Superconducting transmon qubits are a leading technology for quantum information processing, yet their reliable operation rests on meticulous calibration and characterization routines. These processes have been fine-tuned and are relatively well understood by the quantum computing community. Nevertheless, it is often challenging for newcomers to compile all the available information into a practical experimental flow. In this tutorial, we present a comprehensive walkthrough for the characterization and optimization of tunable transmon qubits, demonstrated on a commercial five-qubit processor. Moving beyond theoretical description, we detail in a straightforward manner the complete workflow, from cryogenic setup and wiring to parametric amplifier optimum operation, flux sweet-spot identification, pulse calibration, and readout optimization. We also demonstrate the characterization of qubit-qubit coupling, covering all steps before multiqubit operations. This guide serves as a reference for experimentalists seeking to efficiently bring up transmon-based quantum devices.
Superconducting transmon qubits are a leading technology for quantum information processing, yet their reliable operation rests on meticulous calibration and characterization routines. These processes have been fine-tuned and are relatively well understood by the quantum computing community. Nevertheless, it is often challenging for newcomers to compile all the available information into a practical experimental flow. In this tutorial, we present a comprehensive walkthrough for the characterization and optimization of tunable transmon qubits, demonstrated on a commercial five-qubit processor. Moving beyond theoretical description, we detail in a straightforward manner the complete workflow, from cryogenic setup and wiring to parametric amplifier optimum operation, flux sweet-spot identification, pulse calibration, and readout optimization. We also demonstrate the characterization of qubit-qubit coupling, covering all steps before multiqubit operations. This guide serves as a reference for experimentalists seeking to efficiently bring up transmon-based quantum devices.
Designing a qubit architecture is one of the most critical challenges in achieving scalable and fault-tolerant quantum computing as the performance of a quantum computer is heavily dependent on the coherence times, connectivity and low noise environments. Superconducting qubits have emerged as a frontrunner among many competing technologies, primarily because of their speed of operations, relatively well-developed and offer a promising path toward scalability. Here, we address the challenges of optimizing superconducting qubit hardware through the development of a comprehensive theoretical framework that spans the entire process - from design to the calibration of hardware through quantum gate execution. We develop this framework in four key steps: circuit design, electromagnetic analysis, spectral analysis, and pulse sequencing with calibration. We first refine the qubit's core components - such as capacitance, Josephson junctions, and resonators - to set the foundation for strong performance. The electromagnetic analysis, using the Lumped Oscillator model, allows us to map out the capacitance matrix, ensuring that we minimize spectral dispersion while maximizing coherence times. Following this, we conduct spectral analysis to fine-tune the qubit's frequency spectrum and coherence properties, ensuring that the qubit parameters are optimized. Finally, we focus on pulse sequencing, including pulse-width optimization, DRAG optimization, and randomized benchmarking, to achieve high gate fidelity. We applied this framework to both Transmon and Fluxonium qubits, obtaining results that closely match those found in experimental studies. This work provides a detailed and practical approach to the design, optimization, and calibration of superconducting qubits, contributing to the broader effort to develop scalable quantum computing technologies.
As superconducting circuits emerge as a leading platform for scalable quantum information processing, building comprehensive bridges from the foundational principles of macroscopic quantum phenomena to the architecture of modern quantum devices is increasingly essential for introducing new researchers to the field. This tutorial provides a self-contained, pedagogical introduction to superconducting quantum circuits at the undergraduate level. Beginning with an overview of superconductivity and the Josephson effect, the tutorial systematically develops the quantization of microwave circuits into the framework of circuit quantum electrodynamics (cQED). The transmon qubit is then introduced as a state-of-the-art application, with a detailed derivation of its Hamiltonian and its interaction with control and readout circuitry. The theoretical formalism is consolidated through a numerical simulation of vacuum Rabi oscillations in a driven transmon-resonator system, a canonical experiment that demonstrates the coherent energy exchange characteristic of the strong coupling regime. This work serves as a foundational guide and first point of contact, equipping students and researchers with the conceptual and mathematical tools necessary to understand and engineer superconducting quantum hardware.
Quantum information processing holds the promise of a paradigm shift in computational power for specific problem classes. While contemporary quantum processors operate in the Noisy Intermediate-Scale Quantum (NISQ) regime and remain highly susceptible to errors, ongoing experimental efforts on these near-term devices are crucial for advancing the underlying technology. Among the various hardware implementations, superconducting quantum circuits stand out as one of the most robust architectures for scalable quantum technologies. Nevertheless, the primary bottleneck in these systems is the fragility of quantum information: interactions with the environment inevitably perturb the quantum states, a phenomenon known as decoherence. This rapid loss of stored information imposes a fundamental limit on the time available to reliably execute computations on these devices. Within this context, this thesis focuses on the comprehensive experimental characterization of a planar chip featuring isolated, fixed-frequency superconducting transmon qubits. The measurements were conducted in a cryogenic environment, relying on a dilution refrigerator to maintain the device at millikelvin temperatures. To probe the quantum system under these conditions, custom measurement scripts were developed to operate state-of-the-art microwave control electronics (Keysight Quantum Control System), establishing full control over pulse generation, signal acquisition, and digital demodulation. The experimental workflow systematically mapped the physical properties of the device through a progressive series of characterization steps. Initial spectroscopic techniques probed the coupled resonator-qubit system, identifying its fundamental transition frequencies and relevant energy scales. Building upon these frequency-domain measurements, coherent control was achieved by calibrating resonant microwave pulses to drive single-qubit rotations, enabling the reliable preparation of the qubit in excited or coherent superposition states. Finally, specific time-domain protocols were implemented to evaluate the operational limits of the device. By executing standard pulse sequences, the characteristic decoherence metrics of the system, namely the longitudinal energy relaxation time (T1) and the inhomogeneous dephasing time (T2*), were successfully extracted, providing a quantitative assessment of the qubit's overall performance and establishing a baseline for future implementations of more advanced quantum control protocols.
This review aims to provide researchers, experimentalists, and quantum engineers with an updated and technically grounded perspective on the implementation of quantum gates in superconducting NISQ devices. The goal is to establish a comprehensive bridge between theoretical quantum circuit synthesis and its practical, experimental implementation, focusing on superconducting quantum technologies. We systematically examine the diverse landscape of superconducting qubits and processor architectures, ranging from conventional transmons to alternative and unconventional designs, evaluating their unique design trade-offs, connectivity constraints, device physics, and materials impact. Moving from theory to actual implementation, we detail how single- and two-qubit operations are synthesized via microwave-driven and flux-activated pulses. We here present our pulse engineering, wave shaping, calibration workflows, demonstrating how to bridge the gap between abstract gate models and real-world hardware limitations in the direction of a hardware-software co-design framework. To validate these operations, we choose benchmarking methodologies with the purpose to get the more efficient metric for the specific evaluation aspect, including truth tables and quantum process tomography. Therefore, we both discuss the theoretical concepts behind the gate synthesis and show experimental implementation of most fundamental gates by proposing a practical workflow.
This thesis mainly summarizes two experiments that relate to building a quantum computer out of superconducting transmon qubits. Transmon qubits have emerged as one of the foremost solid state qubits, realizing processors with more than ten qubits and demonstrating small scale quantum algorithms as well as quantum error correction schemes. Right now, there is a race between different academic and industry research groups to scale up transmon qubit processors. The first experiment was a demonstration of qubit control by selective broadcasting in order to reduce the scaling of expensive electronics with the number of qubits for individual single-qubit control. We demonstrated that we can bring two transmon qubits to the same frequency (combining fabrication accuracy and in-situ fine tuning) and use the same hardware to control both, routing the pulses with a nanosecond-timescale vector switch matrix. Despite the compromises required by this technique, we show a scalable path to single qubit control beyond the threshold required for quantum error correction. In benchmarking, we take into account gate leakage due to the fact that transmons are fundamentally multi-level systems. In the second experiment we establish entanglement between two transmon qubits on different chips. We use an entanglement by measurement scheme and demonstrate that we can overcome minor fabrication imperfections by shaping our measurement pulses. Ultimately, performance is mainly limited by photon loss between the chips and up to the amplification chain. This entanglement mediated by traveling photons could be used to make a distributed transmon processor where computations are spread across several chip modules. This modularity could enable connectivities that cannot be realized on chip and ease fabrication requirements, as modules could be individually fabricated and selected. Thus, both of these experiments fit into the larger effort to converge on the hardware, control equipment and architecture of a future large-scale transmon quantum computer. Other experiments I contributed to are summarized in the conclusion chapter to show the diverse physics that can be studied in cQED experiments.
Superconducting quantum processors comprising flux-tunable data and coupler qubits are a promising platform for quantum computation. However, magnetic flux crosstalk between the flux-control lines and the constituent qubits impedes precision control of qubit frequencies, presenting a challenge to scaling this platform. In order to implement high-fidelity digital and analog quantum operations, one must characterize the flux crosstalk and compensate for it. In this work, we introduce a learning-based calibration protocol and demonstrate its experimental performance by calibrating an array of 16 flux-tunable transmon qubits. To demonstrate the extensibility of our protocol, we simulate the crosstalk matrix learning procedure for larger arrays of transmon qubits. We observe an empirically linear scaling in calibration time with system size while maintaining a median qubit frequency error below 300 kHz.