In recent years, superconducting circuits have emerged as a promising platform for quantum computation and quantum simulation. One of the main driving forces behind this progress has been the ability to fabricate relatively low-disorder, low-loss circuits with a high-degree of control over many of the circuit parameters, both in fabrication and in-situ. This coupled with advances in cryogenics and microwave control electronics have significantly improved the rate of progress. The field, which is broadly called circuit quantum electrodynamics (cQED) has become one of the cleanest and most flexible platforms for studying strong interactions between light and matter. This thesis builds upon previous work on small-scale interacting cQED lattices and larger-scale, non-interacting superconducting circuit lattices to investigate nonequilibrium quantum simulation using large-scale, interacting cQED lattices. In the first experiment, construct a 72-site 1D chain of CPW cavities with each cavity coupled to a single transmon qubit. Each transmon imparts a strong nonlinearity on the photons in the cavity lattice. This, coupled with the drive and dissipation in the lattice gives rise to a novel dissipative phase transition, where the system exhibits bistability with time-scales many orders of magnitude slower than any intrinsic decay rates in the system. The next project in this thesis involves the study of non-Euclidean lattices which can be made from CPW lattices. This work relies on the fact that the frequency of the resonators in the lattice is dependent mostly on the total length of the cavities, not the length between the ends of the cavity. This means that we can form lattices from CPW cavities where the edge distance is not the same but they are the same frequency. The first result in this direction is the fabrication and measurement of a finite piece of a hyperbolic graph, formed from a ‘regular’ tiling of heptagons. This lattice had an effective curvature which is quite large and in principle exhibited a gapped flat band. Following up on the hyperbolic lattice work, the last result described in this thesis involves the study of exotic new lattices which have band structures that exhibit exotic features such as gapped flat bands and Dirac cones. This work involves looking at the spectra of graphs and their corresponding line-graphs, which are the graphs which are pertinent to the tight-binding Hamiltonian in CPW lattice devices. Here, we derive the mathematical relationship between the spectrum of a graph and its line graph as well as what is known as the split, or subdivision, graph. These operations allow us to exactly maximize the gap between the flat band and the rest of the spectrum for certain line graph lattices.

The advent of superconducting quantum circuits as a robust scientific platform and contender for quantum computing applications is the result of decades of research in light-matter interaction, low-temperature physics, and microwave engineering. There is growing interest to use this advancing technology to study domains of light-matter interaction that were previously thought to be beyond experimental reach. Our work is part of an initiative to explore non-equilibrium condensed matter physics using photons instead of atoms. Open questions in this area currently pose significant challenges theoretically due to analytical complexity and system sizes which prohibit complete numerical simulations, thus experiment-based research has the potential to lead to significant advancements in this field. Here we examine phenomena that arise when moving beyond standard single-mode strong coupling towards the realm of many-body physics with light in two distinct directions. First we study multimode strong coupling, where a single artificial atom or qubit is simultaneously strongly coupled to a large, but discrete number of non-degenerate photonic modes of a cavity with coupling strengths comparable to the free spectral range. This domain, which falls in between small, discrete and continuum Hilbert spaces, is experimentally realized by coupling a qubit to a low fundamental frequency coplanar waveguide cavity. In this system we report on resonance fluorescence and narrow linewidth emission directly resulting from complex qubit mediated mode-mode interactions. In the second part we explore qubits strongly coupled to photonic crystals, which give rise to exotic physical scenarios, beginning with single and multi-excitation qubit-photon dressed bound states comprising induced, spatially localized photonic modes, centered around the qubits, and the qubits themselves. The localization of these states changes with qubit detuning from the band-edge, offering an avenue of in situ control of bound state interaction. Due to their localization-dependent interaction, these states offer the ability to create one-dimensional chains of bound states with tunable interactions that preserve the qubits' spatial organization, a key criterion for realization of certain quantum many-body models. The unique domains of light-matter interaction discussed here are a subset of exciting research initiatives growing our general understanding of complex, strongly coupled quantum systems.

Circuit quantum electrodynamics (cQED) uses superconducting circuit elements as its building blocks for controllable quantum systems and has become a promising experimental platform for quantum computation and quantum simulation. The ability to tune the coupling rate between circuit elements extends the controllability and flexibility of cQED devices and can be utilized to improve device performance. This thesis presents the study, implementation and application of tunable coupling devices in cQED. The tunability originates from the basic principles of quantum superposition and interference, and unwanted interactions can be suppressed by destructive interference. Following this principle, we design and conduct two experiments that demonstrate the utility of tunable coupling for better device performances in quantum information processing. The first experiment aims to improve the coherence of qubits against noise. We implement a qubit whose frequency and dispersive coupling to a readout resonator can be tuned independently. When the coupling rate is tuned to near zero, the qubit becomes immune to photon number fluctuations in the resonator and exhibits robust coherence time in the presence of noise. The second experiment extends to a multi-qubit system where crosstalk between qubits causes error in quantum gates. We develop a two-qubit device and suppress crosstalk by tuning the ZZ coupling rate between the qubits. The tunable dispersive coupling can also be parametrically modulated to implement a two-qubit entangling gate in the low crosstalk regime. Those devices provide flexible and promising building blocks for cQED systems.

Superconducting circuits have become an ideal platform to implement prototypi- cal quantum computing ideas and to study nonequilibrium quantum dynamics. This thesis covers research topics conducted in both subfields. Fast and reliable readout of volatile quantum states is one of the key requirements to build a universal quantum computer. In the first part, we utilize a number of techniques, ranging from a low noise amplifier to an on-chip stepped-impedance Purcell filter, to improve superconducting qubits readout fidelity. Interestingly, full quantum theory of SIPF requires the understanding of strong coupling quantum electrodynamics near a photonic band-gap. This problem, intimately tied to quantum impurity problems in condensed matter physics, has never been studied experimentally prior to the development of superconducting circuits. This realization then leads to the second part, the study of atom-light interaction in structured vacuum. The word ‘structured’ means the spectral function of the vacuum is drastically different from that of free space. We directly couple a transmon qubit to a microwave photonic crystal and discuss the concepts of photon bound states and quantum dissipative engineering in such a system. Following this research direction, quantum electrodynamics in a driven multimode cavity, another form of structured vacuum, is also investigated both experimentally and theoretically. The most intriguing phenomenon is the multimode ultranarrow resonance fluorescence, attributed to correlated light emission.

Historically our understanding of the microscopic world has been impeded by limitations in systems that behave classically. Even today, understanding simple problems in quantum mechanics remains a dicult task both computationally and experimentally. As a means of overcoming these classical limitations, the idea of using a controllable quantum system to simulate a less controllable quantum system has been proposed. This concept is known as quantum simulation and is the origin of the ideas behind quantum computing. In this thesis, experiments have been conducted that address the feasibility of using devices with a circuit quantum electrodynamics (cQED) architecture as a quantum simulator. In a cQED device, a superconducting qubit is capacitively coupled to a superconducting resonator resulting in coherent quantum behavior of the qubit when it interacts with photons inside the resonator. It has been shown theoretically that by forming a lattice of cQED elements, dierent quantum phases of photons will exist for dierent system parameters. In order to realize such a quantum simulator, the necessary experimental foundation must rst be developed. Here experimental eorts were focused on addressing two primary issues: 1) designing and fabricating low disorder lattices that are readily available to incorporate superconducting qubits, and 2) developing new measurement tools and techniques that can be used to characterize large lattices, and probe the predicted quantum phases within the lattice. Three experiments addressing these issues were performed. In the rst experiment a Kagome lattice of transmission line resonators was designed and fabricated, and a comprehensive study on the eects of random disorder in the lattice demonstrated that disorder was dependent on the resonator geometry. Subsequently a cryogenic 3-axis scanning stage was developed and the operation of the scanning stage was demonstrated in the nal two experiments. The rst scanning experiment was conducted on a 49 site Kagome lattice, where a sapphire defect was used to locally perturb each lattice site. This perturbative scanning probe microscopy provided a means to measure the distribution of photon modes throughout the entire lattice. The second scanning experiment was performed on a single transmission line resonator where a transmon qubit was fabricated on a separate substrate, mounted to the tip of the scanning stage and coupled to the resonator. Here the coupling strength of the qubit to the resonator was mapped out demonstrating strong coupling over a wide scanning range, thus indicating the potential for a scanning qubit to be used as a local quantum probe.

Superconducting circuits have shown promise for exploring quantum optics and computing. This thesis presents an additional element, the tunable coupling qubit (TCQ), to the toolbox available for exploring such physics. The TCQ is shown to have independently tunable qubit energy and dipole coupling strength. High frequency flux control lines allow the varying of the TCQ's properties on very fast time scales. This enables qubit coherence measurements and the calculation of a lower bound on the maximum range of coupling strength tunability. Finally, an experiment demonstrating the TCQ's applicability in quantum state transfer is discussed.