A computação quântica adiabática tem sua pedra angular no teorema adiabático, cuja eficiência está relacionada tradicionalmente à proporção da variação temporal do Hamiltoniano que descreve o sistema e o gap mínimo entre o estado fundamental e o primeiro excitado. Normalmente, esse gap tende a diminuir quando aumenta o número de recursos (bit quântico: qubit) de um processador quântico, exigindo dessa maneira variações lentas do Hamiltoniano para assim garantir uma dinâmica adiabática. Entre os candidatos para a sua implementação física, estão os qubits baseados em circuitos supercondutores os quais têm um grande potencial, por causa de seu alto controle e escalabilidade promissora. No entanto, quando esses qubits são implementados, eles têm uma fonte intrínseca de ruído devido a erros de fabricação, que não podem ser desprezados. Por isso, nesta tese nós estudamos como os efeitos causados pelas flutuações dos parâmetros físicos do qubit afetam o comportamento da fidelidade da computação, realizando com esse propósito a simulação da dinâmica de cadeias de spin pequenas desordenadas. A partir do análise exaustivo desse estúdio foi possível propor uma estratégia que permite aumentar a fidelidade considerando um sistema ruidoso. Por outro lado, motivados pelo interesse de obter critérios suficientes e necessários para satisfazer uma computação quântica adiabática e pelo fato que ainda não existe uma condição de adiabaticidade geral apesar de existir inúmeras propostas, nós apresentamos um novo critério que manifesta suficiência para sistemas mais gerais e finalmente apresentamos evidências de que tal condição seria um quantificador consistente. / Adiabatic quantum computation has its cornerstone in the adiabatic theorem, whose efficiency is traditionally related to the ratio of the Hamiltonian temporal variation that describes the system and the minimum gap between the ground state and the first excited state. Usually, this gap tends to decrease when the number of quantum resources (quantum bit: qubit) of a quantum processor increases, thus it requires slow variations of the Hamiltonian to ensure an adiabatic dynamic. Among the candidates for its physical implementation are the qubits superconducting circuit-based which have great potential because of their high control and promising scalability. However, when these qubits are implemented, they have an intrinsic source of noise due to manufacturing errors that can not be despised. Therefore, in this thesis we study how the effects caused by the fluctuations of the physical parameters of the qubit affect the behavior of the fidelity of the computation, accomplishing with this purpose the simulation of the dynamics of small disordered spin chains. From the exhaustive analysis of this studio, it was possible to propose a strategy that allows to increase the fidelity considering a noisy system. On the other hand, motivated by the interest of obtaining sufficient and necessary criteria to satisfy an adiabatic quantum computation and the fact that there is still no general adiabaticity condition despite there being numerous proposals, we present a new criterion that manifests sufficiency for more general systems and we finally presented evidence that such a condition would be a consistent quantifier.

Abstract Elementary experiments of atomic physics and quantum optics can be reproduced on a circuit board using elements built of superconducting materials. Such systems can show discrete energy levels similar to those of atoms. With respect to their natural cousins, the enhanced controllability of these ‘artificial atoms’ allows the testing of the laws of physics in a novel range of parameters. Also, the study of such systems is important for their proposed use as the quantum bits (qubits) of the foreseen quantum computer. In this thesis, we have studied an artificial atom coupled with a harmonic oscillator formed by an LC-resonator. At the quantum limit, the interaction between the two can be shown to mimic that of ordinary matter and light. The properties of the system were studied by measuring the reflected signal in a capacitively coupled transmission line. In atomic physics, this has an analogy with the absorption spectrum of electromagnetic radiation. To simulate such measurements, we have derived the corresponding equations of motion using the quantum network theory and the semi-classical approximation. The calculated absorption spectrum shows a good agreement with the experimental data. By extracting the power consumption in different parts of the circuit, we have calculated the energy flow between the atom and the oscillator. It shows that, in a certain parameter range, the absorption spectrum obeys the Franck-Condon principle, and can be interpreted in terms of vibronic transitions of a diatomic molecule. A coupling with a radiation field shifts the spectral lines of an atom. In our system, the interaction between the atom and the field is nonlinear, and we have shown that a strong monochromatic driving results in energy shifts unforeseen in natural or, even, other artificial atoms. We have used the Floquet method to calculate the quasienergies of the coupled system of atom and field. The oscillator was treated as a small perturbation probing the quasienergies, and the resulting absorption spectrum agrees with the reflection measurement.

Abstract In this thesis we study the interaction between radiation and matter using superconducting circuits that behave analogously with the conventional photon-atom interaction in quantum optics. The research is done with a system consisting of a waveguide resonator (radiation) strongly coupled to a transmon device (matter). We focus on the phenomena caused by strong coupling between the radiation and matter, and by driving the resonator to higher excited states with a strong monochromatic radiation. These have been studied little in the traditional radiation-matter systems. Increasing the strength of the monochromatic radiation drive, the dynamics of the system experiences a transition from the quantum to the classical regime. Also, the free-particle states of the transmon start being populated. In the weak driving limit, the transmon can be regarded as a two-state system. As a consequence, the resonator-transmon system is conventionally discussed in terms of the linear Jaynes–Cummings model. However, for strong coupling the Bloch–Siegert shift, caused by the terms neglected in the Jaynes–Cummings model, is strong and the Jaynes–Cummings model is insufficient for describing the dynamics of the system. We study the effects caused by strong coupling and the excitation of the higher transmon states instigated by the driving of the resonator. With reflection spectroscopy, we measure the absorption spectrum of the system and compare this with the spectrum calculated numerically using the Floquet–Born–Markov approach. We find that, in the region of the quantum-to-classical transition, the two-state approximation for the transmon is insufficient and the higher transmon states are necessary for accurate simulations. By calculating the average resonator occupation, we compare different numerical models: the Lindblad master equation, the Floquet–Born–Markov, and the semiclassical model. Coupling a transmon to a resonator shifts the energy levels of the resonator. This shift in the energy levels prevents the higher resonator states from being populated if the system is weakly driven with a frequency that is near the resonance frequency of the resonator. We simulate this photon blockade numerically and show that the blockade is substantially different for the two-state and multistate transmon approximations. / Original papers Original papers are not included in the electronic version of the dissertation. Pietikäinen, I., Danilin, S., Kumar, K. S., Vepsäläinen, A., Golubev, D. S., Tuorila, J., & Paraoanu, G. S. (2017). Observation of the Bloch-Siegert shift in a driven quantum-to-classical transition. Physical Review B, 96(2). https://doi.org/10.1103/PhysRevB.96.020501 http://jultika.oulu.fi/Record/nbnfi-fe201803073899 Pietikäinen, I., Danilin, S., Kumar, K. S., Tuorila, J., & Paraoanu, G. S. (2018). Multilevel Effects in a Driven Generalized Rabi Model. Journal of Low Temperature Physics, 191(5–6), 354–364. https://doi.org/10.1007/s10909-018-1857-8 http://jultika.oulu.fi/Record/nbnfi-fe2018061325770 Pietikäinen, I., Tuorila, J., Golubev, D. S., & Paraoanu, G. S. (2019) Quantum-to-classical transition in the driven-dissipative Josephson pendulum coupled to a resonator, Manuscript. https://arxiv.org/abs/1901.05655

Superconducting qubits are a promising technology for building a scalable quantum computer. An important architecture employed in the field is called Circuit Quantum Electrodynamics (circuit QED), where such qubits are combined with high quality microwave cavities to study the interaction between artificial atoms and single microwave photons. The ultra-strong coupling achieved in these systems allows for control and readout of the quantum state of qubits to perform quantum information processing. The work on circuit QED performed in this thesis consisted of realizing an experimental setup for qubit experiments in a new laboratory, investigating the coherence and decay of higher energy levels of superconducting transmon qubits and finally demonstrating a novel coaxial form of circuit QED. Designing and building a 3D circuit QED setup involved the following main accomplishments: producing high quality 3D cavities; designing and installing the cryogenic microwave setup as well as the room temperature amplification and data acquisition circuitry; successfully developing a recipe for the fabrication of Josephson junctions; controlling and measuring superconducting 3D transmon qubits at 10mK. Several qubits were fully characterised and have shown coherence times of several microseconds and relaxation times up to 25μs. Superconducting qubits in fact possess higher energy levels that can provide significant computational advantages in quantum information applications. In experiments performed at MIT, preparation and control of the five lowest states of a transmon qubit was demonstrated, followed by an investigation of the phase coherence and decay dynamics of these higher energy levels. The decay was found to proceed mainly sequentially with relaxation times in excess of 20μs for all transitions. A direct measurement of the charge dispersion of these levels was performed to explore their characteristics of dephasing. This experiment was also reproduced on a 3D transmon fabricated and measured in Oxford, where due to a higher effective qubit temperature a multi-level decay model including thermal excitations was developed to explain the observed relaxation dynamics. Finally, a coaxial transmon, which we name the coaxmon, is presented and measured with a coaxial LC readout resonator and input/output coupling ports placed inline along the third dimension. This novel coaxial circuit QED architecture holds great promise for developing a scalable planar grid of qubits to build a quantum computer.

The work presented in this thesis investigates transitions between quantum states in superconducting double dots (SDDs), a nanoscale device consisting of two aluminium superconducting islands coupled together by a Josephson junction, with each dot connected to a normal state lead. The energy landscape consists of a two level manifold of even charge parity Cooper pair states, and continuous bands corresponding to charge states with single quasiparticles in one or both islands. These devices are fabricated using shadow mask evaporation, and are measured at sub Kelvin temperatures using a dilution refrigerator. We use radio frequency reflectometry to measure quantum capacitance, which is dependent on the quantum state of the device. We measure the quantum capacitance as a function of gate voltage, and observe capacitance maxima corresponding to the Josephson coupling between even parity states. We also perform charge sensing and detect odd parity states. These measurements support the theoretical model of the energy landscape of the SDD. By measuring the quantum capacitance in the time domain, we observe random switching of capacitance between two levels. We determine this to be the stochastic breaking and recombination of single Cooper pairs. By carrying out spectroscopy of the bath responsible for the pair breaking we attribute it to black-body radiation in the cryogenic environment. We also drive the breaking process with a continuous microwave signal, and find that the rate is linearly proportional to incident power. This suggests that a single photon process is responsible, and demonstrates the potential of the SDD as a single photon microwave detector. We investigate this mechanism further, and design an experiment in which the breaking rate is enhanced when the SDD is in the antisymmetric state rather than the symmetric state. We also measure the quantum capacitance of a charge isolated double dot. We observe 2e periodicity, indicating the tunnelling of Cooper pairs and the lack of occupation of quasiparticle states. This work is relevant to the range of experiments investigating the effect of non-equilibrium quasiparticles on the operation of superconducting qubits and other superconducting devices.