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**frequencies**...**frequencies**....**frequency**... network of stochastic**oscillators**...**QUBIT**...**frequencies**);Data Types:- Document

**qubits**Data Types:- Document

- IEEE Transactions on Ultrasonics, FerroElectrics, and
**Frequency**Control...**oscillator**Data Types:- Other

- IEEE Transactions on Ultrasonics, FerroElectrics, and
**Frequency**Control...**oscillator**Data Types:- Other
- Document

- 6-The electron
**oscillating**period as functions of the temperature and the cyclotron**frequency**in triangular quantum dot**qubit**under an electric field.docx... Fig.4. A-Function relationship between the first excited state energy and the temperature and the electron-phonon coupling constant for different cyclotron**frequencies**and ,,,; B-Function relationship between the first excited energy and the temperature and the electric field strength for different cyclotron**frequencies**and ,,,; C-Function relationship between the first excited energy and the temperature and the confinement length for different cyclotron**frequencies**and ,,,; D-Function relationship between the first excited energy and of the temperature and the Coulomb impurity potential for different cyclotron**frequencies**and ,,,... Fig.1. A-Function relationship between the ground state energy and the temperature and the cyclotron**frequency**for different electron-phonon coupling constants and ,,, ; B-Function relationship between the ground state energy and the temperature and the cyclotron**frequency**for different electric field strengths and ,,,; C-Function relationship between the ground state energy and the temperature and the cyclotron**frequency**for different confinement lengths and ,,,; D-Function relationship between the ground state energy and the temperature and the cyclotron**frequency**for different Coulomb impurity potentials and ,,,... Fig.6. A-The electron**oscillation**period as functions of the temperature and the cyclotron**frequency**for different electron-phonon coupling constants and ,,,; B-The electron**oscillation**period as functions of the temperature and the cyclotron**frequency**for different electric field strengths and,,,; C-The electron**oscillation**period as functions of the temperature and the cyclotron**frequency**for different confinement lengths and ,,,; D-The electron**oscillation**period as functions of the temperature and the cyclotron**frequency**for different Coulomb impurity potentials and ,,,... 7-The electron**oscillating**period as functions of the temperature and the electron-phonon coupling constant and etc. in triangular quantum dot**qubit**under an electric field.docx... 2-The first excited state energy as functions of the temperature and the cyclotron**frequency**in triangular quantum dot**qubit**under an electric field.docx... 3-The ground state energy as functions of the temperature and the electron-phonon coupling constant and etc. in triangular quantum dot**qubit**under an electric field.docx... Fig.7. A-The electron**oscillation**period as functions of the temperature and the electron-phonon coupling constant for different cyclotron**frequencies**and ,,,; B-The electron**oscillation**period as functions of the temperature and the electric field strength for different cyclotron**frequencies**and ,,,; C-The electron**oscillation**period as functions of the temperature and the confinement length for different cyclotron**frequencies**and ,,,; D-The electron**oscillation**period as functions of the temperature and the Coulomb impurity potential for different cyclotron**frequencies**and ,,,... 1-The ground state energy as functions of the temperature and the cyclotron**frequency**in triangular quantum dot**qubit**under an electric field.docx... Fig.3. A-Function relationship between the ground state energy and the temperature and the electron-phonon coupling constant for different cyclotron**frequencies**and ,,,; B-Function relationship between the ground state energy and the temperature and the electric field strength for different cyclotron**frequencies**and ,,,; C-Function relationship between the ground state energy and of the temperature and the confinement length for different cyclotron**frequencies**and ,,,; D-Function relationship between the ground state energy and the temperature and the Coulomb impurity potential for different cyclotron**frequencies**and ,,,Data Types:- Dataset
- Document

- In this thesis, we examine an extension of circuit quantum electrodynamics (QED), cavity QED using superconducting circuits, that utilizes multimode cavities as a resource for quantum information processing. We focus on the issue of
**qubit**connectivity in the processors, with an ideal processor having random access -- the ability of arbitrary**qubit**pairs to interact directly. Here, we implement a random access superconducting quantum information processor, demonstrating universal operations on a nine-**qubit**memory, with a Josephson junction transmon circuit serving as the central processor. The quantum memory is a multimode cavity, using the eigenmodes of a linear array of coupled superconducting resonators. We selectively stimulate vacuum Rabi**oscillations**between the transmon and individual eigenmodes through parametric flux modulation of the transmon**frequency**. Utilizing these**oscillations**, we perform a universal set of quantum gates on 38 arbitrary pairs of modes and prepare multimode entangled states, all using only two control lines. We thus achieve hardware-efficient random access multi-**qubit**control. We also explore a novel design for creating long-lived 3D cavity memories compatible with this processor. Dubbed the ``quantum flute'', this design is monolithic, avoiding the loss suffered by cavities with a seam between multiple parts. We demonstrate the ability to manipulate the spectrum of a multimode cavity and also measure photon lifetimes of 0.5-1.3 ms for 21 modes. The combination of long-lived quantum memories with random access makes for a promising architecture for quantum computing moving forward.Data Types:- Document

- In this thesis, we examine an extension of circuit quantum electrodynamics (QED), cavity QED using superconducting circuits, that utilizes multimode cavities as a resource for quantum information processing. We focus on the issue of
**qubit**connectivity in the processors, with an ideal processor having random access -- the ability of arbitrary**qubit**pairs to interact directly. Here, we implement a random access superconducting quantum information processor, demonstrating universal operations on a nine-**qubit**memory, with a Josephson junction transmon circuit serving as the central processor. The quantum memory is a multimode cavity, using the eigenmodes of a linear array of coupled superconducting resonators. We selectively stimulate vacuum Rabi**oscillations**between the transmon and individual eigenmodes through parametric flux modulation of the transmon**frequency**. Utilizing these**oscillations**, we perform a universal set of quantum gates on 38 arbitrary pairs of modes and prepare multimode entangled states, all using only two control lines. We thus achieve hardware-efficient random access multi-**qubit**control. We also explore a novel design for creating long-lived 3D cavity memories compatible with this processor. Dubbed the ``quantum flute'', this design is monolithic, avoiding the loss suffered by cavities with a seam between multiple parts. We demonstrate the ability to manipulate the spectrum of a multimode cavity and also measure photon lifetimes of 0.5-1.3 ms for 21 modes. The combination of long-lived quantum memories with random access makes for a promising architecture for quantum computing moving forward.Data Types:- Document

- In optically controlled quantum computers it may be favorable to address different
**qubits**using light with different**frequencies**, since the optical diffraction does not then limit the distance between**qubits**. Using**qubits**that are close to each other enables**qubit**-**qubit**interactions and gate operations that are strong and fast in comparison to**qubit**-environment interactions and decoherence rates. However, as**qubits**are addressed in**frequency**space, great care has to be taken when designing the laser pulses, so that they perform the desired operation on one**qubit**, without affecting other**qubits**. Complex hyperbolic secant pulses have theoretically been shown to be excellent for such**frequency**-addressed quantum computing [I. Roos and K. Molmer, Phys. Rev. A 69, 022321 (2004)]—e.g., for use in quantum computers based on optical interactions in rare-earth-metal-ion-doped crystals. The optical transition lines of the rare-earth-metal-ions are inhomogeneously broadened and therefore the**frequency**of the excitation pulses can be used to selectively address**qubit**ions that are spatially separated by a distance much less than a wavelength. Here,**frequency**-selective transfer of**qubit**ions between**qubit**states using complex hyperbolic secant pulses is experimentally demonstrated. Transfer efficiencies better than 90% were obtained. Using the complex hyperbolic secant pulses it was also possible to create two groups of ions, absorbing at specific**frequencies**, where 85% of the ions at one of the**frequencies**was shifted out of resonance with the field when ions in the other**frequency**group were excited. This procedure of selecting interacting ions, called**qubit**distillation, was carried out in preparation for two-**qubit**gate operations in the rare-earth-metal-ion-doped crystals. The techniques for**frequency**-selective state-to-state transfer developed here may be also useful also for other quantum optics and quantum information experiments in these long-coherence-time solid-state systems.Data Types:- Document

- Trapped-ions form a promising platform to realize a future large scale quantum computing device.
**Qubits**are typically stored in internal electronic states, which are coupled using their joint motion in the trap potential. In this thesis this control paradigm is reversed. The harmonic motion of a trapped calcium ion forms the main subject of studies, which is controlled via the internal electronic states. A number of new techniques are introduced and examined, primarily based on the implementation of modular variable measurements. These are realized combining an internal state dependent optical dipole force with readout of the internal states. Modular measurements are used to investigate large "Schrödinger cat'' states of the ion's motion, to violate Leggett-Garg tests of macroscopic realism, and finally to realize a logical**qubit**encoded in an error-correcting code based on the trapped-ion**oscillator**. The latter offers an alternative to the standard**qubit**based quantum information processing approach, which when embedded in systems of coupled**oscillators**could lead to a large-scale quantum computer. Measurements of a particle's modular position and momentum have been the focus of various discussions of foundational quantum mechanics. Such modular measurements of the trapped-ion's motion are studied in depth in this thesis, in particular their ability to commute, which forms a key element for the latter work on error-correcting codes. Here we make use of the ability to investigate sequences of measurements on a single harmonic**oscillator**, and study correlations between their results, as well as quantum measurement disturbances between the measurements. In order to achieve the major results of the thesis, it was necessary to characterize and control multiple wave packets in phase space. On the characterization side, the need to cope with states with high energy occupations led to the development of multiple new methods for quantum state tomography, including the use of a squeezed eigenstate basis, and the direct extraction of the characteristic function of the**oscillator**using state-dependent forces. These were used to analyze some of the largest**oscillator**"Schrödinger cat'' states which have been produced to date. The main result of this thesis is encoding and full control of a logical**qubit**in the motional**oscillator**space using a code proposed 18 years ago by Gottesman, Kitaev and Preskill. Logical code states are realized and manipulated using sequences of up to five modular measurements applied to an ion initially prepared in a squeezed motional state. Such sequences realize superpositions of multiple squeezed wave packets, which form the code words. The usage of the**oscillator**enables to encode and in principle correct a logical**qubit**within a single trapped ion, which when compared to typical**qubit**-array based approaches simplifies control and hardware. While the discussion above focuses on the new physics in this thesis, in addition the work required technical upgrades to the system, improving control of both**qubit**and**oscillator**. These form important components which have impact on all experiments in our setup, beyond the bounds of the current thesis.,ISBN:5800134927809,Data Types:- Document

- 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.Data Types:- Other