Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / Repeatedly in the field of Quantum Information Science (QIS) it’s essentially required of physical systems the quantification concerning its quantum phenomena, such as Quantum Coherence (QC) relying in quantum superposition states. Hereafter several quantifiers of QC have been proposed over the years through distance measures in quantum state spaces, called distinguishability measures, playing an important role in QIS correlation phenomena such as Discord and Entanglement with Quantum Cryptography implementation, as example. The aim of this dissertation is to extend the research of QC, published by Jonas Maziero in an article, performing an in-depth analysis regarding the control of local and non-local aspects of Hilbert-Schmidt Coherence (HSC) in multipartite systems and its relations with others QC quantifiers, as well as an analisys of a possible Hilbert-Schmidt Distance (HSD) implication in QC functions over the Non-Monotonicity under Tensor Products (NMuTP) inequality and of limitations between Coherence of state populations and energy. Starting from the generic multipartite state of level quantum energy systems (qudit), defined from the Bloch parameterization, calculations of QC functions concerning its particular cases are considered for 1-qubit, 2-qubit, 1-qutrit and two copies of 1-qubit adopting HSD. Writing the HSC function for the latter case in terms of its local and non-local parts and from the result of 1-qubit it is possible, by manipulating the difference between local populations, to infer a non-local implication in the HSC for that system, in contrast to what has been seen by adopting distinct dissimilarity measures for this function, named l1- Norm Distance and Relative Entropy Distance, cases where there are no implications and where there is a direct consequence with their local populations instead of the previously difference between them, respectively. Notwithstanding, HSD usage provides a description of an awkward relation in QIS towards NMuTP, and a possible implication of that kind of relation in QIS emergent phenomena such as QC function. / Reiteradamente no contexto da Ciência da Informação Quântica (CIQ) é essencialmente necessária a quantificação de sistemas físicos com respeito aos seus fenómenos quânticos, tais como a Coerência Quântica (CQ) intrínseca a estados com superposição quântica. Doravante algumas funções quantificadoras de CQ foram atribuídas ao longo dos anos através de medidas de distância em espaços de estados quânticos, denominadas medidas de dissimilaridade, desempenhando papel importante em fenômenos de correlação na CIQ, tal como Discórdia e Emaranhamento com implementação em Criptografia Quântica, por exemplo. O objetivo desta dissertação é estender a pesquisa dedicada a CQ, publicada em artigo por Jonas Maziero, efetuando uma análise aprofundada com respeito ao controle dos aspectos local e não-local da Coerência de Hilbert-Schmidt (CHS) em sistemas multipartidos e suas relações com outras funções quantificadoras de CQ, bem como a investigação de uma possível implicação da Distância de Hilbert-Schmidt (DHS) na função CQ frente a relação da Não-Monotonicidade sobre o Produto Tensorial (NMsPT) e de limitações entre Coerência e populações de estados e energia. Partindo do estado multipartido genérico de sistemas quânticos com níveis de energia (qudit), definido a partir da parametrização de Bloch, calculamos a função CQ para seus respectivos casos particulares 1-qubit, 2-qubit, 1-qutrit e duas cópias de 1-qubit adotando a DHS. Escrevendo a função CHS para este último caso em termos de suas partes local e não-local e do resultado para 1-qubit é possível, manipulando a diferença entre as populações locais, inferir uma implicação não-local na CHS para este sistema, em contraste ao que se observa adotando distintas medidas de dissimilaridade para esta função, denominadas Distância Norma-l1 e Distância Entropia Relativa, nos casos em que não há implicação e onde há consequência direta com suas populações locais do que anteriormente a diferença entre elas, respectivamente. Não obstante, o emprego da DHS proporciona o caráter de uma estranha relação na CIQ através da NMsPT, e uma possível implicação desta relação em fenômenos emergentes da CIQ tal qual a função CQ.

Neutral atom systems are an appealing platform for the development and testing of quantum control and measurement techniques. This dissertation presents experimental investigations of control and measurement tools using as a testbed the 16-dimensional hyperfine manifold associated with the electronic ground state of cesium atoms. On the control side, we present an experimental realization of a protocol to implement robust unitary transformations in the presence of static and dynamic perturbations. We also present an experimental realization of inhomogeneous quantum control. Specifically, we demonstrate our ability to perform two different unitary transformations on atoms that see different light shifts from an optical addressing field. On the measurement side, we present experimental realizations of quantum state and process tomography. The state tomography project encompasses a comprehensive evaluation of several measurement strategies and state estimation algorithms. Our experimental results show that in the presence of experimental imperfections, there is a clear tradeoff between accuracy, efficiency and robustness in the reconstruction. The process tomography project involves an experimental demonstration of efficient reconstruction by using a set of intelligent probe states. Experimental results show that we are able to reconstruct unitary maps in Hilbert spaces with dimension ranging from d=4 to d=16. To the best of our knowledge, this is the first time that a unitary process in d=16 is successfully reconstructed in the laboratory.

<p>Qudit, a multi-level computational unit for quantum computing, provides a larger state space for information processing, and thus can reduce the circuit complexity, simplify the experimental setup. We promote the qudit-based quantum computing by providing an overview that covers a variety of qudit topics ranging from gate universality, circuit building, algorithm design, to physical realization methods. Among all the important qudit algorithms, we perform the first experimental realization of a qudit-based phase estimation algorithm(PEA) on a photonic platform, utilizing the high dimensionality in time and frequency degrees of freedom (DoFs) in a single photon. In our scheme the controlled-unitary gates can be realized in a deterministic fashion, as the control and target registers are now represented by two DoFs in a single photon. Next we improve the PEA by introducing a new statistical and variational approach to the PEA that we called SPEA. The SPEA can determine any unknown eigenstate-eigenphase pair from a given unitary matrix  by treating the probabilistic output of an Iterative PEA (IPEA)-like circuit as an eigenstate-eigenphase proximity metric, using this metric to estimate the proximity of the input state and input phase to the nearest eigenstate-eigenphase pair and approaching this pair via a variational process on the input state and phase. The SPEA can search over the entire computational space as well as some specified given range efficiently and thus outperforms the original PEA.</p> <p> </p> <p><br></p> <p>The simulation of open quantum dynamics has attracted wide interests recently with a variety of quantum algorithms developed and demonstrated. The second half of the thesis focus on the simulation of the open quantum dynamics which is a useful application for quantum computer based on qudit as well as qubit. We perform the first quantum simulations of the  radical pair mechanism(RPM) in the avian compass with a Sz.-Nagy dilation theorem-based quantum algorithm to demonstrate the generality of the quantum algorithm and to open new opportunities for studying the avian compass with quantum computing devices. Next we apply the same quantum algorithm to simulate open quantum dynamics based on the Generalized Quantum Master Equation (GQME). This approach overcomes the limitations of the Lindblad equation by providing a rigorous derivation of the equations of motion for any subset of elements of the reduced density matrix. We validate our quantum algorithm as applied to the spin-boson benchmark model by analyzing the impact of the quantum circuit depth on the accuracy of the results when the subset is limited to the diagonal elements of the reduced density matrix.  Our findings demonstrate that our approach yields reliable results on  noisy intermediate-scale quantum (NISQ) computers.</p>

One of the major challenges hindering advancement of quantum computing is the sensitive nature of the physical systems used to build a quantum computer. One suggestion for improving reliability is a particular type of logic gates, based on Berry's geometric phase, showing improved robustness to external disturbance of the quantum system over the course of a calculation. Such logic gates have previously been shown for the smallest possible two-level qubits. Using the method of adiabatic shortcut we endevour to discover similarly realistic and robust logic gates for units of quantum information in higher dimensions. The example shown in this paper discusses three-level qutrits, but is expected to apply to theoretically unlimited higher dimensions since new geometric complications are expected to arise primarily when moving from a two-level to a multi-level problem.  We here present a set of primitive single-qutrit gates able to perform universal quantum computations if supplemented by a two-qutrit gate. We also present a set of condensed single-qutrit gates for commonly needed operations. By detailing the underlying mathematical framework, relying on the multi-dimensional generalisation of Berry's phase describing the time evolution of degenerate quantum states, we also suggest an easily scalable geometric interpretation of quantum gates in higher dimensions along with visual representation of logic gates using parameters of the physical system to sequentially unlock and manipulate subspaces of the quantum information unit.

To address key challenges for both quantum communication and quantum computing applications in a simultaneous manner, we propose to employ the photon angular momentum approach by invoking the well-known fact that photons carry both the spin angular momentum (SAM) and the orbital angular momentum (OAM). SAM is associated with polarization, while OAM is associated with azimuthal phase dependence of the complex electric field. Given that OAM eigenstates are mutually orthogonal, in principle, an arbitrary number of bits per single photon can be transmitted. The ability to generate/analyze states with different photon angular momentum, by using either holographic or interferometric methods, allows the realization of quantum states in multidimensional Hilbert space. Because OAM states provide an infinite basis state, while SAM states are 2-D only, the OAM can also be used to increase the security for quantum key distribution (QKD) applications and improve computational power for quantum computing applications. The goal of this paper is to describe photon angular momentum based deterministic universal quantum qudit gates, namely, {generalized-X, generalized-Z, generalized-CNOT} qudit gates, and different quantum modules of importance for various applications, including (fault-tolerant) quantum computing, teleportation, QKD, and quantum error correction. For instance, the basic quantum modules for quantum teleportation applications include the generalized-Bell-state generation module and the QFT-module. The basic quantum module for quantum error correction and fault-tolerant computing is the nonbinary syndrome calculator module. The basic module for entanglement assisted QKD is either the generalized-Bell-state generation module or the Weyl-operator-module. The possibility of implementing all these modules in integrated optics is discussed as well. Finally, we provide security analysis of entanglement assisted multidimensional QKD protocols, employing the proposed qudit modules, by taking into account the imperfect generation of OAM modes.