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Superconducting integrated circuits have demonstrated a tremendous potential to realize integrated quantum computing processors. However, the downside of the solid-state approach is that superconducting qubits suffer strongly from energy dissipation and environmental fluctuations caused by atomic-scale defects in device materials. Further progress towards upscaled quantum processors will require improvements in device fabrication techniques, which need to be guided by novel analysis methods to understand and prevent mechanisms of defect formation. Here, we present a technique to analyse individual defects in superconducting qubits by tuning them with applied electric fields. This provides a spectroscopy method to extract the defects’ energy distribution, electric dipole moments, and coherence times. Moreover, it enables one to distinguish defects residing in Josephson junction tunnel barriers from those at circuit interfaces. We find that defects at circuit interfaces are responsible for about 60% of the dielectric loss in the investigated transmon qubit sample. About 40% of all detected defects are contained in the tunnel barriers of the large-area parasitic Josephson junctions that occur collaterally in shadow evaporation, and only \\[\\approx\\]3% are identified as strongly coupled defects, which presumably reside in the small-area qubit tunnel junctions. The demonstrated technique provides a valuable tool to assess the decoherence sources related to circuit interfaces and to tunnel junctions that is readily applicable to standard qubit samples.

In this paper we are concerned with singular points of solutions to the unstable free boundary problem The problem arises in applications such as solid combustion, composite membranes, climatology and fluid dynamics. It is known that solutions to the above problem may exhibit singularities—that is points at which the second derivatives of the solution are unbounded—as well as degenerate points. This causes breakdown of by-now classical techniques. Here we introduce new ideas based on Fourier expansion of the nonlinearity χ { u >0} . The method turns out to have enough momentum to accomplish a complete description of the structure of the singular set in ℝ 3 . A surprising fact in ℝ 3 is that although can converge at singularities to each of the harmonic polynomials it may not converge to any of the non-axially-symmetric harmonic polynomials α ((1+ δ ) x 2 +(1− δ ) y 2 −2 z 2 ) with δ ≠1/2. We also prove the existence of stable singularities in ℝ 3 .

We prove that suitable weak solutions of the two-dimensional steady capillary gravity water wave problem (even in the presence of vorticity) are smooth. On a technical level, solutions are closely related to critical points of the Mumford–Shah functional, so that our main task is to exclude cusps pointing into the water phase. We prove that cusps do not exist, and that the free surface is smooth.

This paper contains a new approach to regularity and singularity of the obstacle problem: by means of an epiperimetric inequality and a monotonicity formula an energy decay estimate is derived. As a consequence, the increase in the solution's homogeneity when passing to a smaller ball can be estimated. This leads to uniqueness of blow-up limits and regularity in that order.[PUBLICATION ABSTRACT]

Parasitic two-level tunnelling systems originating from structural material defects affect the functionality of various microfabricated devices by acting as a source of noise. In particular, superconducting quantum bits may be sensitive to even single defects when these reside in the tunnel barrier of the qubit’s Josephson junctions, and this can be exploited to observe and manipulate the quantum states of individual tunnelling systems. Here, we detect and fully characterize a system of two strongly interacting defects using a novel technique for high-resolution spectroscopy. Mutual defect coupling has been conjectured to explain various anomalies of glasses, and was recently suggested as the origin of low-frequency noise in superconducting devices. Our study provides conclusive evidence of defect interactions with full access to the individual constituents, demonstrating the potential of superconducting qubits for studying material defects. All our observations are consistent with the assumption that defects are generated by atomic tunnelling. Material defects create spurious two-level systems that are a source of noise in nanostructured devices. Lisenfeld et al. use a superconducting qubit to perform high-resolution defect spectroscopy, providing direct evidence of quantum coherent interaction between two defects.

Solid-state quantum coherent devices are quickly progressing. Superconducting circuits, for instance, have already been used to demonstrate prototype quantum processors comprising a few tens of quantum bits. This development also revealed that a major part of decoherence and energy loss in such devices originates from a bath of parasitic material defects. However, neither the microscopic structure of defects nor the mechanisms by which they emerge during sample fabrication are understood. Here, we present a technique to obtain information on locations of defects relative to the thin film edge of the qubit circuit. Resonance frequencies of defects are tuned by exposing the qubit sample to electric fields generated by electrodes surrounding the chip. By determining the defect’s coupling strength to each electrode and comparing it to a simulation of the field distribution, we obtain the probability at which location and at which interface the defect resides. This method is applicable to already existing samples of various qubit types, without further on-chip design changes. It provides a valuable tool for improving the material quality and nano-fabrication procedures towards more coherent quantum circuits.

In structurally disordered solids, some atoms or small groups of atoms are able to quantum mechanically tunnel between two nearly equivalent sites. These atomic tunneling systems have been identified as the cause of various low-temperature anomalies of bulk glasses and as a source of decoherence of superconducting qubits where they are sparsely present in the disordered oxide barrier of Josephson junctions. We demonstrated experimentally that minute deformation of the oxide barrier changes the energies of the atomic tunneling systems, and we measured these changes by microwave spectroscopy of the superconducting qubit through coherent interactions between these two quantum systems. By measuring the dependence of the energy splitting of atomic tunneling states on external strain, we verify a central hypothesis of the two-level tunneling model for disordered solids.

Recent progress with microfabricated quantum devices has revealed that an ubiquitous source of noise originates in tunneling material defects that give rise to a sparse bath of parasitic two-level systems (TLSs). For superconducting qubits, TLSs residing on electrode surfaces and in tunnel junctions account for a major part of decoherence and thus pose a serious roadblock to the realization of solid-state quantum processors. Here, we utilize a superconducting qubit to explore the quantum state evolution of coherently operated TLSs in order to shed new light on their individual properties and environmental interactions. We identify a frequency-dependence of TLS energy relaxation rates that can be explained by a coupling to phononic modes rather than by anticipated mutual TLS interactions. Most investigated TLSs are found to be free of pure dephasing at their energy degeneracy points, around which their Ramsey and spin-echo dephasing rates scale linearly and quadratically with asymmetry energy, respectively. We provide an explanation based on the standard tunneling model, and identify interaction with incoherent low-frequency (thermal) TLSs as the major mechanism of the pure dephasing in coherent high-frequency TLS.

AbstractObjectiveTo determine the effect of a novel brief general practitioner (GP)-led narrative exposure intervention on post-traumatic stress disorder (PTSD) symptoms after intensive care.DesignMulticentre, observer blind, randomised controlled trial (PICTURE).SettingPrimary care in 319 general practices across Germany.Participants319 adults (18-85 years) who have survived critical illness with symptoms of PTSD, discharged from intensive care and randomised to receive the intervention (n=160) or improved usual care (n=159) from a general practitioner.InterventionsIntervention group participants had three narrative exposure consultations with a general practitioner and eight scheduled contacts with a nurse. Control group participants received improved treatment as usual based on the German PTSD guideline.Main outcome measuresThe primary clinical outcome was self-reported PTSD symptoms using the Post-Traumatic Diagnostic Scale for DSM-5 (PDS-5, range 0-80, higher scores indicating more severe symptoms) at six months. The minimal clinically important difference was six points. Secondary outcomes included changes in depression, anxiety, patient activation, health related quality of life and disability at six and 12 months.ResultsBetween 21 October 2018 and 18 January 2023, 1283 patients discharged from an intensive care unit were screened for PTSD symptoms. 319 study participants were randomly assigned either to the control group (n=159) or the intervention group (n=160). The mean patient age was 57.7 years (standard deviation (SD) 12.7), and 61% of participants were male. The mean baseline PDS-5 score was 30.6 (SD 13.3) in both groups. 271 (85%) study participants completed follow-up assessment after six months and 247 (77%) after 12 months. The intervention effect showed a mean between-group difference in the PDS-5 score of 4.7 points ((95% confidence interval 1.6 to 7.8); P=0.003, Cohen’s d=0.37)) at six months and 5.4 points ((1.8 to 9.0); P=0.003, Cohen’s d=0.41)) at 12 months. Among secondary outcomes, patients in the intervention group had greater improvements in depression, health related quality of life, and disability.ConclusionsIn adults with symptoms of PTSD after critical illness, a brief narrative exposure intervention was feasible and showed a reduction of symptoms, which was less than the predefined minimal clinically important difference. The effect was found to be sustained at 12 months’ follow-up. These findings support the further evaluation of this intervention in primary care.Trial registrationClinicalTrials.gov, NCT03315390; DRKS-ID DRKS00012589

An amendment to this paper has been published and can be accessed via a link at the top of the paper.An amendment to this paper has been published and can be accessed via a link at the top of the paper.