This master thesis was dedicated to design, fabricate, and characterize subsystems of superconducting transmon qubits. Especially, focus was on investigating the predictability of the plasma frequency of the transmon, from which its operational properties are govern. In turn, the plasma frequency is governed by the normal state resistance of the two Josephson junctions along with its total capacitance. In\nprevious experiments, this frequency predictability relied entirely upon successful simulations of the system. However, even small simulation errors prove to generate\nsevere consequences for the system and a better, more systematic control is desired.\nIn order to identify and minimize this uncertainty, subsystems of the transmon were isolated and investigated. Test structures were fabricated and used to measure the normal state resistance of tunnel junctions with different areas and oxidation parameters using a four-point probe setup. A regime within which the reproducibility is increased was statistically identified. The shunt capacitance, i.e. the largest contribution to the total capacitance, of transmons was extracted by coupling identical capacitors to resonators. The coupling capacitance of a resonator is related to its external quality factor which was measured from analyzing the reflected microwave signal at cryogenic temperatures.\nThe smallest standard deviation of normal state resistances for 110 junction pairs was measured for junctions with an area 2.37 um^2 to be 1.48%, corresponding to an uncertainty contribution of 2 MHz for a designed plasma frequency of 6 GHz. Six resonators were measured throughout the shunt capacitance experiment and a linear t was used to compare the results with a written model based on conformal mapping.
This master thesis was dedicated to design, fabricate, and characterize subsystems of superconducting transmon qubits. Especially, focus was on investigating the predictability of the plasma frequency of the transmon, from which its operational properties are govern. In turn, the plasma frequency is governed by the normal state resistance of the two Josephson junctions along with its total capacitance. In\nprevious experiments, this frequency predictability relied entirely upon successful simulations of the system. However, even small simulation errors prove to generate\nsevere consequences for the system and a better, more systematic control is desired.\nIn order to identify and minimize this uncertainty, subsystems of the transmon were isolated and investigated. Test structures were fabricated and used to measure the normal state resistance of tunnel junctions with different areas and oxidation parameters using a four-point probe setup. A regime within which the reproducibility is increased was statistically identified. The shunt capacitance, i.e. the largest contribution to the total capacitance, of transmons was extracted by coupling identical capacitors to resonators. The coupling capacitance of a resonator is related to its external quality factor which was measured from analyzing the reflected microwave signal at cryogenic temperatures.\nThe smallest standard deviation of normal state resistances for 110 junction pairs was measured for junctions with an area 2.37 um^2 to be 1.48%, corresponding to an uncertainty contribution of 2 MHz for a designed plasma frequency of 6 GHz. Six resonators were measured throughout the shunt capacitance experiment and a linear t was used to compare the results with a written model based on conformal mapping.
In a quantum computer, the information carriers, which are bits in ordinary computers, are implemented as devices that exhibit coherent superpositions of physical states and entanglement. Such components, known as quantum bits or qubits, can be realized with various different types of two-state quantum systems. Quantum computers will be built for computational speed, with hoped for applications especially in cryptography and in other tasks where classical computers remain inefficient. Circuit quantum electrodynamics (cQED) is a quantum-computer architecture which employs superconducting electronic components and microwave photon fields as building blocks. Compared to cavity quantum electrodynamics (CQED), where atoms are trapped in physical cavities, cQED is more attractive in that its qubits are tunable and conveniently integrable with the electronics already in use. This architecture has shown some of the most promising qubit designs, despite their coherence times reaching tens of microseconds, are still below the state of the art with spin qubits, which reach milliseconds. Coherence times are historically the most relevant parameters describing the fitness of a qubit, although these days not necessarily the limiting factor. This thesis presents a comprehensive set of theoretical and experimental methods for measuring the characteristic parameters of superconducting qubits. We especially study transmission-line-shunted plasma oscillation qubits, or transmons, and presents experimental results for a single sample. Transmon capacitively couples a superconducting quantum interference device (SQUID) with a coplanar waveguide (CPW) resonator, often with added frequency tunability utilizing an external magnet. The number of superconducting charge carriers tunnelled through a junction in the SQUID are used as qubit degrees of freedom. Readout of the qubit state is carried out by measuring transmission through the CPW. A cryogenic setup is employed with measurement and driving pulses delivered from microwave sources. Steady-state spectroscopy is employed to determine the resonance frequencies of the qubit and the resonator, qubit-resonator coupling constants, and the energy parameters of the qubit. Pulse-modulated measurements are employed to determine the coherence times of the qubit. The related analysis- and simulation programs and scripts are collected togithub.com/patomaki.
The reproducibility of qubit parameters is a challenge for scaling up superconducting quantum processors. Signal cross talk imposes constraints on the frequency separation between neighboring qubits. The frequency uncertainty of transmon qubits arising from the fabrication process is attributed to deviations in the Josephson junction area, tunnel barrier thickness, and the qubit shunt capacitor. We decrease the sensitivity to these variations by fabricating larger Josephson junctions and reduce the wafer-level standard deviation in resistance down to 2%. We characterize 32 identical transmon qubits and demonstrate the reproducibility of the qubit frequencies with a 40 MHz standard deviation (i.e., 1%) with qubit quality factors exceeding 2 million. We perform two-level-system (TLS) spectroscopy and observe no significant increase in the number of TLSs causing qubit relaxation. We further show by simulation that for our parametric-gate architecture, and accounting only for errors caused by the uncertainty of the qubit frequency, we can scale up to 100 qubits with an average of only three collisions between quantum-gate transition frequencies, assuming 2 cross talk and 99.9 target gate fidelity.
The quest to design a realizable quantum computer is a dream for many for the past few decades. At the moment, one of the promising designs is the transmon qubit, which is a superconducting qubit is the focus of this work. In order to analyze and design different components of a quantum chip, an understanding of the circuitry is required. By varying the circuit parameters, one can design the system according to requirements by constructing the required physical geometry that incorporates the design parameters. In this thesis work, part of the focus was to understand the transmon qubit circuit parameters, extract the circuit parameters such as capacitances from a physical geometry, build analytic and numerical 3D FEM models. Using a circuit model of the qubit system, the interdependence of the resonators that connects qubits with each other can be studied. Their resonances play a role in the qubit Hamiltonian and can be estimated by constructing accurate simulation models. This problem statement has been dealt with in the thesis work by constructing a hybrid circuitry of standard circuit components and 3D FEM simulated qubit unit cells. The quality factor of the measurement readout resonator of a qubit system needs to be characterized in a qubit system in order to target the rate and resolution at which the measurements can be done. In order to do so, the circuit parameters that affect the quality factor needs to be investigated. This problem statement has also been treated in this work.
We demonstrate a superconducting transmon qubit in which a Josephson junction has been engineered to act as its own parallel shunt capacitor. This merged-element transmon potentially offers a smaller footprint than conventional transmons. Because it concentrates the electromagnetic energy inside the junction, it reduces the relative electric field participation from other interfaces. By combining micrometer-scale Al/AlOx/Al junctions with long oxidations, we produce functional devices with EJ/EC in the low-transmon regime (${E}_{J}/{E}_{C}\ensuremath{\lesssim}30$). Cryogenic I-V measurements show a sharp dI/dV structure with low subgap conduction. Qubit spectroscopy of tunable versions shows a small number of avoided level crossings, suggesting the presence of two-level systems. We observe mean T1 times typically in the range of $10--90\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{s}$, with some annealed devices exhibiting ${T}_{1}>100\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{s}$ over several hours. The results suggest that energy relaxation in conventional small-junction transmons is not limited by junction loss.
This dissertation examines the design, fabrication, and characterization of a superconducting lumped-element tunable LC resonator that is used to vary the coupling between two superconducting qubits. Some level of qubit-qubit coupling is needed to perform gating operations. However, with fixed coupling, single qubit operations become considerably more difficult due to dispersive shifts in their energy levels transitions that depend on the state of the other qubit. Ideally, one wants a system in which the qubit-qubit coupling can be turned off to allow for single qubit operations, and then turned back on to allow for multi-qubit gate operations. I present results on a device that has two fixed-frequency transmon qubits capacitively coupled to a tunable thin-film LC resonator. The resonator can be tuned in situ over a range of 4.14 GHz to 4.94 GHz by applying an external magnetic flux to two single-Josephson junction loops, which are incorporated into the resonator’s inductance. The qubits have 0-to-1 transition frequencies of 5.10 GHz and 4.74 GHz. To isolate the system and provide a means for reading out the state of the qubit readout, the device was mounted in a 3D Al microwave cavity with a TE101 mode resonance frequency of about 6.1 GHz. The flux-dependent transition frequencies of the system were measured and fit to results from a coupled Hamiltonian model. With the LC resonator tuned to its minimum resonance frequency, I observed a qubit-qubit dispersive shift of 2χ_qq≈ 0.1 MHz, which was less than the linewidth of the qubit transitions. This dispersive shift was sufficiently small to consider the coupling “off”, allowing single qubit operations. The qubit-qubit dispersive shift varied with the applied flux up to a maximum dispersive shift of 2χ_qq≈ 6 MHz. As a proof-of-principle, I present preliminary results on performing a CNOT gate operation on the qubits when the coupling was “on” with 2χ_qq≈ 4 MHz. This dissertation also includes observations of the temperature dependence of the relaxation time T1 of three Al/AlOx/Al transmons. We found that, in some cases, T1 increased by almost a factor of two as the temperature increased from 30 mK to 100 mK. We found that this anomalous behavior was consistent with loss due to non-equilibrium quasiparticles in a transmon where one electrode in the tunnel junction had a smaller volume and slightly smaller superconducting energy gap than the other electrode. At sufficiently low temperatures, non-equilibrium quasiparticles accumulate in the electrode with a smaller gap, leading to an increased density of quasiparticles at the junction and a corresponding decrease in the relaxation time. I present a model of this effect, use the model to extract the density of non-equilibrium quasiparticles in the device, and find the values of the two superconducting energy gaps.
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.