# Browsing by Subject "quantum computing"

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Item Entanglement generation and applications in quantum information(Texas A&M University, 2006-08-16) Di, TiegangShow more This dissertation consists of three sections. In the first section, we discuss the generation of arbitrary two-qubit entangled states and present three generation methods. The first method is based on the interaction of an atom with classical and quantized cavity fields. The second method is based on the interaction of two coupled two-level atoms with a laser field. In the last method, we use two spin-1/2 systems which interact with a tuned radio frequency pulse. Using those methods we have generated two qubit arbitrary entangled states which is widely used in quantum computing and quantum information. In the second section, we discuss a possible experimental implementation of quantum walk which is based on the passage of an atom through a high-Q cavity. The chirality is determined by the atomic states and the displacement is characterized by the photon number inside the cavity. Our scheme makes quantum walk possible in a cavity QED system and the results could be widely used on quantum computer. In the last section, we investigate the properties of teleporting an arbitrary superposition of entangled Dicke states of any number of atoms (qubits) between two distant cavities. We also studied teleporting continuous variables of an optical field. Teleportation of Dicke states relies on adiabatic passage using multiatom dark states in each cavity and a conditional detection of photons leaking out of both cavities. In the continuous variables teleportation scheme we first reformulate the protocol of quantum teleportation of arbitrary input optical field states in the density matrix form, and established the relation between the P-function of the input and output states. We then present a condition involving squeeze parameter and detection efficiency under which the P-function of the output state becomes the Q function of the input state such that any nonclassical features in the input state will be eliminated in the teleported state. Based on the research in this section we have made it possible of arbitrary atomic Dicke states teleportation from one cavity to another, and this teleortation will play an essential role in quantum communication. Since quantum properties is so important in quantum communication, the condition we give in this section to distinguish classical and quantum teleportation is also important.Show more Item Improvements in communication complexity using quantum entanglement(Texas A&M University, 2008-10-10) Kamat, Angad MohandasShow more Quantum computing resources have been known to provide speed-ups in computational complexity in many algorithms. The impact of these resources in communication, however, has not attracted much attention. We investigate the impact of quantum entanglement on communication complexity. We provide a positive result, by presenting a class of multi-party communication problems wherein the presence of a suitable quantum entanglement lowers the classical communication complexity. We show that, in evaluating certains function whose parameters are distributed among various parties, the presence of prior entanglement can help in reducing the required communication. We also present an outline of realizing the required entanglement through optical photon quantum computing. We also suggest the possible impact of our results on network information flow problems, by showing an instance of a lower bound which can be broken by adding limited power to the communication model.Show more Item Quantum error control codes(Texas A&M University, 2008-10-10) Abdelhamid Awad Aly Ahmed, SalaShow more It is conjectured that quantum computers are able to solve certain problems more quickly than any deterministic or probabilistic computer. For instance, Shor's algorithm is able to factor large integers in polynomial time on a quantum computer. A quantum computer exploits the rules of quantum mechanics to speed up computations. However, it is a formidable task to build a quantum computer, since the quantum mechanical systems storing the information unavoidably interact with their environment. Therefore, one has to mitigate the resulting noise and decoherence effects to avoid computational errors. In this dissertation, I study various aspects of quantum error control codes - the key component of fault-tolerant quantum information processing. I present the fundamental theory and necessary background of quantum codes and construct many families of quantum block and convolutional codes over finite fields, in addition to families of subsystem codes. This dissertation is organized into three parts: Quantum Block Codes. After introducing the theory of quantum block codes, I establish conditions when BCH codes are self-orthogonal (or dual-containing) with respect to Euclidean and Hermitian inner products. In particular, I derive two families of nonbinary quantum BCH codes using the stabilizer formalism. I study duadic codes and establish the existence of families of degenerate quantum codes, as well as families of quantum codes derived from projective geometries. Subsystem Codes. Subsystem codes form a new class of quantum codes in which the underlying classical codes do not need to be self-orthogonal. I give an introduction to subsystem codes and present several methods for subsystem code constructions. I derive families of subsystem codes from classical BCH and RS codes and establish a family of optimal MDS subsystem codes. I establish propagation rules of subsystem codes and construct tables of upper and lower bounds on subsystem code parameters. Quantum Convolutional Codes. Quantum convolutional codes are particularly well-suited for communication applications. I develop the theory of quantum convolutional codes and give families of quantum convolutional codes based on RS codes. Furthermore, I establish a bound on the code parameters of quantum convolutional codes - the generalized Singleton bound. I develop a general framework for deriving convolutional codes from block codes and use it to derive families of non-catastrophic quantum convolutional codes from BCH codes. The dissertation concludes with a discussion of some open problems.Show more