This report is an introduction to quantum computation and quantum information.\nWe present a two-part theory section followed by data analysis of a transmon qubit.\nThe ¯rst theory part, needed for the analysis, introduces fundamental properties of\nqubit states and the Bloch sphere description. The qubit manipulation, interaction\nwith a electromagnetic ¯eld, is then studied in the Rabi model (semi-classical) and the\nJaynes-Cummings model (fully quantized). The second theory part is a qualitative\npresentation of the density matrix representation, decoherence (e®ects of noise) and\nread-out, which are useful topics in more advanced analysis.\nWe also present a summary of qubit realizations, with focus on the superconduct-\ning qubits: charge, phase and transmon.\nIn the last part of the report, we analyze spectroscopic measurements on a trans-\nmon qubit in a cavity resonator, performed atMC2 Chalmers. The data was compared\nto the expected behavior from the Jaynes-Cummings Hamiltonian and then the full\nHamiltonian for the transmon. The comparison enabled us to extract the parame-\nters of the transmon. The ratio of the Josephson energy and the charge energy was\ndetermined to be EJ=EC = 34:5644 § 0:9456 GHz, which is in the transmon regime.\nFurthermore, the coupling strength between the cavity resonator and the qubit was\ndetermined to be 2¯eV 0\nrms = 0:1301 § 0:00095 GHz, with a 68% con¯dence interval.
This report is an introduction to quantum computation and quantum information.\nWe present a two-part theory section followed by data analysis of a transmon qubit.\nThe ¯rst theory part, needed for the analysis, introduces fundamental properties of\nqubit states and the Bloch sphere description. The qubit manipulation, interaction\nwith a electromagnetic ¯eld, is then studied in the Rabi model (semi-classical) and the\nJaynes-Cummings model (fully quantized). The second theory part is a qualitative\npresentation of the density matrix representation, decoherence (e®ects of noise) and\nread-out, which are useful topics in more advanced analysis.\nWe also present a summary of qubit realizations, with focus on the superconduct-\ning qubits: charge, phase and transmon.\nIn the last part of the report, we analyze spectroscopic measurements on a trans-\nmon qubit in a cavity resonator, performed atMC2 Chalmers. The data was compared\nto the expected behavior from the Jaynes-Cummings Hamiltonian and then the full\nHamiltonian for the transmon. The comparison enabled us to extract the parame-\nters of the transmon. The ratio of the Josephson energy and the charge energy was\ndetermined to be EJ=EC = 34:5644 § 0:9456 GHz, which is in the transmon regime.\nFurthermore, the coupling strength between the cavity resonator and the qubit was\ndetermined to be 2¯eV 0\nrms = 0:1301 § 0:00095 GHz, with a 68% con¯dence interval.
Three-dimensional(3D) transmon is a kind of superconducting qubit with long decoherence time, which has important applications in superconducting quantum computation, quantum optics, cavity quantum electrodynamics, et al. Rabi oscillation is a vital method to characterize the decoherence time of quantum system, and it is also a basic experiment to demonstrate the energy level evolution of quantum system. In order to test the Rabi oscillation of 3D transmon, strict timing control is necessary, and the process of testing and debugging is complicated. In this paper, 3D transmon samples are fabricated and their basic parameters EC = 348.74 MHz and EJ = 11.556 GHz are tested and characterized. The coupling coefficient g2/Δ between qubit and the 3D cavity is 43 MHz, which is located in the dispersive regime. The qubit’s first transition frequency f01 = 9.2709 GHz, and the second transition frequency f12 = 9.0100 GHz. The 3D resonator is fabricated by the material 6061T6 aluminum, the loaded quality factor is 4.8 × 105, and the bare frequency of the resonator is 8.108 GHz. Through comparison, it is found that the Rabi oscillation time obtained by the proposed method is shorter than by the Jaynes-Cummings method. The main reasons are as follows. First, the measurement of network analyzer is a continuous measurement, and the test signal always affects the decoherence process of 3D transmon. Second, the quantum bit is in the ground state after decoherence, and the ground state measured by the network analyzer accounts for a relatively high proportion, which causes the curve measured by the network analyzer to be one-sided attenuation oscillation. Third, the dispersive readout method is related to the quality factor of the superconducting cavity. The storage time of microwave photons in the superconducting cavity is longer than the decoherence time of 3D transmon, so the quantum information is partially decohered before leaving the superconducting cavity, which will shorten the Rabi oscillation time. An innovative Rabi oscillation test method based on network analyzer is presented. The test system based on this method is simple to build and can be used as a new way to quickly verify whether 3D transmon has quantum characteristics. This method can also be extended to other quantum systems for preliminarily verifying the time domain characteristics.
The topic of these lectures lies in the new and rapidly growing field of quantum computing,which explores connections between physics and computing in general. Quantum informa-tion processing is a cross-disciplinary field and is of great importance from both a funda-mental, as well as technological perspective [27]. From the fundamental perspective we havedeepened our understanding of the relationship between physics, information and computa-tion in general, and have also gained a deeper understanding of the fundamental aspects ofquantum theory - non-locality and entanglement in particular [31]. From the technologicalperspective we have manipulated larger and larger quantum systems and obtained power-ful practical applications in the domain of communication and cryptography such as theunconditionally secure quantum cryptography (key exchange) and quantum teleportation[7, 14, 5].Historically, the greater potential of the quantum computer was first realised by Feyn-man, who noted that quantum systems appear to be exponentially hard to simulate withclassical computers [15]. He speculated that, therefore, quantum computers could poten-tially be much more powerful than their classical counterparts. This intuition has beenproven to be correct for some tasks, such as factoring large numbers and searching unstruc-tured databases. Every computer is fundamentally a physical system, and any computationis just a physical process undergone by this system. Quantum physics is the most accurateway of describing physical systems and their behaviour in general. Encoding informationinto quantum systems and processing it according to the laws of quantum physics results innew features which do not exist in the classical computation.Large scale quantum computation is still hypothetical. However, Moore’s law
This paper presents an electromagnetic-to-Hamiltonian workflow for modeling a two-qubit coupled transmon superconducting device circuit. The device layout, comprising two coupled transmon qubits with individual readout resonators, is designed and parameterized in Qiskit Metal and analyzed using 3D eigenmode simulations in Ansys HFSS. Adaptive-pass refinement converges the eigenfrequencies and electromagnetic fields, yielding reliable modal data for quantization. Energy-participation ratio values from HFSS are processed through the pyEPR–Qiskit Metal flow to extract effective capacitances, anharmonicities, and qubit–resonator couplings. These parameters define a multimode Duffing–Jaynes–Cummings Hamiltonian that captures the transmon nonlinearities and their interactions with the resonator modes. Frequency-convergence checks and coupling diagnostics verify a consistent, physically accurate mapping from the layout geometry to the device circuit-level model. The Hamiltonian workflow offers a reproducible and scalable framework for modeling and analyzing superconducting transmon architectures in quantum chip design.
Cette thèse se concentre sur le traitement de l’information quantique à l’aide d’un dispositif supraconducteur, en particulier sur la réalisation de portes quantiques et d’algorithmes dans des systèmes quantiques ouverts. Un tel dispositif est construit par des qubits supraconducteurs de type transmon couplés à un résonateur supraconducteur. Pour la réalisation des portes quantiques et des algorithmes, une approche en une seule étape est utilisée. Nous proposons des schémas plus rapides et plus efficaces pour réaliser des portes de X-rotation et des portes d’enchevêtrement pour deux et trois qubits. Au cours de ces opérations, le nombre de photons du résonateur est annulé en raison du fort champ de micro-ondes ajouté. Elles ne nécessitent pas que le résonateur soit initialement préparé dans l’état de vide et les schémas est insensible à la désintégration du résonateur. En outre, la robustesse de ces opérations est démontrée en incluant l’effet de la décohérence des systèmes transmon et la désintégration du résonateur dans une équation maîtresse, ce qui permet d’obtenir une grande fidélité dans la simulation quantique. En outre, en utilisant les portes de X-rotation mises en oeuvre ainsi que les portes de phase, nous présentons une autre façon de mettre en oeuvre l’algorithme de Grover pour deux et trois qubits qui ne nécessite pas une série de portes simples. En outre, nous démontrons en simulant numériquement l’utilisation de la tomographie des processus quantiques pour caractériser pleinement la performance d’une porte d’enchevêtrement à un seul coup pour deux et trois qubits et nous obtenons des fidélités de processus supérieures à 93%. Ces portes sont utilisées pour créer des états intriqués de Bell et de Greenberger-Horne-Zeilinger (GHZ).
This thesis describes the investigation of superconducting multi-mode cavity architecture for superconducting transmon-based quantum computing. The dissertation highlights useful features of radio-frequency cavities used for quantum computing, with a brief discussion on the advantages of superconducting cavities. In the subsequent section, the concept of transmon is introduced and the mechanism of coupling with a cavity is analyzed. Once the foundations of the topic are laid down, the thesis focuses on optimizing a multi-mode superconducting rf cavity design originally developed for high-energy physics applications. Such section articulates in two main parts, the first part concerning the "bare" cavity remake via finite-elements eigenmode simulations using a computer-aided design software called CST Studio Suite®. In the second part, a transmon qubit is physically inserted into the modified cavity to assess the qubit-cavity coupling of the new design. In evaluating said coupling, two distinct analysis methods are used, namely the black-box quantization method and the energy participation ratio method, both implemented using Ansys® High-Frequency Electromagnetic-Field Simulator, or HFSS™. Results from the two evaluations, compared together, show that the optimized design meets the requisites to be used for quantum computing purposes.
Mesures quantiques utilisant une molécule artificielle supraconductrice en électrodynamiques quantique des circuits En circuit-QED, la technique la plus usuelle pour lire l'état d'un qubit est d'utiliser le couplage transverse entre le qubit et une cavité micro-onde dans la limite dispersive. Cependant, malgré d'importants progrès au cours de cette décennie, obtenir une lecture rapide, en un seul coup et hautement fidèle d'un qubit reste un défi majeur. En effet, la distinction de l'état d'un qubit est limitée par le compromis entre vitesse d'acquisition et précision. Cette limite a pour origine le couplage transverse qui impose deux importantes contraintes expérimentales : premièrement, augmenter les interactions pour lire plus rapidement restreint la durée de vie du qubit via l'effet Purcell. La seconde contrainte est sur la force du signal, qui est limitée pour éviter des transitions non voulues et induites par la mesure. Par conséquent, le défi expérimental à relever avec le couplage transverse est d'acquérir un signal faible en un temps court...Pour surmonter ces limitations, nous voulons changer de paradigme en introduisant un nouveau schéma de lecture qui se base sur un couplage cross-Kerr direct. Ce schéma est obtenu grâce à une molécule artificielle supraconductrice couplée à une cavité micro-onde 3D. La molécule est construite en couplant inductivement deux atomes transmons supraconducteurs. Elle manifeste alors deux modes propres : le mode symétrique qubit transmon et le mode antisymétrique ancilla. En insérant cette molécule dans la cavité de manière optimale, une hybridation transverse entre l'ancilla et la cavité conduit à deux résonateurs faiblement anharmoniques, appelés polaritons. Ces derniers possèdent un couplage cross-Kerr direct et large avec le qubit transmon. En mesurant le signal micro-onde transmis par un polariton, l'état du qubit peut être résolu.Théoriquement, dans ce nouveau paradigme, le qubit est immunisé contre les limitations du couplage transverse tel que l'effet Purcell. Cependant, pour les deux échantillons étudiés, un couplage transverse résiduel existe à cause d'imperfections expérimentales. Même faible, il limite pour l'instant la durée de vie du qubit et nos performances de lecture. Malgré cela, nous avons obtenu une lecture du qubit en un seul coup avec une fidélité allant jusqu'à 97.2 % en 500 ns par une mesure dite de verrouillage grâce à la non-linéarité du polariton. Dans une limite linéaire à faible nombre de photons, nous démontrons une fidélité atteignant 94.7 % en seulement 50 ns de lecture grâce à l'ajout d'un amplificateur paramétrique Josephson. Dans ce régime, les sauts quantiques sont résolus et le qubit est lu de manière non-destructive 99.2 % du temps.