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Silicon **Qubits**

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Superconducting **Qubits**

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The current variety of treatment options for epilepsy leaves 30% of those who suffer from this chronic neurological disease without a cure. Therefore, this senior thesis project aims to uncover new insights about the brain structure that underlies susceptibility to epilepsy in hopes that a greater understanding of this underlying structure will catalyze the discovery of novel therapeutic methods which target these underlying differences in brain structure. To drive the discovery of new insights about underlying structure, this project addresses the following tension found in the literature: high **frequency** **oscillations** occur in both the brains of those with epilepsy and in the brains of those without epilepsy. Only when high **frequency** **oscillations** occur in the brains of those with epilepsy does the brain enter a state of unstable dynamics and seizure activity. This suggests that there is a difference in underlying structure between epileptic and non-epileptic brains, and this study uses computational modeling of neuronal firing to characterize these differences.
First, based on a firing rate model, we find that within the phase space of the weight values, there is a band of stability from which one might predict the stability of a set of weights. Then, in the next two versions of the model, we add Hebbian plasticity and homeostatic plasticity. Only through the addition of Hebbian plasticity and homeostatic plasticity does high **frequency** **oscillation**, the manipulation described in our driving question, have a lasting effect on the weights. With the addition of a rate based Hebbian plasticity model to the base firing rate model, we find that weights can be perturbed from this band of stability through Hebbian plasticity. Adding a weight based homeostatic plasticity model to the base firing rate and Hebbian plasticity model then gives insight into the fact that having a target weight within a certain location with respect to the band of stability can rescue stability of a set of original weights from the destabilizing effects of Hebbian plasticity. Finally, we explore the effect of high **frequency** **oscillation** on various weight combinations within the phase space, and we find that certain weight combinations are projected to an unstable state through high **frequency** **oscillation** while other weight combinations remain at a stable state even in the face of high **frequency** **oscillation**. The unifying characteristic of those weights which remain stable in the face of high **frequency** **oscillation** remains an open question. However, in the process of investigating high **frequency** **oscillations**, it was found that weights on the edge of the band of stability are more robust to instability through Hebbian plasticity than weights on the band of stability that are further from the edge.
These results suggest that the differential response to high **frequency** **oscillation** between epileptic and non-epileptic brains can be attributed at least in part to the location of weights with respect to the band of stability.

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This thesis presents the results of experimental work aimed at realizing the multimodal Rabi Hamiltonian of quantum optics in a circuit QED device. We have
fabricated and tested three coplanar waveguide resonators of fundamental **frequency**
¿0/(2¿) = 92 MHz, two of which contained superconducting transmon **qubits**. Both
**qubit** devices failed to exhibit signs of light-matter coupling, as deduced through
two different measurement techniques. The experimental progress was supplemented
with numerical simulations of the multimodal Jaynes-Cummings and Rabi Hamiltonians, which attempted to study cavity-**qubit** dynamics in the multimodal regime
for various light-matter coupling strengths. For a 2-mode Rabi model, we report
the observation of a novel localization-delocalization transition in photon occupation
between the two modes, which displays signatures that should be readily measured
in experiment. Future work should continue attempts to realize strong, multimodal
light-matter coupling in circuit QED so as to verify the existence of this transition.

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- Other

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We present a design for a heterojunction bipolar transistor based Colpitts **oscillator** for cryogenic capacitance measurement. We also present the design of an interdigitated capacitor to detect changes in dielectric constant of a fluid on the surface of a printed circuit board, along with **frequency** measurements of this system in air and liquid nitrogen. Designs and **frequency** measurements are also presented for a tunnel diode based **oscillator**.

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- Other

Army ants (Eciton burchellii) have been studied for nearly a century, but
observable patterns in their traffic organization have not yet been explored,
despite the fact that this organization contributes greatly to their optimal foraging.
Using pheromones and tactile cues to transmit information from ant to ant, they
coordinate their movements in order to optimize traffic and create a collective
behavior that increases the overall efficiency of the colony. Garnier et al. (2013)
discovered that E. burchellii traffic possesses regular, periodic **oscillations** that
allow it to gain maximum stability. In this paper, we explored these traffic
**oscillations** at trail junctions to determine how army ants optimize their network of
foraging trails. After conducting research at La Selva Biological Station in Costa
Rica, we found that the mean **oscillation** **frequencies** and periods of army ant
traffic are uniform and unrelated to traffic direction. Despite this overarching
uniformity, each zone of a trail junction possesses a different **oscillation** **frequency**
compared to the other two zones of the same junction. Lastly, **oscillation** **frequency**
increases as traffic becomes more unidirectional. By displaying differential
oscillatory behavior at trail junctions, army ants spontaneously adapt to their
constantly changing environment in order to optimize traffic dynamics. Finally, we
propose ideas for future research that have the potential to delve deeper into the
study of trail junctions.

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- Other

Circuit quantum electrodynamics (cQED) uses superconducting circuit elements as its building blocks for controllable quantum systems and has become a promising experimental platform for quantum computation and quantum simulation. The ability to tune the coupling rate between circuit elements extends the controllability and flexibility of cQED devices and can be utilized to improve device performance.
This thesis presents the study, implementation and application of tunable coupling devices in cQED. The tunability originates from the basic principles of quantum superposition and interference, and unwanted interactions can be suppressed by destructive interference. Following this principle, we design and conduct two experiments that demonstrate the utility of tunable coupling for better device performances in quantum information processing.
The first experiment aims to improve the coherence of **qubits** against noise. We implement a **qubit** whose **frequency** and dispersive coupling to a readout resonator can be tuned independently. When the coupling rate is tuned to near zero, the **qubit** becomes immune to photon number fluctuations in the resonator and exhibits robust coherence time in the presence of noise. The second experiment extends to a multi-**qubit** system where crosstalk between **qubits** causes error in quantum gates. We develop a two-**qubit** device and suppress crosstalk by tuning the ZZ coupling rate between the **qubits**. The tunable dispersive coupling can also be parametrically modulated to implement a two-**qubit** entangling gate in the low crosstalk regime. Those devices provide flexible and promising building blocks for cQED systems.

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- Other

The advent of superconducting quantum circuits as a robust scientific platform and contender for quantum computing applications is the result of decades of research in light-matter interaction, low-temperature physics, and microwave engineering. There is growing interest to use this advancing technology to study domains of light-matter interaction that were previously thought to be beyond experimental reach. Our work is part of an initiative to explore non-equilibrium condensed matter physics using photons instead of atoms. Open questions in this area currently pose significant challenges theoretically due to analytical complexity and system sizes which prohibit complete numerical simulations, thus experiment-based research has the potential to lead to significant advancements in this field. Here we examine phenomena that arise when moving beyond standard single-mode strong coupling towards the realm of many-body physics with light in two distinct directions.
First we study multimode strong coupling, where a single artificial atom or **qubit** is simultaneously strongly coupled to a large, but discrete number of non-degenerate photonic modes of a cavity with coupling strengths comparable to the free spectral range. This domain, which falls in between small, discrete and continuum Hilbert spaces, is experimentally realized by coupling a **qubit** to a low fundamental **frequency** coplanar waveguide cavity. In this system we report on resonance fluorescence and narrow linewidth emission directly resulting from complex **qubit** mediated mode-mode interactions.
In the second part we explore **qubits** strongly coupled to photonic crystals, which give rise to exotic physical scenarios, beginning with single and multi-excitation **qubit**-photon dressed bound states comprising induced, spatially localized photonic modes, centered around the **qubits**, and the **qubits** themselves. The localization of these states changes with **qubit** detuning from the band-edge, offering an avenue of in situ control of bound state interaction. Due to their localization-dependent interaction, these states offer the ability to create one-dimensional chains of bound states with tunable interactions that preserve the **qubits**' spatial organization, a key criterion for realization of certain quantum many-body models.
The unique domains of light-matter interaction discussed here are a subset of exciting research initiatives growing our general understanding of complex, strongly coupled quantum systems.

Data Types:

- Other

Experiments are conducted to better understand the effects of flexibility in generating unsteady bio-inspired propulsion. It is found that by exploiting the effects of flexibility, the thrust production and propulsive efficiency can be up to twice that of a rigid propulsor. The wakes are highly dependent on the input parameters to the system such as the **oscillation** **frequency** and chordwise traveling wave wavelength that develops along a flexible surface. In general, the wakes of flexible propulsors tend to concentrate their momentum in the direction of motion whereas the wakes of rigid propulsors have relatively larger momentum in the transverse direction leading to a decrease in propulsive efficiency. A linear stability analysis is conducted on the wakes to determine the wake resonant **frequencies**. It is found that when the driving **oscillation** **frequency** of the apparatus matches the wake resonant **frequency** there is a local peak in propulsive efficiency. The global peak in efficiency occurs only when the structural resonant **frequency** of the flexible structure is coincident with the wake resonant **frequency**, which only occurs under very specific conditions. This implies that there is an optimum flexibility to maximize propulsive efficiency; being either too stiff or too flexible is detrimental to propulsive performance. Since both the structural resonant **frequency** and wake resonant **frequencies** are finite, this also suggests that animals must utilize flexible propulsive surfaces if they are to optimize their efficiencies. Finally, a non-dimensional scaling argument is made that is shown to collapse the thrust production, power input to the fluid, and propulsive efficiency for a range of propulsors with various flexibilities and aspect ratio.

Data Types:

- Other