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 $10^7$, (iv) the qubit coherence time reproducibly exceeds $100~μ\rm{s}$ and can reach above $300~μ\rm{s}$ 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 $2\times 10^{-3}$ error and achieve $4\times 10^{-3}$ state assignment error. These results encourage in-depth explorations of potentially transformative advantages of high-frequency cavities without compromising existing qubit functionality.
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.
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.
Millimeter waves are emerging as an enabling technology for connecting and enhancing different quantum platforms such as Rydberg atoms, optomechanics, and superconducting qubits. In this work, we explore the interaction between millimeter wave photons and conventional transmon qubits, specifically for qubit readout. We study a circuit quantum electrodynamic (cQED) system consisting of a millimeter wave cavity at ωr=2π×34.7 GHz and a transmon qubit at ωq=2π×3.1 GHz coupled at rate g=2π×1.3. With such a large detuning between cavity and qubit, ωr/ωq>10, we are able to suppress drive induced unwanted resonant state transitions, enabling strong drives for qubit readout. We measure no resonant state transitions even when driving with more than 100 photons and read out the qubit state with more than 100 photons to achieve a measurement fidelity greater than 99% without the aid of a quantum limited amplifier.
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.
Metamaterial resonant structures made from arrays of superconducting lumped-circuit elements can exhibit microwave-mode spectra with left-handed dispersion for the standing-wave resonances, resulting in a high density of modes in the same frequency range where superconducting qubits are typically operated, as well as a bandgap at lower frequencies that extends down to dc. Using this regime for multimode circuit quantum electrodynamics, we perform a series of measurements of such a superconducting metamaterial resonator coupled to a flux-tunable transmon qubit. Through microwave measurements of the metamaterial, we observe the coupling of the qubit to each of the modes that it passes through. Using a separate readout resonator, we probe the qubit dispersively and characterize the qubit energy relaxation as a function of frequency, which is strongly affected by the Purcell effect in the presence of the dense mode spectrum. Additionally, we investigate the ac Stark shift of the qubit as the photon number in the various metamaterial modes is varied. Through numerical simulations, we explore designs based on this scheme with enhanced coupling so that the coupling energy between the qubit and the metamaterial modes can exceed the intermode spacing in future devices with achievable circuit parameters. The ability to tailor the dense mode spectrum through the choice of circuit parameters and manipulate the photonic state of the metamaterial through interactions with qubits makes this a promising platform for analog quantum simulation with microwave photons and quantum memories.
Circuit quantum electrodynamics (cQED) is a prominent platform for quantum information processing, in which microwave photons are confined into resonant cavities coupled to superconducting quantum bits (qubits). The large effective dipole moment of the qubit, in combination with the high energy density of the quasi 1-D resonator allow these systems to enter the so-called strong coupling regime. The quantum state of the qubit can then be assessed by probing the frequency of the resonator, protecting the qubit from otherwise losing its energy to the environment. However, eventhough this so-called dispersive readout technique has proven useful, it is often in itself insufficient to render single-shot readout performance | one of the crucial tasks required for realizing a quantum computer. This thesis describes the demonstration of a single-shot readout technique forsuperconducting quantum bits, based on coupling the qubit to a frequency-tunable resonator. The backbone of our device is a 5 GHz quarter-wavelength coplanar waveguide resonator, terminated at one end by a non-linear inductance provided by a superconducting quantum interference device (SQUID). The SQUID acts as a flux-controlled boundary condition, which effectively changes the electrical length of the resonator. This enables the modulation of the resonant frequency by coupling microwave magnetic flux into the SQUID, using an on-chip transmission line. The modulation occurs on a timescale much faster than the photon loss out of the resonator and if the pump strength exceeds a threshold value set by the damping rate of the resonator, an intense photon field will build up inside the resonator | known as "parametric oscillations". By heterodyne detection of the output signal from the Josephson parametric oscillator (JPO), we first extracted two leading nonlinear effects of the system (dominating in different limits of applied magnetic flux). Next, we couple a qubit to the JPO and demonstrate that we can encode its quantum state onto the strong output field of the parametric oscillator (or lack thereof), rendering a signal-to-noise ratio sufficient for single-shot state detection and therefore also obviating a quantum limited parametric amplifier. The thesis also contains results from microscopic studies of the Josephson junctions, which we use to provide the necessary nonlinearities in the above mentioned devices. In particular, we show how the microstructure of the barrier layer and its atomic composition can be used to infer important electrical properties of the junctions. This knowledge allows us to better tailor the properties of Josephson-based devices.