<p>WKB theory provides a plausible link between classical mechanics and quantum mechanics in its semi-classical limit. Connecting the WKB wave function across the turning points in a quantum well, leads to the WKB quantization condition. In this work, I focus on some improvements and recent developments related to the WKB quantization condition. First I discuss how the combination of super-symmetric quantum mechanics and WKB, gives the SWKB quantization condition which is exact for a large class of potentials called shape invariant potentials. Next I turn to the fact that there is always a probability of refection when the potential is not constant and the phase of the wave function should account for this refection. WKB theory ignores refection except at turning points. I explain the work of Friedrich and Trost who showed that by including the correct "refection phase" at a turning point, the WKB quantization condition can be made to give exact bound state energies. Next I discuss the work of Cao and collaborators which takes refection of the wave function into account everywhere. We show that Cao's method provides a way to compute the F-T refection phase. Finally I discuss a paper of Fabre and Guery-Odelin who used the exponential potential to study the accuracy of WKB. In their results the accuracy deteriorates as the energy increases, which is inconsistent with Bohr's correspondence principle. Using the Friedrich and Trost method, we resolved this problem.</p> / Master of Science (MSc)

<p> Successful implementation of fault-tolerant quantum computation on a system of qubits places severe demands on the hardware used to control the many-qubit state. It is known that an accuracy threshold <i>P_a</i> exists for any quantum gate that is to be used for such a computation to be able to continue for an unlimited number of steps. Specifically, the error probability Pe for such a gate must fall below the accuracy threshold: <i> P_e</i> &lt; <i>P_a.</i> Estimates of <i> P_a</i> vary widely, though <i>P_a</i> &sim; 10^&minus;4 has emerged as a challenging target for hardware designers. I present a theoretical framework based on neighboring optimal control that takes as input a good quantum gate and returns a new gate with better performance. I illustrate this approach by applying it to a universal set of quantum gates produced using non-adiabatic rapid passage. Performance improvements are substantial comparing to the original (unimproved) gates, both for ideal and non-ideal controls. Under suitable conditions detailed below, all gate error probabilities fall by 1 to 4 orders of magnitude below the target threshold of 10^&minus;4. </p><p> After applying the neighboring optimal control theory to improve the performance of quantum gates in a universal set, I further apply the general control theory in a two-step procedure for fault-tolerant logical state preparation, and I illustrate this procedure by preparing a logical Bell state fault-tolerantly. The two-step preparation procedure is as follow: Step 1 provides a one-shot procedure using neighboring optimal control theory to prepare a physical qubit state which is a high-fidelity approximation to the Bell state |&beta;₀₁&rang; = 1/&radic;2(|01&rang; + |10&rang;). I show that for ideal (non-ideal) control, an approximate |&beta;₀₁&rang; state could be prepared with error probability &epsis; &sim; 10^&minus;6 (10^&minus;5) with one-shot local operations. Step 2 then takes a block of <i>p</i> pairs of physical qubits, each prepared in |&beta;₀₁&rang; state using Step 1, and fault-tolerantly prepares the logical Bell state for the <i>C</i>₄ quantum error detection code.</p>

The nitrogen vacancy (NV) center in diamond is a unique quantum system that combines solid state spin qubits with coherent optical transitions. The spin states of the NV center can be initialized, read out, and controlled with RF fields at room temperature. It can be coupled to other spin systems in the environment while at the same time maintaining an extraordinary degree of quantum coherence. Experiments utilizing the NV center's spin states have led to a wide range of demonstrations from quantum error correction to high-sensitivity magnetometry. This thesis, however, focuses on creating an interface between NV centers and light in the visible domain by making use of its optical transitions. Such an interface connects the quantum system consisting of NV centers and nuclear spins to photons, which can then be used to both manipulate the spin qubits themselves or transport quantum information over large distances. / Physics

<p> A quantum computer has the potential to efficiently solve problems that are intractable for classical computers. Constructing a large-scale quantum processor, however, is challenging due to errors and noise inherent in real-world quantum systems. One approach to this challenge is to utilize modularity&mdash;a pervasive strategy found throughout nature and engineering&mdash;to build complex systems robustly. Such an approach manages complexity and uncertainty by assembling small, specialized components into a larger architecture. These considerations motivate the development of a quantum modular architecture, where separate quantum systems are combined via communication channels into a quantum network. In this architecture, an essential tool for universal quantum computation is the teleportation of an entangling quantum gate, a technique originally proposed in 1999 which, until now, has not been realized deterministically, Using the circuit quantum electrodynamics platform, this thesis reports on the experimental demonstration of a teleported controlled-NOT operation made deterministic by utilizing real-time adaptive control. Additionally, we take a crucial step towards implementing robust, error-correctable modules by enacting the gate between logical qubits, encoding quantum information redundantly in the states of superconducting cavities. Such teleported operations have significant implications for fault-tolerant quantum computation, and when realized within a network can have broad applications in quantum communication, metrology, and simulations. Our results illustrate a compelling approach for implementing multi-qubit operations on logical qubits within an error-protected quantum modular architecture.</p><p>

The progress in modern quantum information processing (QIP) strongly depends on new algorithms and on the development of novel quantum entanglement processing elements enabling to perform quantum computation and quantum simulation effectively. Several examples of quantum information processing applications based on freshly designed linear-optics devices are presented. A beam splitter (BS) is a central device in linear-optical quantum information processing because it can split the incoming photon amplitudes into spatially distinct modes to establish conditions for quantum superposition. The BS naturally possesses directional-bias in a sense that incoming photons can only propagate in a forward manner. When the execution of certain quantum information tasks would require multiple operations, this directionality condition becomes a serious obstacle by creating significant overhead in the number of needed elements and other supporting devices. We introduce a family of amplitude-controllable fully-reversible linear-optical quantum information processors, called directionally-unbiased linear-optical multiports, in order to achieve significant reduction in the number of required hardware. The theoretical analysis of the device design as well as the experimental realization of three-port unit using bulk linear optics is demonstrated. These devices offer several fresh approaches in quantum-walk-based applications such as quantum simulation of solid-state Hamiltonians, topological protection of polarization qubits against errors, and quantum communication. Topological photonics is an emerging and actively developing field because of its capability to stabilize and protect some quantum states from perturbation errors by ensuring the environment carries a distinct topological signature. Topology-dependent quantum information processing is globally stable due to the entire system being engaged in the information manipulation. We demonstrate suppression of quantum amplitude transfer between two distinct bulk regions of a system. This results in error avoidance for a two-photon polarization-entangled state under specific conditions. The goal of modern quantum communication is a reliable distribution of quantum entanglement between multiple nodes performing quantum operations such as quantum memories and quantum computers. We demonstrated that local quantum information processing using new fully-reversible four-port linear-optical structures could find an immediate application in quantum communication. A quantum information routing device is introduced based on the use of four-dimensional Grover matrices and beam splitters. Several multiport-based units are developed to demonstrate new higher-dimensional Hong-Ou-Mandel (HOM) effect and directionally-controllable entangled state distribution while changing only phases in a waveguided unit. Several such operational elements could be linked to form a reconfigurable network of quantum users without losing control of quantum amplitudes. This allows controllable routing of entangled photons and sharing entanglement between any designated users in the future quantum computational networks. / 2022-05-15T00:00:00Z

Multi-photon nonlinear processes in atoms have served as important tools for quantum metrology, quantum communications, and quantum sensing. In this thesis, we experimentally address the interplay of various multi-photon Raman processes in hot Rb vapor, with the four-wave mixing (FWM) process being a central theme. FWM is the nonlinear response of a medium to a strong optical pump field inelastically scattering off atomic resonances and resulting in the generation of additional photons in different modes. FWM is a detrimental, but inherent part of electromagnetically induced transparency (EIT) and Raman based quantum memories. However, we were able to weaken the four-photon resonance by utilizing two-photon absorption to remove the additional photons without interfering with the signal beam. We also demonstrate the ability to tailor FWM to generate new photons in a controlled fashion for mode conversion. With this, we showed the conversion of 795 nm light to 420 nm light. While FWM is a source of noise in quantum memories, it can also be used for the generation squeezed twin-beams. Such beams have relative intensity noise reduced below the classical shot noise limit and share mode dependence based on the phase-matching conditions. Using this, we demonstrated that twin-beams can be generated with largely different spatial structure (optical angular momentum) and still share strong correlations, so long as the phase-matching conditions are satisfied. We then constructed and demonstrated the operation of a polarization-based quantum interferometer using squeezed twin-beams and showed that our beams were entangled under the inseparability condition. Using this interferometer, we were also able to achieve squeezing at low detection frequencies, which is necessary for things like quantum imaging and gravitational wave detection. We also demonstrated that squeezed twin-beams can be utilized to enhance the sensitivity of two-photon absorption spectroscopy. This research has touched on many different subjects related to quantum information science and improved upon some of the tools needed for the implementation of such technologies.

In high-precision optical measurements, noise due to quantum fluctuations in the amplitude and phase of the probing field becomes the limiting factor in detection sensitivity. While this quantum noise is fundamental and not a result of detection, it is possible to engineer a quantum state that has reduced noise in either amplitude or phase (at the cost of increasing noise in the other) called a quadrature-squeezed state. In this dissertation, we study the use of quadrature-squeezed vacuum states for low-light imaging and develop a quantum detection method to measure the spatial dependence of the quantum noise using a camera instead of the traditional homodyne detection. Our novel quantum imaging scheme paves the way for ultra-low-light imaging due to the inherently few photons in the squeezed vacuum state. We also expand the method beyond camera limitations using single-pixel imaging techniques, making the detection method accessible to a broad range of wavelengths where quantum-limited cameras may be difficult to find.

No description available.

Green's operator for Hamiltonians with Coulomb plus polynomial potentials

<p>In this thesis we solve the Feshbach-Villars equations for spin-zero particles through use of matrix continued fractions. The Feshbach-Villars equations are derived from the Klein-Gordon equation and admit, for the Coulomb potential on an appropriate basis, a Hamiltonian form that has infinite symmetric band-matrix structure. The corresponding representation of the Green's operator of such a matrix can be given as a matrix continued fraction. Furthermore, we propose a finite dimensional representation for the potential operator such that it retains some information about the whole Hilbert space. Combining these two techniques, we are able to solve relativistic quantum mechanical problems of a spin-zero particle in a Coulomb-like potential with a high level of accuracy.