We report experiments on superconducting flux qubits in a circuit quantum electrodynamics (cQED) setup. Two qubits, independently biased and controlled, are coupled to a coplanar waveguide resonator. Dispersive qubit state readout reaches a maximum contrast of 72%. We measure energy relaxation times at the symmetry point of 5 and $10\ensuremath{\mu}\mathrm{s}$, corresponding to 7 and $20\ensuremath{\mu}\mathrm{s}$ when relaxation through the resonator due to Purcell effect is subtracted out, and levels of flux noise of 2.6 and $2.7\phantom{\rule{0.222222em}{0ex}}\ensuremath{\mu}{\mathrm{\ensuremath{\Phi}}}_{0}/\sqrt{\text{Hz}}$ at 1 Hz for the two qubits. We discuss the origin of decoherence in the measured devices. The strong coupling between the qubits and the cavity leads to a large, cavity-mediated, qubit-qubit coupling. This coupling, which is characterized spectroscopically, reaches 38 MHz. These results demonstrate the potential of cQED as a platform for fundamental investigations of decoherence and quantum dynamics of flux qubits.
We report experiments on superconducting flux qubits in a circuit quantum electrodynamics (cQED) setup. Two qubits, independently biased and controlled, are coupled to a coplanar waveguide resonator. Dispersive qubit state readout reaches a maximum contrast of 72%. We measure energy relaxation times at the symmetry point of 5 and 10\ensuremathμs, corresponding to 7 and 20\ensuremathμs when relaxation through the resonator due to Purcell effect is subtracted out, and levels of flux noise of 2.6 and 2.7\ensuremathμ\ensuremathΦ0/Hz at 1 Hz for the two qubits. We discuss the origin of decoherence in the measured devices. The strong coupling between the qubits and the cavity leads to a large, cavity-mediated, qubit-qubit coupling. This coupling, which is characterized spectroscopically, reaches 38 MHz. These results demonstrate the potential of cQED as a platform for fundamental investigations of decoherence and quantum dynamics of flux qubits.
This thesis presents circuit quantum electrodynamic (cQED) experiments done with artificial atoms coupled to a high quality factor superconducting microwave resonator. This work discusses the theoretical framework, design, fabrication, implementation and characterization of a multi-qubit system using superconducting persistent current qubits, often referred as flux qubits. \n \nWe developed a new type of cryogenic aid for fast turnaround microwave experiments. The minimum turnaround time to perform microwave experiments in dilution refrigerators is typically a few days, as required by cooling down and warming up the entire refrigerator. The cryogenic microwave payload and wiring needed for each qubit and resonator add a significant heat load to \nthe system which typically only has a few µW s of cooling power at millikelvin temperatures. We present a new experimental approach we developed in which a suitable sample holder is attached to a cold-insertable probe and brought in contact with transmission lines permanently mounted inside the cryostat. The total turnaround time is reduced to 8 hours if the target temperature is 80 mK. This new measurement method increased our ability to successfully identify good devices with fast design-characterization iterations, while allowing months-long measurements at 30 mK. \n \nOur device architecture uses several qubits, each of which is controlled via on-chip fast flux bias lines. Readout of the qubit’s quantum state is performed by homodyne detection of the resonator field at large driving power. We observe long coherence times at the optimal bias point of the flux qubits and present decoherence measurements around this optimal point, where the \nflux qubits couple mostly to magnetic flux noise. Dynamical decoupling techniques employing fast microwave pulses are used to protect the qubit’s coherence and allow calculating the magnetic flux noise power spectral density of the qubit’s environment. Photon-mediated interaction between distant qubits in the resonator allows the implementation of a two-qubit controlled-NOT gate \nusing the selective darkening technique. \n \nThis multi-qubit superconducting design is an interesting platform to study the decoherence properties of flux qubits, the properties of strong interaction of electromagnetic radiation with macroscopic quantum systems. These results demonstrate the potential of cQED as a platform for fundamental investigations of decoherence and quantum dynamics of flux qubits.
Abstract Superconducting quantum circuits are a leading platform for quantum-information processing, but their development requires expertise spanning device design, microfabrication, cryogenic operation, microwave control, and quantum characterization. In this work, we report the realization of a flux-tunable superconducting transmon platform and present an integrated workflow encompassing design, fabrication, measurement, and numerical modeling. The device consists of an Al/AlOx/Al transmon coupled to a three-dimensional microwave cavity operating in the circuit quantum electrodynamics (cQED) dispersive regime. Two-tone spectroscopy reveals a fundamental transition frequency of ω01=5.0122GHz and an anharmonicity of α/2π=−202.4MHz , corresponding to EJ/EC≈82.9 . Flux spectroscopy yields a cavity-qubit coupling strength of g/2π=260MHz , while the cavity linewidth gives a loaded quality factor of QL=6127 and a Purcell limit of T1Purcell≈82μs . Time-domain measurements yield coherence times of T1=17.4μs and T2∗=5.8μs . To investigate coherence and dissipation in the device, the experimental observations are analyzed within a Lindblad master-equation framework describing cavity photon loss and thermal excitation, qubit energy relaxation, and pure dephasing processes. Using a set of experimentally extracted parameters, the model reproduces the measured spectroscopic and time-domain observables, providing a quantitative description of the open-system dynamics of the transmon-cavity platform. The analysis shows that the measured coherence is primarily limited by pure dephasing and energy-relaxation processes, whereas thermal excitation plays a minor role under the experimental conditions. Inspired by the broader framework of quantum dissipation in macroscopic quantum systems pioneered by Caldeira and collaborators, this approach enables a quantitative analysis of relaxation and dephasing processes in superconducting quantum circuits. Beyond the characterization of a single device, the present work demonstrates the establishment of the expertise, infrastructure, and experimental workflow required for the design, fabrication, measurement, and modeling of superconducting quantum circuits, contributing to the development of quantum technologies in Brazil and related applications.
We fabricate a three-Josephson-junction flux qubit, a nonlinear superconducting circuit acting as a quantum two-level system with a macroscopic degree of freedom. First, the capacitance per unit area of the used Josephson junctions, C s =(100±25)fF/µm 2 ,
is determined from DC SQUID voltage steps. Next, we probe the coherence times of our qubit using a novel variant of the switching-DC-SQUID readout. At the optimal point, our device is relaxation-limited with T 1 ≅100ns and T φ ≅2µs. Ramsey
and spin echo experiments reveal 1/f-noise and suggest microscopic fluctuators in the tunnel barriers as its source. As in other experiments, the 1/f-noise magnitude is ≅(10 -6 Φ 0 ) 2 . Finally, the qubit is coupled to a linear
LC-resonator in a circuit quantum electrodynamics experiment. Spectroscopically, an upconversion mechanism enabled by controlled symmetry breaking is demonstrated.
The basic element of circuit quantum electrodynamics (cQED) is a cavity resonator strongly coupled to a superconducting qubit. Since the inception of the field, the choice of the cavity frequency was, with a few exceptions, been limited to a narrow range around 7 GHz due to a variety of fundamental and practical considerations. Here we report the first cQED implementation, where the qubit remains a regular transmon at about 5 GHz frequency, but the cavity's fundamental mode raises to 21 GHz. We demonstrate that (i) the dispersive shift remains in the conventional MHz range despite the large qubit-cavity detuning, (ii) the quantum efficiency of the qubit readout reaches 8%, (iii) the qubit's energy relaxation quality factor exceeds 107, (iv) the qubit coherence time reproducibly exceeds 100μs and can reach above 300μs with a single echoing π-pulse correction. The readout error is currently limited by an accidental resonant excitation of a non-computational state, the elimination of which requires minor adjustments to the device parameters. Nevertheless, we were able to initialize the qubit in a repeated measurement by post-selection with 2×10−3 error and achieve 4×10−3 state assignment error. These results encourage in-depth explorations of potentially transformative advantages of high-frequency cavities without compromising existing qubit functionality.
Circuit quantum electrodynamics (cQED), exemplified by a coupled system of a superconducting qubit and a microwave cavity, is a powerful framework for the quantum control and measurement of macroscopic quantum states in solid-state circuits. Quantum circuits based on superconducting qubits have emerged as one of the leading platforms in the pursuit of fault-tolerant quantum computing. Despite significant progress in extending qubit lifetimes, refining experimental protocols, and scaling up quantum processors, errors arising from the control and measurement of superconducting qubits continue to hinder the realization of a universal quantum computer. To investigate the error mechanisms for state-of-the-art qubits, we realize long-lived superconducting transmon qubits that exhibit fluctuating lifetimes, with an average of 0.2 ms and a maximum exceeding 0.4 ms. We then investigate their dominant error mechanism. By introducing novel time-resolved error measurements that are synchronized with the operation of the pulse tube cooler in a dilution refrigerator, we find that mechanical vibrations from the pulse tube induce nonequilibrium dynamics in highly coherent qubits, leading to their correlated bit-flip errors. Our findings not only deepen our understanding of qubit error mechanisms but also provide valuable insights into potential error-mitigation strategies for achieving fault tolerance by decoupling superconducting qubits from their mechanical environments. We also present a novel scheme for operating a cQED system in a regime where the cavity is largely displaced. We find that a qubit drive at the bare cavity frequency can effectively displace the cavity field while minimizing the cavity-drive-induced dephasing and the ac Stark shift. Furthermore, we demonstrate that standard cQED protocols, such as qubit control, readout, and cavity single-photon generation, remain compatible with largely displaced cavity fields, even beyond the critical photon number. These findings open new pathways for exploring cQED dynamics in large-photon-number regimes, including the study of nonlinear phenomena in microwave cavities, the saturation of two-level system baths for extending the coherence of microwave quantum states, and the acceleration of the dispersive readout. Finally, mechanical resonators have emerged as integral components in quantum computing for storing and transducing quantum information. Low-frequency mechanical resonators, with extremely low energy dissipation rates, are particularly interesting for extending the lifetimes of stored quantum information. However, integrating low-frequency mechanical resonators with qubits is challenging because their small energy gaps make coherent energy exchange and ground-state preparation difficult. In this thesis, we report the first steps towards the characterization of a hybrid quantum device, consisting of a Transmon qubit and a circuit optomechanical system, both coupled to a 3D microwave cavity.
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.