Frequency instability of superconducting resonators and qubits leads to dephasing and time-varying energy-loss and hinders quantum-processor tune-up. Its main source is dielectric noiseoriginating in surface oxides. Thorough noise studies are needed in order to develop a comprehensive understanding and mitigation strategy of these fluctuations. Here we use a frequency-locked loop to track the resonant-frequency jitter of three different resonator types—one niobium-nitride superinductor, one aluminium coplanar waveguide, and one aluminium cavity—and we observe strikingly similar random-telegraph-signal fluctuations. At low microwave drive power, the resonators exhibit multiple, unstable frequency positions, which for increasing power coalesce into one frequency due to motional narrowing caused by sympathetic driving of individual two-level-system defects by the resonator. In all three devices we probe a dominant fluctuator, finding that its amplitude saturates with increasing drive power, but its characteristic switching rate follows the power-law dependence of quasiclassical Landau-Zener transitions.

We investigate the circuit quantum electrodynamics of superconducting nanowire oscillators. The sample circuit consists of a capacitively shunted nanowire with a width of about 20 nmand a varying length up to 350 nm, capacitively coupled to an on-chip resonator. By applying microwave pulses we observe Rabi oscillations, measure coherence times and the anharmonicity of the circuit. Despite the very compact design, simple top-down fabrication and high degree of disorder in the oxidized (granular) aluminum material used, we observe lifetimes in the microsecond range.

Motivated by recent experiments on Josephson junction arrays in microwave cavities, we construct a quantum phase model and calculate the susceptibility of this model in linear response.Both charge and vortex degrees of freedom are considered, as well as circuits containing either Josephson junctions or coherent quantum phase slip elements. The effects of decoherence are considered via a Lindblad master equation.

We present the design of a passive, on-chip microwave circulator based on a ring of superconducting tunnel junctions. We investigate two distinct physical realisations, based on eitherJosephson junctions (JJ) or quantum phase slip elements (QPS), with microwave ports coupled either capacitively (JJ) or inductively (QPS) to the ring structure. A constant bias applied to the center of the ring provides the symmetry breaking (effective) magnetic field, and no microwave or rf bias is required. We find that this design offers high isolation even when taking into account fabrication imperfections and environmentally induced bias perturbations and find a bandwidth in excess of 500 MHz for realistic device parameters.

Amorphous solids show surprisingly universal behaviour at low temperatures. The prevailing wisdom is that this can be explained by the existence of two-state defects within the material.The so-called standard tunneling model has become the established framework to explain these results, yet it still leaves the central question essentially unanswered – what are these two-level defects? This question has recently taken on a new urgency with the rise of superconducting circuits in quantum computing, circuit quantum electrodynamics, magnetometry, electrometry and metrology. Superconducting circuits made from aluminium or niobium are fundamentally limited by losses due to two-level defects within the amorphous oxide layers encasing them. On the other hand, these circuits also provide a novel and effective method for studying the very defects which limit their operation. We can now go beyond ensemble measurements and probe individual defects – observing the quantum nature of their dynamics and studying their formation, their behaviour as a function of applied field, strain, temperature and other properties. This article reviews the plethora of recent experimental results in this area and discusses the various theoretical models which have been used to describe the observations. In doing so, it summarises the current approaches to solving this fundamentally important problem in solid-state physics.

Identifying the microscopic origins of decoherence sources prevalent in Josephson junction based circuits is central to their use as functional quantum devices. Focussing on so called„strongly coupled“ two-level defects, we construct a theoretical model using the atomic position of the oxygen which is spatially delocalised in the oxide forming the Josephson junction barrier. Using this model, we investigate which atomic configurations give rise to two-level behaviour of the type seen in experiments. We compute experimentally observable parameters for phase qubits and examine defect response under the effects of applied electric field and strain.

One of the key problems facing superconducting qubits and other Josephson
junction devices is the decohering effects of bi-stable material defects.
Although a variety of phenomenologicalmodels exist, the true microscopic
origin of these defects remains elusive. For the first time we show that these
defects may arise from delocalisation of the atomic position of the oxygen in
the oxide forming the Josephson junction barrier. Using a microscopic model, we
compute experimentally observable parameters for phase qubits. Such defects are
charge neutral but have non-zero response to both applied electric field and
strain. This may explain the observed long coherence time of two-level defects
in the presence of charge noise, while still coupling to the junction electric
field and substrate phonons.