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High-fidelity **qubit** initialization is of significance for efficient error correction in fault tolerant quantum algorithms. Combining two best worlds, speed and robustness, to achieve high-fidelity state preparation and manipulation is challenging in quantum systems, where **qubits** are closely spaced in **frequency**. Motivated by the concept of shortcut to adiabaticity, we theoretically propose the shortcut pulses via inverse engineering and further optimize the pulses with respect to systematic errors in **frequency** detuning and Rabi **frequency**. Such protocol, relevant to **frequency** selectivity, is applied to rare-earth ions **qubit** system, where the excitation of **frequency**-neighboring **qubits** should be prevented as well. Furthermore, comparison with adiabatic complex hyperbolic secant pulses shows that these dedicated initialization pulses can reduce the time that ions spend in the excited state by a factor of 6, which is important in coherence time limited systems to approach an error rate manageable by quantum error correction. The approach may also be applicable to superconducting **qubits**, and any other systems where **qubits** are addressed in **frequency**.

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This dissertation examines the design, fabrication, and characterization of a superconducting lumped-element tunable LC resonator that is used to vary the coupling between two superconducting **qubits**. Some level of **qubit**-**qubit** coupling is needed to perform gating operations. However, with fixed coupling, single **qubit** operations become considerably more difficult due to dispersive shifts in their energy levels transitions that depend on the state of the other **qubit**. Ideally, one wants a system in which the **qubit**-**qubit** coupling can be turned off to allow for single **qubit** operations, and then turned back on to allow for multi-**qubit** gate operations. I present results on a device that has two fixed-**frequency** transmon **qubits** capacitively coupled to a tunable thin-film LC resonator. The resonator can be tuned in situ over a range of 4.14 GHz to 4.94 GHz by applying an external magnetic flux to two single-Josephson junction loops, which are incorporated into the resonator’s inductance. The **qubits** have 0-to-1 transition **frequencies** of 5.10 GHz and 4.74 GHz. To isolate the system and provide a means for reading out the state of the **qubit** readout, the device was mounted in a 3D Al microwave cavity with a TE101 mode resonance **frequency** of about 6.1 GHz. The flux-dependent transition **frequencies** of the system were measured and fit to results from a coupled Hamiltonian model. With the LC resonator tuned to its minimum resonance **frequency**, I observed a **qubit**-**qubit** dispersive shift of 2χ_qq≈ 0.1 MHz, which was less than the linewidth of the **qubit** transitions. This dispersive shift was sufficiently small to consider the coupling “off”, allowing single **qubit** operations. The **qubit**-**qubit** dispersive shift varied with the applied flux up to a maximum dispersive shift of 2χ_qq≈ 6 MHz. As a proof-of-principle, I present preliminary results on performing a CNOT gate operation on the **qubits** when the coupling was “on” with 2χ_qq≈ 4 MHz. This dissertation also includes observations of the temperature dependence of the relaxation time T1 of three Al/AlOx/Al transmons. We found that, in some cases, T1 increased by almost a factor of two as the temperature increased from 30 mK to 100 mK. We found that this anomalous behavior was consistent with loss due to non-equilibrium quasiparticles in a transmon where one electrode in the tunnel junction had a smaller volume and slightly smaller superconducting energy gap than the other electrode. At sufficiently low temperatures, non-equilibrium quasiparticles accumulate in the electrode with a smaller gap, leading to an increased density of quasiparticles at the junction and a corresponding decrease in the relaxation time. I present a model of this effect, use the model to extract the density of non-equilibrium quasiparticles in the device, and find the values of the two superconducting energy gaps.

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Quantum states can contain correlations which are stronger than is possible in classical systems. Quantum information technologies use these correlations, which are known as entanglement, as a resource for implementing novel protocols in a diverse range of fields such as cryptography, teleportation and computing. However, current methods for generating the required entangled states are not necessarily robust against perturbations in the proposed systems. In this thesis, techniques will be developed for robustly generating the entangled states needed for these exciting new technologies.
The thesis starts by presenting some basic concepts in quantum information proccessing. In Ch. 2, the numerical methods which will be used to generate solutions for the dynamic systems in this thesis are presented. It is argued that using a GPU-accelerated staggered leapfrog technique provides a very efficient method for propagating the wave function.
In Ch. 3, a new method for generating maximally entangled two-**qubit** states using a pair of interacting particles in a one-dimensional harmonic **oscillator** is proposed. The robustness of this technique is demonstrated both analytically and numerically for a variety of interaction potentials. When the two **qubits** are initially in the same state, no entanglement is generated as there is no direct **qubit**-**qubit**
interaction. Therefore, for an arbitrary initial state, this process implements a root-of-swap entangling quantum gate. Some possible physical implementations of this proposal for low-dimensional semiconductor
systems are suggested.
One of the most commonly used **qubits** is the spin of an electron. However, in semiconductors, the spin-orbit interaction can couple this **qubit** to the electron's momentum. In order to incorporate this e ffect
into our numerical simulations, a new discretisation of this interaction is presented in Ch. 4 which is signi ficantly more accurate than traditional methods. This technique is shown to be similar to the standard discretisation for magnetic fields.
In Ch. 5, a simple spin-precession model is presented to predict the eff ect of the spin-orbit interaction on the entangling scheme of Ch. 3. It is shown that the root-of-swap quantum gate can be restored by introducing an additional constraint on the system. The robustness of the gate to perturbations in this constraint is demonstrated by presenting numerical solutions using the methods of Ch. 4.

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Portico **Frequency** of free **oscillations** Resonance Stiffness matrix method.

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circular **oscillations**

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Lock-on; streamwise **oscillation**; transverse
**oscillation**; fluid forces

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FIGURE 6. Hyalessa maculaticollis. Echemes structure. A, Power **frequency** spectrum represented with overlay of 52 spectra computed from echemes with high amplitude **oscillations** showing a dominant **frequency** marked by F3. B, Detailed oscillogram showing the first echeme with low amplitude **oscillations** and the second echeme with high amplitude **oscillations**. C, Power **frequency** spectrum represented with overlay of 71 spectra computed from echemes with low amplitude **oscillations** showing dominant **frequencies** marked by F1 and F2.

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