The field of quantum computing is growing at a rapid rate with the promise of dramatic improvements in the ability to solve critical computational problems. A leading approach for implementing fault-tolerant quantum computers is based on superconducting circuits containing Josephson junctions to form qubits. These qubits have many attractive qualities, but predicting the device performance requires detailed knowledge of the junction properties. Thus, precise characterization is crucial for realizing different qubit designs. The coherence of superconducting qubits is limited by several sources in the circuit en- vironment. Building a quantum computer requires effort to reduce gate errors caused by decoherence. This is typically achieved with quantum error correction. An alternative ap- proach involves designing qubits that are intrinsically protected from noise sources. One such design is the charge-parity qubit, which combines Josephson junctions in a novel regime. The capacitance of the junctions is a critical parameter for this qubit design that directly affects the engineered protection against decoherence. Beyond the conventional geometric capaci- tance, there is an excess contribution from virtual quasiparticle tunneling; we refer to this component as the electronic capacitance. This thesis focuses on the characterization of the capacitance of Josephson junctions, with the goal of isolating and measuring the electronic capacitance contribution, particularly for use in the charge-parity qubit. The thesis first reviews the initial implementation of the charge-parity qubit and the challenges that were encountered. Next, the theoretical origin is described and a framework for measuring the junction capacitance using superconducting resonant circuits is described. This technique is then applied to arrays of junctions fabricated with different parameters and the scaling of the electronic capacitance is presented. Finally, based on this knowledge of the junction capacitance, second-generation charge-parity qubits are implemented and the experimental results are presented.
The field of quantum computing is growing at a rapid rate with the promise of dramatic improvements in the ability to solve critical computational problems. A leading approach for implementing fault-tolerant quantum computers is based on superconducting circuits containing Josephson junctions to form qubits. These qubits have many attractive qualities, but predicting the device performance requires detailed knowledge of the junction properties. Thus, precise characterization is crucial for realizing different qubit designs. The coherence of superconducting qubits is limited by several sources in the circuit en- vironment. Building a quantum computer requires effort to reduce gate errors caused by decoherence. This is typically achieved with quantum error correction. An alternative ap- proach involves designing qubits that are intrinsically protected from noise sources. One such design is the charge-parity qubit, which combines Josephson junctions in a novel regime. The capacitance of the junctions is a critical parameter for this qubit design that directly affects the engineered protection against decoherence. Beyond the conventional geometric capaci- tance, there is an excess contribution from virtual quasiparticle tunneling; we refer to this component as the electronic capacitance. This thesis focuses on the characterization of the capacitance of Josephson junctions, with the goal of isolating and measuring the electronic capacitance contribution, particularly for use in the charge-parity qubit. The thesis first reviews the initial implementation of the charge-parity qubit and the challenges that were encountered. Next, the theoretical origin is described and a framework for measuring the junction capacitance using superconducting resonant circuits is described. This technique is then applied to arrays of junctions fabricated with different parameters and the scaling of the electronic capacitance is presented. Finally, based on this knowledge of the junction capacitance, second-generation charge-parity qubits are implemented and the experimental results are presented.
While quantum computation has the potential to revolutionize the scientific community, to date no architecture has been developed which offers the necessary combination of high coherence times and massive scalability. Superconducting flux qubits satisfy the second requirement well but to date useful devices are limited to coherence times of typically only a few &mus. In this dissertation we examine the possibilities of improving the coherence performance of the flux qubit to the levels required for fault-tolerant quantum computation. We find that coherence times for many devices are limited by photon-induced quasiparticles and mitigation of these quasiparticles increases coherence times by more than a factor of two. Beyond this, however, we find little improvement in flux qubit performance compared to prior results. Despite improved fabrication techniques and varied device designs we find flux qubit coherence times are still typically below 5 &mus. Furthermore, wide device-to-device variations are observed which prevent effective scaling of the flux qubit to quantum information circuits.Based on the proposal by You, et al. we develop of a capacitively-shunted version of the flux qubit called the C-shunt flux qubit. With the addition of a capacitive shunt across the small junction of the flux qubit we are able to reduce the amplitude sensitivity to both charge and flux noise by more than a factor of three. The result is a predicted ten-fold enhancement in the coherence times compared to the unshunted flux qubit. At the same time we preserve much of the anharmonicity of the flux qubit resulting in a device with coherence times comparable to modern transmons but with a factor of four better anharmonicity and more flexible coupling configurations.By using a high-quality MBE aluminum shunt process on an annealed sapphire substrate coupled with a more conventional electron-beam-evaporated aluminum Josephson junction process we fabricate hybrid C-shunt flux qubits. We also incorporate a new bridgeless junction technique which offers more robust and repeatable fabrication processing. This technique enables improved accuracy of the junction sizing, a trait which will become essential as we move to multi-qubit experiments. T1 and T2 times for these C-shunt devices reach in excess of 40 &mus at degeneracy, achieving the predicted ten-fold improvement based on the reduced noise sensitivity. At the same time we see decreased device-to-device variation with typical T1 times exceeding 20&ndash25 &mus at all bias points. Combined with the high anharmonicity and standard planar fabrication techniques these coherence times make the C-shunt flux qubit a competitive candidate for fault-tolerant quantum computation.
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.
Superconducting qubits have in recent years become a promising candidate for the implementation of a quantum computer due to their design flexibility, good protection from decohering elementary excitations, and availability of well developed fabrication and measurement techniques. Superconducting flux qubits, for which the effect of offset charge noise is reduced due to the fact that the Josephson energy dominates over the charging energy, correspond to one of the proposed means of designing a superconducting qubit. A nonlinear dispersive readout scheme of flux qubits involving a DC SQUID magnetometer that avoids the effects of on-chip dissipation can be readily implemented, yielding high contrast output for single qubit readout. Coupling schemes via nonlinear Josephson elements have also been realized. On the other hand, while the means of isolating superconducting qubits from external noise sources has been found, the mechanisms by which they undergo relaxation and decoherence due to intrinsic noise sources in the junctions themselves are not very well understood, and the question of how to deal with these noise sources remains unanswered in the general case. Other questions deal with the problem of experimentally observing entanglement in an array of coupled superconducting qubits, and finding the means by which the existence of entanglement in a typical laboratory setup may to some extent be verified by measurements on a global scale. Following a brief introductory review, we will first investigate the influence of a Two-Level Fluctuator on a DC SQUID driven by a finite current bias. Then we introduce a directly measurable signature of multiqubit entanglement for a large system of qubits and show that it is compatible to a recently introduced measure of global entanglement.
The superconducting qubit quantum computer is one of the most promising quantum computing architectures for large-scale integration due to its maturity and close proximity to the well-established semiconductor manufacturing infrastructure. From an education perspective, it also bridges classical microwave electronics and quantum electrodynamics. In this paper, we will review the basics of quantum computers, superconductivity, and Josephson junctions. We then introduce important technologies and concepts related to DiVincenzo's criteria, which are the necessary conditions for the superconducting qubits to work as a useful quantum computer. Firstly, we will discuss various types of superconducting qubits formed with Josephson junctions, from which we will understand the trade-off across multiple design parameters, including their noise immunity. Secondly, we will discuss different schemes to achieve entanglement gate operations, which are a major bottleneck in achieving more efficient fault-tolerant quantum computing. Thirdly, we will review readout engineering, including the implementations of the Purcell filters and quantum-limited amplifiers. Finally, we will discuss the nature and review the studies of two-level system defects, which are currently the limiting factor of qubit coherence time. DiVincenzo's criteria are only the necessary conditions for a technology to be eligible for quantum computing. To have a useful quantum computer, large-scale integration is required. We will review proposals and developments for the large-scale integration of superconducting qubit devices. By comparing with the application of electronic design automation (EDA) in semiconductors, we will also review the use of EDA in superconducting qubit quantum computer design, which is necessary for its large-scale integration.
Micro-fabricated superconducting circuits have emerged as a leading candidate for quantum computers. However, typical error rates of 10-3 for quantum gates remain a challenge for performing error correction and need to be further decreased for achieving practical quantum computation. Improving qubit coherence times for superconducting qubits is a continuous endeavor in order to decrease error rates. As part of this effort, a topic addressed in this dissertation is the study of the generation mechanism and dynamics of non-equilibrium quasiparticles (QPs), which are electron-like excitations of a superconductor. This source of decoherence was studied by measuring the rate of single-electron changes in the parity state of multiple charge-sensitive transmon qubits under different conditions. The presence of non-equilibrium QPs in superconducting resonators and qubits operating at millikelvin temperature has been known for decades. Understanding the sources and dynamics of these QPs is crucial to evaluate and improve the performance of the devices. Specifically, for superconducting qubits, a single QP tunneling across the Josephson junction changes the total charge parity from even to odd or vice versa, and can induce energy relaxation and dephasing, limiting the coherence of the device. To study the dynamics of non-equilibrium QPs, I utilized a Ramsey-like pulse sequence to measure the rate of single-electron parity changes in transmon qubits, which had a weak charge dispersion, with different shunting capacitor geometries and materials. I started out by measuring a charge parity rate of ~ 33 s-1 for a grounded "x-mon" qubit and ~ 17 s-1 for a galvanically isolated "two-pads" qubit with our standard setup. These rates decreased to ~ 5 s-1 and ~ 2 s-1 for the x-mon and two-pads respectively when IR-filters and extra layers of shielding were installed. From my measurements, I found that the charge parity rates are sensitive to the geometry of the shunting capacitor, weakly depend on the amount of shielding surrounding the device, and independent of using Al or Ta for the superconducting shunting capacitor. To distinguish between two possible mechanisms for the parity switching, I measured the parity rates after cooling one of the qubit devices in an external magnetic field to induce vortices in the superconducting electrodes. After increasing the magnetic field above 23 μT, I measured a faster QP trapping rate and a much smaller T1, suggesting that at least one vortex was added to the superconducting electrode near the Josephson junction. On the other hand, the measured charge parity rates exhibited no clear dependence on the background QP trapping rates. These data suggest that a large portion of parity switching events occurs from QPs being produced at the Josephson junction, where pair-breaking radiation is rectified into QPs by the junction, as opposed to tunneling of QPs residing in the electrodes. To understand the difference in the measured parity rates, I simulated the absorption efficiency of pair-breaking radiation for my two designs and observed a similar difference in absorption rates when a single-mode blackbody radiation with an effective temperature T* ~ 300 mK was assumed to be illuminating the devices. This large T*, which is significantly higher than the device's nominal temperature of 20 mK, is consistent with values reported in the literature. However, its physical origin remains not fully understood. For the other part of my dissertation, I developed a new simplified process for making superconducting air bridges. Air bridges are used to suppress unwanted extraneous high frequency chip modes parasitic to superconducting quantum circuits that can couple to qubits and cause decoherence. Traditional ways of making air bridges utilize thermal reflow to create arched photoresist scaffolds that are limited in heights. This results in insufficient mechanical strength of the bridges which tend to collapse when spanning to larger lengths. My simplified fabrication method that utilizes two-photon lithography, a technique that enables creation of three-dimensional micron-scale structures, relaxes this limitation and is capable of making mechanically stable bridges with lengths up to 100 μm. The resulting Al air bridges, having a superconducting transition temperature of Tc = 1.08 mK and a dc residual resistivity ratio of 3.85, were confirmed to form a good electrical contact with the base metal layers and exhibit a small measurable amount of rf loss when placed over coplanar waveguide resonators, on par with other air bridge fabrication methods.
Superconducting quantum computing is a solid state quantum computing technology based on Josephson junction circuits. It becomes one of the most promising candidates for realizing practical quantum computer/simulator, because of its scalability, easy to coupling and control, compatibility to semiconductor technologies, etc. As the complicated electromagnetic environment in solid state metal and insulator, superconducting quantum bits (qubits) suffered from shot coherence time since its early development. In this review, we described some recently developed superconducting qubit structures, including Transmon/Xmon, Fluxonium and C-shunt flux qubit. Although these new qubit structures have very different circuit parameters and energy scales, they all find their way to effectively suppress environmental noises. As a result, their coherence time were improved significantly. Transmon, a transmission-line shunted plasma oscillation qubit, was now among the most popular structures for building a multi-qubit superconducting quantum circuit. It introduced a relatively large shunt capacitor to remarkably reduce the charge dispersion. Although the non-linearity is also decreased, by operating in a properly chosen EJ/Ec, transmon can greatly reduce the charge noise while only sacrificing a small amount of non-linearity. Xmon can be considered as a modified version of transmon. It is designed and optimized for multi-qubit operation and measurement with separate X/Y and Z control lines for each qubit, and a readout bus (a transmission line or a low-Q bandpass filter) for simultaneous readout of all the qubits. Fluxonium provide another solution for suppressing the charge noise in Cooper-pair box (CPB). It introduces a large shunt inductance to filter low-frequency offset charge in the small capacitor of the phase-slip junction (the small junction). To keep the qubit operating in the charge region, the shunt inductor should be large enough to keep the impedance larger than the superconducting impedance quantum RQ~1 kΩ. As a result, the inductance can only be provided by a large series of Josephson junctions. Fluxonium keeps the advantage of high anharmonicity of CPB. In addition, it introduces another degree of freedom: external flux Φext. Quasiparticles (electrons or holes) tunneling at the small junction add coherently to produce a ″1+cosφ″ term. As a result, when Φext= Φ0/2, dissipation caused by quasiparticle tunneling is suppressed and the energy relaxation time (T1) increases drastically. C-shunt flux qubit (CSFQ) decreases α and EJ to suppress flux noise in the qubit. While the charge noise becomes the dominant noise source, a large shunt capacitor is added to suppress the charge noise, similar to that in a transmon qubit. It is worth to notice that in CSFQ, the α decreases to below but near 1/2. As a result, the double-well potential no longer exists. The energy structure become similar to transmon, with the anharmonicity be opposite. CSFQ can get a much improved coherence time, while its anharmonicity can be larger than that of transmon. Those new superconducting qubit structures provide different solutions to improve the coherence time. Although it looks much different in circuit models and parameters, they have ideas in common, and may act as guides to other novel designs with longer coherence time. We can summarize as below. (1) The qubit circuit should be free of small superconducting islands. Charge fluctuation in small islands is a major source of decoherence. As a result, increase the area of the islands, that is, increase the capacitance becomes a straight forward way to suppress the charge noise. In Fluxonium, the small junction is connected with a large series of large junctions that there is also no small islands in the whole loop. (2) Remove superconducting loops in the qubit circuit, or minimize the loop size and loop current to suppress flux noise. (3) Bias the phase difference of the small junction to π, where dissipation caused by quasiparticle tunneling can be suppressed coherently. (4) Decrease the coupling bandwidth of qubit to the environment. In a circuit-QED readout scheme, a high-Q readout resonator that dispersively coupled to the qubit protects the qubit from exposed to the electromagnetic environment of the readout circuit. A ″Purcell filter″ can also be added to suppress such decoherence further. In conclusion, we overviewed some qubit engineering techniques or ideas to improve the coherence time, which is a very important figure for building practical quantum computer/simulator. We hope that someone can combine and optimize these ideas, while interact with developments in materials and micro-fabrication technologies, to develop novel new generation superconducting qubit structures in the near future.