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.
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.
In this licentiate thesis, I present the design, fabrication, and characterization of superconducting parametric resonators, for use in quantum information processing. These devices are quarter-wavelength coplanar waveguide resonators (~5 GHz), terminated at one end by a non-linear inductance provided by a SQUID (superconducting quantum interference device). 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 on-chip transmission lines. The modulation occurs on a timescale much faster than the photon loss out of the resonator. The non-linearity provides several different regimes for operating this device. I focused on the parametric regime, in which the non-linear element was being modulated (pumped) at or near twice the resonant frequency. This pumping can lead to amplification and frequency conversion of an incoming signal. It can also give rise to instabilities and self-oscillations "parametric oscillations" - that is, the generation of an intense electric field in the resonator (the creation of photons). Parametric oscillations set in when the pumping strength exceeds a threshold value, and also depends on the pump-frequency detuning from twice the resonance and on the static flux through the SQUID. I characterized the devices over a wide parameter range by doing homodyne detection of the reflected signal or of the emitted field oscillations. In particular, I investigated the damping and two leading nonlinearities, dominating in different operating regimes, which influence the dynamics of the parametric resonator. First, I extracted the Duffing nonlinearity by studying the line width of the resonator as a function of the input signal (without pumping the SQUID). Second, with high pump amplitude, I extracted the pump-induced nonlinearity by determining the threshold parameters (pump amplitude and detuning) for the onset of parametric oscillations; this nonlinearity leads to the generation of higher-order pump terms that complicate the system dynamics, but can be mitigated now that they have been understood. My results validate a recent theoretical model for the classical, non-linear dynamics of parametric resonance, and helps determine workable design parameters. Finally, I helped develop a linearized model − the "pumpistor" - describing this device in terms of a flux-controlled impedance. This will be useful when designing more complex circuits. One goal of this work is to demonstrate single-shot measurements on superconducting qubits (quantum bits of information). We will use the parametric resonator as a threshold discriminator, associating the qubit's two energy eigenstates with the parametric oscillations either turning on or not. This would be a very useful device in the quantum engineer's toolbox when designing systems for quantum information processing and communication.
Parametric oscillations are well studied phenomena, with applications in amplification, quantum optics, and quantum information processing. They can occur as a parameter of a system, such as the resonant frequency, is being modulated or “pumped” by an external field. A nonlinearity of the system can then transfer power from the pumping frequency to two frequencies called signal and idler. When the signal falls within a resonance, and when the pump amplitude exceeds an instability threshold, parametric oscillations occur. When signal and idler fall within the same resonance, the pumping is called degenerate.Due to somewhat different implementations, in combination with rich nonlinear physics, the details of the parametric oscillations can differ in different systems. In this work, we expand on the research done on parametric oscillations using a superconducting microwave resonator with a tunable boundary condition. Previously, a degenerate Josephson parametric oscillator (JPO) has been demonstrated by modulation of this boundary condition at twice the resonator's resonant frequency. We further use the JPO to implement a novel read-out method for a superconducting qubit. Moreover, we demonstrate a different, nondegenerate regime of the JPO, which we denote the NJPO, by modulating the frequency at the sum of two resonant frequencies of a multimode resonator.Both the JPO qubit read-out and the NJPO have applications within quantum information processing. The perhaps most promising platform for quantum information processing is represented by the circuit-QED architecture with superconducting resonators and artificial atoms, where the two lowest atomic levels represent the qubit. We make these circuits using lithographic techniques, and control and measure them at low temperature using microwaves. The qubit's state is fragile and difficult to read out with high fidelity. To this end, we have developed a method based on the JPO, in which the qubit state is mapped onto a zero-amplitude or a large-amplitude state of the JPO. We achieved a large contrast (185±15 photons), therefore eliminating the need for a following quantum-limited parametric amplifier. Our readout fidelity was 81.5 %, and by carefully modeling we can distinguish fidelity loss from the qubit and the readout, respectively. This analysis displays an actual readout fidelity of 98.7 %.An alternative model for quantum computing is based on continuous variables, and uses harmonic oscillators instead of qubits. Entangled states, which can be used as quantum resources, can then be created, for example, by two-mode squeezing of the oscillator ground state. The state of the NJPO produces correlated oscillations in its two modes, which might be useful for continuous-variable quantum computing. In this work we fully characterize the classical properties of the NJPO, and show good quantitative agreement with a theoretical model.
We propose and demonstrate a read-out technique for a superconducting qubit by dispersively coupling it with a Josephson parametric oscillator. We employ a tunable quarter wavelength superconducting resonator and modulate its resonant frequency at twice its value with an amplitude surpassing the threshold for parametric instability. We map the qubit states onto two distinct states of classical parametric oscillation: one oscillating state, with 185±15 photons in the resonator, and one with zero oscillation amplitude. This high contrast obviates a following quantum-limited amplifier. We demonstrate proof-of-principle, single-shot read-out performance, and present an error budget indicating that this method can surpass the fidelity threshold required for quantum computing.
In this thesis, measurements on superconducting electrical circuits that exhibit quantum mechanical effects are presented. Nonlinear superconducting circuits can be regarded as artificial atoms with energy spectra that can be engineered. The artificial atoms can be used as quantum bits for quantum computation. By coupling the artificial atoms to the electromagnetic field inside a transmission line resonator, quantum optical effects can be studied in these electrical circuits.The possibility of using a frequency tunable transmission line resonators for coupling of superconducting quantum bits is investigated. Tunable superconducting resonators consisting of coplanar waveguide structures, terminated to ground in one end via a superconducting quantum interference device (SQUID), are characterized. By applying a magnetic field to the SQUID loop, the boundary condition of the resonator changes leading to a change in resonance frequency.A change of the resonance frequency by more than 250 linewidths is demonstrated. It is also demonstrated that the resonator can be tune by several hundred MHz on a time scale that is much shorter than the photon lifetime of the resonator.Circuits containing both one and two transmon qubits coupled to the resonator are characterized. Quantum mechanical interactions between the resonator and the qubits, in form of vacuum Rabi splitting, are observed. Coherent control of a single qubit coupled to the resonator is demonstrated by performing Rabi oscillations of the qubit. In the two qubit case, coherent interaction between the qubits is observed in terms of a nonlinear scaling of the coupling strength between the resonator and the collective two qubit system.Measurements on a strongly driven single Cooper-pair box, using a quantum capacitance readout, are also presented. A rich structure in the response is well explained in terms of longitudinal dressed states of the single-Cooper pair box.When measuring the response of a single-electron box, a gate dependent excess dissipation is observed. The dissipation is understood by considering the internal dynamics of the single electron box. The excess dissipation is modeled as an effective resistance named the Sisyphus resistance.
Abstract : Circuit Quantum Electrodynamics (cQED) is a highly promising platform for quantum control, quantum simulation, and quantum optics in a solid-state environment. Such systems consist of arti cial atoms coupled to superconducting resonators, and can be probed with microwave signals on a chip. This thesis theoretically and experimentally studies a method of quantum-limited Josephson parametric ampli cation for the improvement of such microwave measurements. A theoretical analysis of parametric ampli cation with a nonlinear quantum oscillator is given, along with an analysis of a particular implementation with a superconducting coplanar waveguide resonator shunted by an array of SQUIDs. A parametric ampli er chip is designed and a fabrication process is engineered. Measurements and analysis of a successfully fabricated device are presented, and future outlook is discussed.
Though superconducting qubits offer the potential for a scalable quantum computing architecture, the high-fidelity readout necessary to execute practical algorithms has thus far remained elusive. Moreover, achievements toward high fidelity have been accompanied by either long measurement times or demolition of the quantum state. In this dissertation, we address these issues with the novel integration of two ultralow-noise, superconducting amplifiers into separate dispersive flux qubit measurements. We first demonstrate a flux qubit inductively coupled to a 1.294-GHz nonlinear oscillator formed by a capacitively shunted DC SQUID. The frequency of the oscillator is modulated by the state of the qubit and is detected via microwave reflectometry. A microstrip SQUID (Superconducting QUantum Interference Device) amplifier (MSA) is used to increase the sensitivity of the measurement over that of a semiconductor amplifier. In the second experiment, we report measurements of a flux qubit coupled via a shared inductance to a quasi-lumped element 5.78-GHz readout resonator formed by the parallel combination of an interdigitated capacitor and a meander line inductor. The system noise is substantially reduced by a near-quantum-limited Josephson parametric amplifier (paramp).We present measurements of increased fidelity and reduced measurement backaction using the MSA at readout excitation levels as low as one hundredth of a photon in the readout resonator, observing a 4.5-fold increase in the readout visibility. Furthermore, at low readout excitation levels below one tenth of a photon in the readout resonator, no reduction in T1 is observed, potentially enabling continuous monitoring of the qubit state. Using the paramp, we demonstrate a continuous, high-fidelity readout with sufficient bandwidth and signal-to-noise ratio to resolve quantum jumps in the flux qubit. This is enabled by a readout which discriminates between the readout pointer state distributions to an error below one part in 1000. This, along with the ability to make many successive readouts in a time T1, permits the use of heralding to ensure initialization to a fiducial state, such as the ground state. This method enables us to eliminate errors due to spurious thermal population, increasing the fidelity to 93.9%. Finally, we use heralding to introduce a simple, fast qubit reset protocol without changing the system parameters to induce Purcell relaxation.