwidth products, which denote the number of possible storage trials within the memory lifetime. Since large time-bandwidth products enable multiple synchronisation trials of probabilistically operating quantum gates via memory-based temporal multiplexing, the Raman memory is a promising tool for such tasks. Particularly, the broad spectral bandwidth allows for direct and technologically simple interfacing with other photonic primitives, such as heralded single photon sources. Here, this kind of light-matter interface is implemented using a warm caesium vapour Raman memory. Firstly, we study the storage of polarisation-encoded quantum information, a common standard in quantum information processing. High quality polarisation preservation for bright coherent state input signals can be achieved, when operating the Raman memory in a dual-rail configuration inside a polarisation interferometer. Secondly, heralded single photons are stored in the memory. To this end, the memory is operated on-demand by feed-forward of source heralding events, which constitutes a key technological capability for applications in temporal multiplexing. Prior to storage, single photons are produced in a waveguide-based spontaneous parametric down conversion source, whose bespoke design spectrally tailors the heralded photons to the memory acceptance bandwidth. The faithful retrieval of stored single photons is found to be currently limited by noise in the memory, with a signal-to-noise ratio of approximately 0.3 in the memory output. Nevertheless, a clear influence of the quantum nature of an input photon is observed in the retrieved light by measuring the read-out signal's photon statistics via the g⁽²⁾-autocorrelation function. Here, we find a drop in g⁽²⁾ by more than three standard deviations, from g⁽²⁾ ~ 1.69 to g⁽²⁾ ~ 1.59 upon changing the input signal from coherent states to heralded single photons. Finally, the memory noise processes and their scalings with the experimental parameters are examined in detail. Four-wave-mixing noise is determined as the sole important noise source for the Raman memory. These experimental results and their theoretical description point towards practical solutions for noise-free operation.

No description available.

Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-08-06T19:17:03Z No. of bitstreams: 1 HERON ARAGÃO MONTEIRO - DISSERTAÇÃO PPGCC 2012..pdf: 15948168 bytes, checksum: e445512265f530700a45c3924f68aa02 (MD5) / Made available in DSpace on 2018-08-06T19:17:03Z (GMT). No. of bitstreams: 1 HERON ARAGÃO MONTEIRO - DISSERTAÇÃO PPGCC 2012..pdf: 15948168 bytes, checksum: e445512265f530700a45c3924f68aa02 (MD5) Previous issue date: 2012-05-31 / Com o avanço da nanotecnologia, a computação quântica tem recebido grande destaque no meio científico. Utilizando os fundamentos da mecânica quântica, têm sido propostos diversos algoritmos quânticos. E, até então, os mesmos têm apresentado ganhos significativos com relação às suas versões clássicas. Na intenção de poder ser verificada a eficiência dos algoritmos quânticos, diversos simuladores vêm sendo desenvolvidos, visto que a confecção de um computador quântico ainda não foi possível. Há duas grandes vertentes de simuladores: os simuladores por software e os simuladores por hardware, chamados de emuladores. Na primeira classe se encontram os programas desenvolvidos em um computador clássico, procurando implementar os fundamentos da mecânica quântica, fazendo uso das linguagens de programação clássicas. Na segunda, são utilizados recursos que não estejam vinculados à plataforma do computador clássico. Dentre os emuladores, particularmente, estudos têm sido realizados fazendo uso de hardware dedicado (mais especificamente, FPGAV). O presente trabalho propõem a verificação da real utilidade da plataforma FPGA, com a intenção de se desenvolver um emulador universal, que permita a emulação de qualquer classe de circuitos, e que os mesmos possam ser implementados com um maior número de q-bits em relação aos circuitos tratados nos trabalhos anteriores. / With the progress of nanotechnology, quantum computing has received great emphasis in scientific circles. Using the basis of quantum mechanics, different quantum algorithms have been proposed. And so far, they have presented significant gains with respect to its classic versions. In order to verify the efficiency of quantum algorithms, several simulators have been developed, since the construction of a quantum computer is not yet possible. There are two major classes of simulators, simulators via software and via hardware. The latter being also called emulators. In the first class, programs are developed in a classical computer, attempting to implement the fundamentais of quantum mechanics, making use of classic programming languages. In the second, resources are used that are not related to the classic computer platform. Among the emulators, in particular, studies have been made using dedicated hardware (more specifically, FPGA's2). The present work proposes the use of the FPGA boards in emulation of quantum circuits aiming a gain scale in relation to the alternatives presented so far. The present work proposes checking the usefulness of the FPGA with the intention of developing an universal emulator that is able to emulate any type of circuit, and that they can be implemented with a larger number of q-bit in respect to the circuits treated in the previous works.

Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-10-01T16:46:31Z No. of bitstreams: 1 ELLOÁ BARRETO GUEDES DA COSTA - DISSERTAÇÃO PPGCC 2011..pdf: 1433883 bytes, checksum: fb9fa0561b94ab2b495915f5f377c364 (MD5) / Made available in DSpace on 2018-10-01T16:46:31Z (GMT). No. of bitstreams: 1 ELLOÁ BARRETO GUEDES DA COSTA - DISSERTAÇÃO PPGCC 2011..pdf: 1433883 bytes, checksum: fb9fa0561b94ab2b495915f5f377c364 (MD5) Previous issue date: 2011-03-25 / Este trabalho apresenta um ataque quântico de comprometimento permanente ao gerador pseudo-aleatório de Blum-Micali. A segurança deste gerador, classificado como criptograficamente seguro, baseia-se na hipótese de intratabilidade do problema do logaritmo discreto perante a Computação Clássica. O ataque proposto faz uso do algoritmo quântico de busca em conjunto com o algoritmo quântico para o logaritmo discreto para comprometer a imprevisibilidade do gerador, recuperando todas as saídas passadas e futuras do mesmo. O presente trabalho também descreve generalizações deste ataque que o adequam a uma gama mais vasta de geradores, incluindo geradores da Construção de Blum-Micali e geradores com múltiplos predicados difíceis. Tais generalizações também abrangem a realização de ataques em situações adversas, por exemplo, quando o adversário captura bits não consecutivos ou quando há menos bits que o requerido. Comparado à sua contrapartida clássica, o algoritmo quântico proposto nesse trabalho possui um ganho quadrático em relação à recuperação do representante do estado interno do gerador, seguido de um ganho superpolinomial na obtenção dos demais elementos do estado interno. Estes resultados caracterizam ameaças,elaboradas com Computação Quântica, contra a segurança de geradores utilizados em diversas aplicações criptográficas. / This dissertation presents a quantum permanent compromise attack to the Blum-Micali pseudorandom generator. The security of this generator, classified as cryptographically secure, is based on the hypothesis of intractability of the discrete logarithm problem in Classical Computing. The proposed attack is based on the quantum search algorithm jointly with the quantum discrete logarithm procedure and aims to compromise the unpredictability of the referred generator, recovering all of its past and future outputs. This work also describes generalizations that enables attacks to generators from the Blum-Micali construction and also to generators with multiple hard-core predicates. Such generalizations also allow attacks when the adversary intercepts non-consecutive bits or when there are less bits than required. Compared to its classical counterpart, the proposed algorithm has a quadractic speedup regarding the retrieval of the representant of the generator’s internal state followed by a super polynomial speedup regarding the obtention of the entire generator’sinternalstate. These results represent menaces of the Quantum Computing paradigm against the security of pseudorandom generators adopted in many real-world cryptosystems.

Utvecklandet av kvantdatorn är ett ytterst lovande projekt som kombinerar teoretisk och experimental kvantfysik, matematik, teori om kvantinformation och datalogi. Under första steget i utvecklandet av kvantdatorn låg huvudintresset på att skapa några algoritmer med framtida tillämpningar, klargöra grundläggande frågor och utveckla en experimentell teknologi för en leksakskvantdator som verkar på några kvantbitar. Då dominerade förväntningarna om snabba framsteg bland kvantforskare. Men det verkar som om dessa stora förväntningar inte har besannats helt. Många grundläggande och tekniska problem som dekoherens hos kvantbitarna och instabilitet i kvantstrukturen skapar redan vid ett litet antal register tvivel om en snabb utveckling av kvantdatorer som verkligen fungerar. Trots detta kan man inte förneka att stora framsteg gjorts inom kvantteknologin. Det råder givetvis ett stort gap mellan skapandet av en leksakskvantdator med 10-15 kvantregister och att t.ex. tillgodose de tekniska förutsättningarna för det projekt på 100 kvantregister som aviserades för några år sen i USA. Det är också uppenbart att svårigheterna ökar ickelinjärt med ökningen av antalet register. Därför är simulering av kvantdatorer i klassiska datorer en viktig del av kvantdatorprojektet. Självklart kan man inte förvänta sig att en kvantalgoritm skall lösa ett NP-problem i polynomisk tid i en klassisk dator. Detta är heller inte syftet med klassisk simulering. Den klassiska simuleringen av kvantdatorer kommer att täcka en del av gapet mellan den teoretiskt matematiska formuleringen av kvantmekaniken och ett förverkligande av en kvantdator. Ett av de viktigaste problemen i vetenskapen om kvantdatorn är att utveckla ett nytt symboliskt språk för kvantdatorerna och att anpassa redan existerande symboliska språk för klassiska datorer till kvantalgoritmer. Denna avhandling ägnas åt en anpassning av det symboliska språket Mathematica till kända kvantalgoritmer och motsvarande simulering i klassiska datorer. Konkret kommer vi att representera Simons algoritm, Deutsch-Joszas algoritm, Grovers algoritm, Shors algoritm och kvantfelrättande koder i det symboliska språket Mathematica. Vi använder samma stomme i alla dessa algoritmer. Denna stomme representerar de karaktäristiska egenskaperna i det symboliska språkets framställning av kvantdatorn och det är enkelt att inkludera denna stomme i framtida algoritmer. / Quantum computing is an extremely promising project combining theoretical and experimental quantum physics, mathematics, quantum information theory and computer science. At the first stage of development of quantum computing the main attention was paid to creating a few algorithms which might have applications in the future, clarifying fundamental questions and developing experimental technologies for toy quantum computers operating with a few quantum bits. At that time expectations of quick progress in the quantum computing project dominated in the quantum community. However, it seems that such high expectations were not totally justified. Numerous fundamental and technological problems such as the decoherence of quantum bits and the instability of quantum structures even with a small number of registers led to doubts about a quick development of really working quantum computers. Although it can not be denied that great progress had been made in quantum technologies, it is clear that there is still a huge gap between the creation of toy quantum computers with 10-15 quantum registers and, e.g., satisfying the technical conditions of the project of 100 quantum registers announced a few years ago in the USA. It is also evident that difficulties increase nonlinearly with an increasing number of registers. Therefore the simulation of quantum computations on classical computers became an important part of the quantum computing project. Of course, it can not be expected that quantum algorithms would help to solve NP problems for polynomial time on classical computers. However, this is not at all the aim of classical simulation. Classical simulation of quantum computations will cover part of the gap between the theoretical mathematical formulation of quantum mechanics and the realization of quantum computers. One of the most important problems in "quantum computer science" is the development of new symbolic languages for quantum computing and the adaptation of existing symbolic languages for classical computing to quantum algorithms. The present thesis is devoted to the adaptation of the Mathematica symbolic language to known quantum algorithms and corresponding simulation on the classical computer. Concretely we shall represent in the Mathematica symbolic language Simon's algorithm, the Deutsch-Josza algorithm, Grover's algorithm, Shor's algorithm and quantum error-correcting codes. We shall see that the same framework can be used for all these algorithms. This framework will contain the characteristic property of the symbolic language representation of quantum computing and it will be a straightforward matter to include this framework in future algorithms.

Quantum simulations, where controllable quantum systems are used to simulate other quantum systems, originally proposed by Richard Feynman, are one of the most remarkable applications of quantum information science. Compared to computation, quantum simulations require much less number of qubits for the m to be practical. In the work described in this thesis, we have performed a few quantum simulations of small quantum systems using Nuclear Magnetic Resonance(NMR) techniques. These simulations have been used to experimentally demonstrate the underlying interesting quantum protocols. All the experiments presented have been carried out using liquid-state or liquid crystal NMR. Numerical pulse optimization techniques have been utilized in some of the experiments, to achieve better control over the spin systems. The first chapter contains “Introduction” to quantum information processing, NMR, and numerical pulse optimization techniques. In chapter 2, we describe quantum simulation of a 3-spin Heisenberg-XY spin chain having only nearest neighbour interactions. Recently, spin chains having pre-engineered short-range interactions have been proposed to efficiently transfer quantum information between different parts of a quantum information processor. Other important proposals involving these spin chains include generating entangled states and universal quantum computation. However, such engineered interactions do not occur naturally in any system. In such a scenario, the experimental viability of these proposals can be tested by simulating the spin chains in other controllable quantum systems. In this work, we first theoretically study the time evolution of bipartite and tripartite entanglement measures for a 3-spin open ended XY spin chain. Then, by simulating the XY interactions in a 3-spin nuclear spin system, we experimentally generate, (i)a bipartite maximally(pseudo-)entangled state(Bell state) between end qubits, and(ii) multipartite(pseudo-)entangled states(Wand GHZ states),starting from separable pseudo-pure states. Bell state has been generated by using only the natural unitary evolution of the XY spin chain. W-state and GHZ-state have been generated by applying a single-qubit rotation to the second qubit, and a global rotation of all the three qubits respectively after the unitary evolution of the spin chain. In chapter 3, we simulate a 3-spin quantum transverse Ising spin system in a triangular configuration, and show that multipartite quantum correlations can be used to distinguish between the frustrated and non-frustrated regimes in the ground state of this spin system. The ground state of the spin system has been prepared by using adiabatic state preparation method. Gradient ascent pulse engineering technique has been utilized to efficiently realize the adiabatic evolution of the spin system. To analyse the experimental ground state of the system, we employ two different multipartite quantum correlation measures, generated from monogamy studies of bipartite quantum correlations. Chapter 4 contains a digital quantum simulation of the mirror inversion propagator corresponding to the time evolution of an XY spin chain. This simulation has been used to experimentally demonstrate the mirror inversion of quantum states, proposed by Albanese et al.[Phys.Rev.Lett.93,230502(2004)], by which entangled states can be transferred from one end of the chain to the other end. The experiments have been performed in a 5-qubit dipolar coupled nuclear spin system. For simulation, we make use of the recently proposed unitary operator decomposition algorithm along with the numerical pulse optimization techniques, which assisted in achieving high experimental fidelities. Chapter 5 contains a digital quantum simulation of the unitary propagator of a transverse Ising spin chain, which has been used to experimentally demonstrate the perfect state transfer protocol of Di Franco et al. [Phys.Rev.Lett.101,230502(2008)]. The importance of this protocol arises due to the fact that it achieves perfect state transfer from one end of the chain to the other end without the necessity of initializing the intermediate spins of the chain, whereas most of the previously proposed protocols require initialization. The experiments have been performed in a 3-spin nuclear spin system. The simulation has also been used to demonstrate the generation of a GHZ state.

Title: Quantum computing algorithms for quantum chemistry Author: Jakub Višňák Abstract: The topic of this study is the simulation of the quantum algorithm for the diagonalization of the matrix representation of the all-electron Dirac-Coulomb hamiltonian of the SbH molecule. Two different limited CI expansions were used to describe both the ground state (X 0+ ) and the first excited doublet (A 1) by simulating the Iterative Phase Estinamtion Algorith (IPEA). In the simulations numerically performed in this work, the "compact mapping" has been employed for the representation of the evolution operator exp(i Hˆ t); in the theoretical part of the work, the "direct mapping" is described as well. The influence of the metodics for choosing the initial eigenvector estimate is studied in both IPEA A and IPEA B variants. For those variants, the success probabilities pm are computed for different single-points on the SbH dissociation curves. The initial eigenvector estimates based on the "CISD(2)" method are found to be sufficient for both studied LCI-expansions up to internuclear distance R  6 a0. The pm dependence on the overlap between the eigenvector in question and its inital estimate - 2 0  is studied the for IPEA B method. The usability of the both variants of the IPEA in possible later calculations is...