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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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frequency stability... Oscillator circuit is one that converts DC power into AC power at a frequency without any input signal. Oscillators are commonly used in communication systems to generate carrier frequency ranging from audio frequency 20 Hz to radio frequency 100G Hz . There are two main classes of oscillators, harmonic oscillator with sinusoidal output e.g. sine wave and relaxation oscillator with non sinusoidal output e.g. square wave, triangle wave, etc. . In this paper, class A Colpitts oscillator with LC feedback circuit is designed as a radio frequency oscillator to generate the output signals at 5M Hz. After designing, this circuit is simulated with Multisim software to analyze the effect of power supply on its frequency stability. Three supply voltages, 14 V, 12 V and 10 V are set as sample parameters to analyze the variation of frequency and voltage of the output signal. Changing DC power supply one by one as the above selected parameters in Multisim, the change of value of frequencies are noted and output signal results are also shown with the help of virtual oscillator. Thit Waso Khine "Designing Class a Colpitts Oscillator and Analyzing the Effect of DC Power Supply on its Frequency Stability" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd28022.pdf... Colpitts oscillator
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Oscillators... Linear models for oscillator noise predict an improvement in frequency stability with increasing Quality factor. Although it is well known that this result does not apply to non-linear oscillators, systematic experimental investigations of the impact of damping on frequency stability of non-linear MEMS oscillators has not been previously reported. This paper studies the frequency stability of a nonlinear MEMS oscillator under variable damping conditions. Analytical and experimental investigation of a MEMS square-wave oscillator embedding a double-ended tuning fork resonator driven into the non-linear regime is introduced. The experimental results indicate that for a pre-set drive level, the variation of air-damping changes the onset of nonlinear behaviour in the resonator, which not only impacts the output frequency but also the phase/frequency noise of a nonlinear MEMS square wave oscillator. The random walk frequency noise and flicker frequency noise levels are strongly correlated with the non-linear operating point of the resonator, whereas the white phase and white frequency noise levels are impacted both by the output power and by operative nonlinearities.
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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.... In the modern world, high-rise buildings are in vogue, each year more and more large buildings built. One of the most common schemes for high-rise buildings is portico system, formed by combination of vertical (columns) and horizontal (beams) supporting members. However, as building grows in height, it must have enough strength and stiffness to withstand lateral loads imposed by wind or moderate earthquakes. Over last ten decades, there was therefore significant renewed interest in structures stability problem subjected to time-dependent loads. Considering dynamic problems in civil engineering field is necessary to ensure structure reliability in many applications. But dynamics problems study is often complex for inertia forces come from structure displacements which in turn depend on structures free oscillations frequency. The coincidence of this frequency of free oscillation with that of the forced oscillations caused by the wind involves the phenomenon of resonance which is very dangerous for the structures. It is therefore necessary to know how to determine the frequency of the free oscillations of the systems which constitutes the starting point for a dynamic study. To do this, the stiffness matrix method was used to determine the free oscillation frequencies of the multi-storey portico structures. It has been observed, therefore, that the frequencies of free oscillations don?t depend on time, neither on the amplitude of the oscillations, nor on the phase angle, but rather on the rigidity and the mass of the structures.
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frequency stability... CMOS, x frequency stability, delay time... ring oscillator... A combined skewed ring oscillator by different type of delay stages is presented. This paper aims to drive a high stable and relatively high frequency but still use a full transistor circuit for ring oscillator with combined delay stages and skewed connections. First we propose two types of common inverters then calculate their delay time and analysis their dependence of delay time to variation of power supply voltage. The simulation results verify that delay time of these two CMOS inverters show opposite behaviour versus power supply changing. So a combined structure can obtain more appropriate frequency stability versus power supply noise. Also in order to increase oscillation frequency we have used the negative skewed delay connections. The simulation results using HSPICE for 0.18 µm CMOS shows a good agreement with analysis results. In addition in this paper the mathematical justification for improved functioning of this combined skewed ring oscillator has been proved. This justification shows appropriate agreement with the simulation results. From mathematical point of view the proposed ring oscillator has better frequency stability in comparison with other types of ring oscillators. In fact, the oscillation frequency sensitivity to supply voltage noise is reduced considerably.
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circular oscillations... Through superposition of the linear oscillations of two leaf springs of almost equal frequencies, linear, elliptic and circular oscillations can be generated and shown by optical projection.
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Smoke Test on 17Jul2019 natscilivecustomer (Dataset-1) Smoke Test on 17Jul2019 natscilivecustomer (Dataset-2)
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Lock-on; streamwise oscillation; transverse oscillation; fluid forces... This paper presents results obtained from the numerical solution for the flow past an oscillating circular cylinder at Reynolds number of 200. The frequency of oscillation was fixed to the vortex shedding frequency from a fixed cylinder, f0, while the amplitudes of oscillations were varied from to 1.1a, where a represents the radius of the cylinder. The response of the flow through the fluid forces acting on the surface of the cylinder are investigated. The lock-on phenomenon is captured at low oscillation amplitudes.
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