Coherent control of trapped ions using off-resonant lasers

In this paper we develop a unified framework to study the coherent control of trapped ions subject to state-dependent forces. Taking different limits in our theory, we can reproduce two different designs of a two-qubit quantum gate --the pushing gate [1] and the fast gates based on laser pulses from Ref. [2]--, and propose a new design based on continuous laser beams. We demonstrate how to simulate Ising Hamiltonians in a many ions setup, and how to create highly entangled states and induce squeezing. Finally, in a detailed analysis we identify the physical limits of this technique and study the dependence of errors on the temperature. [1] J.I. Cirac, P. Zoller, Nature, 404, 579, 2000. [2] J.J. Garcia-Ripoll, P. Zoller, J.I. Cirac, PRL 67, 062318, 200

Use and misuse of variances for quantum systems in pure or mixed states

As a consequence of the place ascribed to measurements in the postulates of quantum mechanics, if two differently prepared systems are described with the same density operator \r{ho}, they are said to be in the same quantum state. For more than fifty years, there has been a lack of consensus about this postulate. In a 2011 paper, considering variances of spin components, Fratini and Hayrapetyan tried to show that this postulate is unjustified. The aim of the present paper is to discuss major points in this 2011 article, and in their reply to a 2012 paper by Bodor and Diosi claiming that their analysis was irrelevant. Facing some ambiguities or inconsistencies in the 2011 paper and in the reply, we first try to guess their aim, then establish results useful in this context, and finally discuss the use or misuse of several concepts implied in this debate

Canonical quantization of superconducting circuits

226 p.Los circuitos superconductores han surgido como una de las implementaciones físicas más prometedorasen tecnologías cuánticas, fusionando la física, la ingeniería y las matemáticas. Esta tesis expone modeloshamiltonianos matemáticamente consistentes y precisos para describir redes superconductoras idealesformadas por un número arbitrario de elementos concentrados y distribuidos como condensadores,inductores, uniones de Josephson, giradores, y líneas de transmisión. Aunque son ideales, hemosdemostrado que estos modelos que están basados en las leyes de Kirchhoff, son finitos y no presentanproblemas de divergencias, disipando malentendidos de la literatura previa. Finalmente se describe unaextensión de la teoría estándar para cuantizar circuitos que incluyen elementos ideales no recíprocos deforma sistemática, y se allana el camino para su extensión a giradores y circuladores dependientes defrecuencia

Quantum protocols for few-qubit devices

Quantum computers promise to dramatically speed up certain algorithms, but remain challenging to build in practice. This thesis focuses on near-term experiments, which feature a small number (say, 10-200) of qubits that lose the stored information after a short amount of time. We propose various theoretical protocols that can get the best out of such highly limited computers. For example, we construct logical operations, the building blocks of algorithms, by exploiting the native physical behavior of the machine. Moreover, we describe how quantum information can be sent between qubits that are only indirectly connected

Measuring Non-Markovianity of Noise in the Cenrtal Spin System

In this thesis, we explore non-Markovian noise in the central spin system due to the coupling between the central spin and the environment. We use a solid state nuclear magnetic resonance system to do the experiment since we have control over both the central spin and environment. In particular, we can manipulate the interaction between the central spin and the environment and the interaction between spins from the environment to study their effects individually. A powder of triphenylphosphine is used in the experiment. A change of local field seen by the central spin caused by interaction between spins in the environment is measured experimentally. A quantitative measure of non-Markovianity of noise on the central spin and a method to estimate non-Markovianity using the randomized benchmarking protocol are introduced

Delta rhythms as a substrate for holographic processing in sleep and wakefulness

PhD ThesisWe initially considered the theoretical properties and benefits of so-called holographic processing in a specific type of computational problem implied by the theories of synaptic rescaling processes in the biological wake-sleep cycle. This raised two fundamental questions that we attempted to answer by an experimental in vitro electrophysiological approach. We developed a comprehensive experimental paradigm based on a pharmacological model of the wake-sleep-associated delta rhythm measured with a Utah micro-electrode array at the interface between primary and associational areas in the rodent neocortex. We first verified that our in vitro delta rhythm model possessed two key features found in both in vivo rodent and human studies of synaptic rescaling processes in sleep: The first property being that prior local synaptic potentiation in wake leads to increased local delta power in subsequent sleep. The second property is the reactivation in sleep of neural firing patterns observed prior to sleep. By reproducing these findings we confirmed that our model is arguably an adequate medium for further study of the putative sleep-related synaptic rescaling process. In addition we found important differences between neural units that reactivated or deactivated during delta; these were differences in cell types based on unit spike shapes, in prior firing rates and in prior spike-train-to-local-field-potential coherence. Taken together these results suggested a mechanistic chain of explanation of the two observed properties, and set the neurobiological framework for further, more computationally driven analysis. Using the above experimental and theoretical substrate we developed a new method of analysis of micro-electrode array data. The method is a generalization to the electromagnetic case of a well-known technique for processing acoustic microphone array data. This allowed calculation of: The instantaneous spatial energy flow and dissipation in the neocortical areas under the array; The spatial energy source density in analogy to well-known current source density analysis. We then refocused our investigation on the two theoretical questions that we hoped to achieve experimental answers for: Whether the state of the neocortex during a delta rhythm could be described by ergodic statistics, which we determined by analyzing the spectral properties of energy dissipation as a signature of the state of the dynamical system; A more explorative approach prompting an investigation of the spatiotemporal interactions across and along neocortical layers and areas during a delta rhythm, as implied by energy flow patterns. We found that the in vitro rodent neocortex does not conform to ergodic statistics during a pharmacologically driven delta or gamma rhythm. We also found a delta period locked pattern of energy flow across and along layers and areas, which doubled the processing cycle relative to the fundamental delta rhythm, tentatively suggesting a reciprocal, two-stage information processing hierarchy similar to a stochastic Helmholtz machine with a wake-sleep training algorithm. Further, the complex valued energy flow might suggest an improvement to the Helmholtz machine concept by generalizing the complex valued weights of the stochastic network to higher dimensional multi-vectors of a geometric algebra with a metric particularity suited for holographic processes. Finally, preliminary attempts were made to implement and characterize the above network dynamics in silico. We found that a qubit valued network does not allow fully holographic processes, but tentatively suggest that an ebit valued network may display two key properties of general holographic processing