Superconducting qubits are one of the most promising platforms for realizing the quantum circuit model of computation in a physical machine. Indeed, over the last 30 years rapid progress has been made in the design, fabrication, and control of superconducting qubit systems, culminating in a number of recent demonstrations of quantum error correction. However, much yet remains to be done if superconducting qubits are to eventually be used to perform useful tasks, and in this thesis we report on some progress in characterizing and mitigating sources of energy relaxation in superconducting qubits, which is one of the most critical sources of error in current hardware.

In recent years, superconducting quantum computing has been established as a potential candidate for building a scalable quantum computer. This is exemplified by recent claims of quantum supremacy and by significant improvements in qubit coherence times in the past several years. Superconducting quantum computing is understood through the field of circuit quantum electrodynamics (cQED). Improving understanding of the field’s fundamentals is critical to push further into the future of superconducting quantum computing. Given the rich energy level structure of the fluxonium qubit, it can probe various properties of cQED devices and thus enhance our understanding of the basics of cQED. In this thesis, we explore two such examples. It was long believed in cQED that the allocation of external flux to different circuit elements was equivalent until theory work in 2019 suggested that under the influence of time-dependent flux, the choice affects the resulting Hamiltonian. Performing a fast flux ramping experiment, we verify the theory for properly handling time-dependent flux in cQED. Additionally, there is an open question in the field as to why superconducting qubits exhibit anomalously high excited state populations when in thermal equilibrium. We explore the relationship between effective qubit temperature and qubit frequency using fluxonium’s tunable energy level structure. Our initial results suggest that the effective qubit temperature depends on the transition frequency, with higher frequencies exhibiting higher effective temperatures than lower frequencies.

Since their advent more than two decades ago, superconducting quantum devices have been a leading platform for quantum computation. Year by year, coherence times increase, gate errors decrease, and new records are set for the number of qubits in a system. As the challenges of scaling continue to accumulate, there is more room than ever for innovation at all levels of the quantum computing stack. This thesis explores the concept of heterogeneity in superconducting quantum computer design at two different levels. At the level of the two-qubit entangling gate, this thesis investigates two novel tunable coupler architectures for parametric gates. Devices are designed to optimize the trade-off between gate speed and fidelity while providing a platform to study leakage outside the computational subspace. At the quantum computer architecture level, we design and simulate a heterogeneous architecture for lattice surgery of surface codes based on ideas from quantum networking. A co-design approach leads to a hardware-aware error-correcting architecture that aims to improve the efficiency of Pauli-based computation.

Circuit quantum electrodynamics (cQED) serves as a promising platform for scalable quantum computation, where precise microwave control of qubits lays the foundation for achieving high-fidelity quantum gates. Despite recent progress in developing various quantum gates, controlling artificial qubits remains a considerable challenge due to intricate Hamiltonian systems and the fragile nature of quantum states. Therefore, further research is needed to improve qubit gates and protect quantum states from qubit decoherence. This thesis presents two studies: 1) controlling cQED systems through black-box optimization to achieve state-of-the-art gate fidelity, 2) stabilizing an entangled two-qubit state indefinitely via engineering dissipation channels. The first study establishes the feasibility of direct black-box optimization as a method to discover novel qubit gates from simple initial conditions. We develop robust quantum optimization algorithms to efficiently learn novel qubit gates and evaluate these algorithms through simulations and experiments. Our findings show the potential to learn high-fidelity qubit gates without depending on the specifics of the system Hamiltonian. In the second study, our objective is to realize entanglement stabilization through quantum reservoir engineering. By coupling two qubits near resonance with a leaky resonator acting as a reservoir, we induce a strong correlated decay of the qubits. We experimentally demonstrate the subradiant effect of an entangled Bell state and, through simulation, reveal the robustness of this system in stabilizing a high-fidelity Bell state.

The potential for quantum computing to expand the number of solvable problems has driven researchers across academia and industry, in multiple disciplines, to develop a variety of different qubit platforms, algorithms, and scaling strategies. At its core, quantum computation relies on the robustness, or coherence, of its building blocks (qubits"). In current small-scale superconducting qubit processors, the fidelity of operations is often limited by qubit coherence. The coherence time of a single qubit depends on its lifetime $T_1$ and pure dephasing time $T_{\phi}$. In this thesis, we focus on the problem of improving $T_1$. Strategies for improving lifetimes are informed by models for relaxation - specifically Fermi's Golden Rule. Relaxation rates depend on noise properties of the environment and on properties of the qubit states. This dependence suggests two strategies for engineering longer lifetimes: environment engineering involves mitigating or filtering the noise that the qubit sees, and Hamiltonian engineering refers to optimizing the qubit circuit and its resulting eigenstates to optimize $T_1$. Significant enhancements of qubit lifetimes will require paradigm shifts in our approaches to both environment and Hamiltonian engineering. First, I present a side-by-side study of transmon coherence and materials measurements of the constituent Nb films, including synchrotron x-ray spectroscopy and electron microscopy. We found correlations between qubit lifetimes and materials properties such as grain size, grain boundary quality, and surface suboxides. This study expands the scope of superconducting qubit research by presenting a broad set of materials analyses alongside device measurements. Second, I will give an overview of Hamiltonian engineering, including the concepts behind intrinsic protection against relaxation and dephasing processes. I'll describe the soft $\mathrm{0-\pi}$ qubit, which is the first experimentally realized superconducting qubit to show signatures of simultaneous $T_1$ and $T_2$ protection. We improved coherence in the soft $\mathrm{0-\pi}$ through optimized fabrication processes. We have also characterized the effects of non-computational levels on gate fidelity, specifically AC Stark shifts and leakage. From the results in this thesis, we have gained a deeper understanding of what limits qubit coherence, informing future directions on both the materials and Hamiltonian engineering fronts.

A useful quantum computer requires a full stack of components, where each layer in the stack can actually scale. In this thesis we go through each layer of the quantum computing stack, from the bottom to the top. First, we discuss planar tantalum transmon qubit fabrication. We iterate on the design and fabrication of an entangling gate module with two fixed-frequency transmon qubits and a tunable coupler. We share our perspective on making a robust parametric entangling gate architecture for planar superconducting qubits. Next, we introduce the QICK (Quantum Instrumentation Control Kit), which is a standalone open source controller for both superconducting and atomic qubits as well as various detectors. Highly integrated open source firmware and software has been designed to allow the QICK to scale to hundreds of qubits. We develop the QICK for the superconducting qubit platform and use it to conduct the first single and multi-qubit experiments. Finally, we develop two modular simulation frameworks---one for a multinode quantum computer, and one for heterogeneous qubit architectures.

Superconducting quantum circuits are a promising platform for quantum computation. The building block for most quantum processors is a qubit (quantum bit) which can store information in a superposition of two states. Superconducting qubits are lithographically defined from metals, often niobium or aluminum. However, these devices have limited use because the information they store decays before most useful computations can take place. In this thesis we explore the cause of these losses. Specifically, we employ tantalum as the capacitor pad of a two-dimensional transmon qubit and find lifetimes and coherence times with dynamical decoupling over 300 us. We then switch to a resonator geometry to probe tantalum materials properties. We develop a power and temperature dependent measurement to quantify sources of decay. We find our resonators are primarily limited by two-level system loss at materials interfaces. Finally we employ this resonator characterization method to determine the effects of processing treatments and new packages onresonator decay, showing a buffered-oxide etch before measurement reduces two-level system loss.

Over the past decade, quantum circuits have been transitioning from being useful solely in fundamental physics research to having applications in a wide variety of fields. This has been made possible by the advancements in the coherence, coupling and optimal control of various elements of these quantum circuits. The experiments presented in this thesis solve critical challenges for the above mentioned areas. We provide the first experimental realization of a protected qubit having simultaneous robustness to relaxation and dephasing processes. We show a 40-fold improvement in the coherence time in fluxonium qubit by harnessing insights from Floquet engineering. Furthermore, we also demonstrate a coupling architecture for suppressing qubit-qubit crosstalk. The above works unlock new directions for improving the state of quantum systems

In recent years, superconducting circuits have become a promising architecture for quantum computing and quantum simulation. This advancing technology offers excellent scalability, long coherence times, and large photon nonlinearities, making it a versatile platform for studying non-equilibrium condensed matter physics with light. This thesis covers a series of experiments and theoretical developments aimed at probing strongly correlated states of interacting photons. Building upon previous efforts on nonlinear superconducting lattices, this work focuses on establishing new platforms for generating interactions between microwave photons in multi-mode circuits. The first experiment presents a new paradigm in exploiting the nonlinearity of a Josephson junction to tailor the Hilbert space of harmonic oscillators using a dynamical three-wave mixing process. This allows a single microwave resonator to be addressed as a two-level system, offering a promising pathway to long-lived qubits. A theoretical proposal is outlined for building a field-programmable quantum simulator, harnessing this dynamical nonlinearity for stimulating strong photon-photon interactions. The system consists of a lattice of harmonic modes in synthetic dimensions, where particle hopping and on-site interactions can be independently controlled via frequency-selective flux modulation. Numerical studies show that for strong interactions the driven-dissipative steady-state develops a crystalline phase for photons. The second experiment explores the physics of quantum impurities, where a single well-controlled qubit is coupled to the many modes of a photonic crystal waveguide. The light-matter coupling strength is pushed into the ultrastrong coupling regime, where the qubit is simultaneously hybridized with many modes and the total number of excitations is not conserved. Probing transport through the waveguide reveals that the propagation of a single photon becomes a many-body problem as multi-photon bound states participate in the scattering dynamics. Furthermore, the effective photon interactions induced by just this single impurity leads to interesting inelastic emission of photons. Probing correlations in the field emission reveals signatures of multi-mode entanglement. This work presents opportunities for exploring large-scale lattices with strongly interacting photons. These platforms are compatible with well-established techniques for generating artificial magnetic fields and stabilizing many-body states through reservoir engineering, complementing growing efforts in the quest for building synthetic quantum materials with light.

Over the past 10 years, improvements to the fundamental components in supercon- ducting qubits and the realization of novel circuit topologies have increased the life- times of qubits and catapulted this architecture to become one of the leading hardware platforms for universal quantum computation. Despite the progress that has been made in increasing the lifetime of the charge qubit by almost six orders of magnitude, further improvements must be made to climb over the threshold for fault tolerant quantum computation. Two complimentary approaches towards achieving this goal are investigating and improving upon existing qubit designs, and looking for new types of superconducting qubits which would offer some intrinsic improvements over existing designs. This thesis will explore both of these directions through a detailed study of new materials, circuit designs, and coupling schemes for superconducting qubits. In the first experiment, we explore the use of disordered superconducting films, specifically Niobium Titanium Nitride, as the inductive element in a fluxonium qubit and measure the loss mechanisms limiting the qubit lifetime. In the second experiment, we work towards the experimental realization of the 0 − π qubit archi- tecture, which offers the promise of intrinsic protection in lifetime and decoherence compared to existing superconducting qubits. In the final experiment, we design and measure a two qubit device where the static σz ⊗ σz crosstalk between the two qubits is eliminated via destructive interference. The use of multiple coupling elements re- moves the σz ⊗ σz crosstalk while maintaining the large σz ⊗ σx interaction needed to perform two qubit gates.