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  • frequencies... frequencies.... frequency... network of stochastic oscillators... QUBIT... frequencies);
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  • IEEE Transactions on Ultrasonics, FerroElectrics, and Frequency Control... oscillator
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  • 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 ,,,
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  • 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.
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  • 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.
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  • 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.
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  • 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,
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  • Semiconductor qubits rely on the control of charge and spin degrees of freedom of electrons or holes confined in quantum dots. They constitute a promising approach to quantum information processing, complementary to superconducting qubits. Here, we demonstrate coherent coupling between a superconducting transmon qubit and a semiconductor double quantum dot (DQD) charge qubit mediated by virtual microwave photon excitations in a tunable high-impedance SQUID array resonator acting as a quantum bus. The transmon-charge qubit coherent coupling rate (~21 MHz) exceeds the linewidth of both the transmon (~0.8 MHz) and the DQD charge qubit (~2.7 MHz). By tuning the qubits into resonance for a controlled amount of time, we observe coherent oscillations between the constituents of this hybrid quantum system. These results enable a new class of experiments exploring the use of two-qubit interactions mediated by microwave photons to create entangled states between semiconductor and superconducting qubits.,Nature Communications, 10 (1),ISSN:2041-1723,
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  • Ever since its discovery, quantum mechanics has remained an intensely active field, and its real-world applications continue to unfold rapidly. In 1982, Richard Feynman proposed a new type of computer operating directly under quantum mechanics laws: – the quantum computer \cite{Feynman1982}. Compared with the classical computer, whose information is encoded in “bits”, the quantum computer, whose information is encoded in “quantum bits”, or “qubits”, will be able to perform calculations exponentially faster for such problems as factoring large integers into primes and simulating complicated quantum systems. Due to their extremely powerful calculation speeds and abilities, quantum computers have been the long-pursued dreams for both experimentalists and theorists in many research groups, government agencies, industrial companies, etc., and the fast-paced developments in their architecture and speed continue to make them more and more attractive. There are two principal models of quantum computing: the circuit model and the measurement-based model. The circuit model is similar to a traditional computer where there are inputs, gates and outputs. The measurement-based model is different, as it is crucially based on the cluster state, a type of highly entangled quantum state. In this new model, quantum computing begins with an initial cluster state and then carries out calculations by physical measurements of the cluster state itself along with feedforward. Thus, the cluster state serves as the material and resource for the entire set of calculations, and it is an extremely important part of measurement-based quantum computing. This thesis will discuss an experimental and theoretical work that holds the world record for the largest entangled cluster state ever created whose 60 qumodes (optical versions of qubits) are all available simultaneously. Moreover, the entangled state we created is not random, and it is a cluster state which meets the specific requirements for implementing quantum computing. In the race to build a practical quantum computer, the ability to create such a large cluster state is paramount. Also, our creative optical method to generate massive entanglement advances many other methods due to its high efficiency, super-compactness and large scalability. The entanglement proceeds from interfering multiple EPR entangled pairs, which are generated from the down-converting process of a nonlinear crystal in an optical parametric oscillator, into a very long dual-rail wire cluster state. Moreover, many copies of the same state can easily be obtained by merely adjusting the frequencies of the pump lasers. These cluster states serve as building blocks of the universal quantum computer, and also are, in their own right, important resources for studying and exploring quantum mechanics in large systems.
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