General guarantees for randomized benchmarking with random quantum circuits

In its many variants, randomized benchmarking (RB) is a broadly used technique for assessing the quality of gate implementations on quantum computers. A detailed theoretical understanding and general guarantees exist for the functioning and interpretation of RB protocols if the gates under scrutiny are drawn uniformly at random from a compact group. In contrast, many practically attractive and scalable RB protocols implement random quantum circuits with local gates randomly drawn from some gate-set. Despite their abundance in practice, for those non-uniform RB protocols, general guarantees under experimentally plausible assumptions are missing. In this work, we derive such guarantees for a large class of RB protocols for random circuits that we refer to as filtered RB. Prominent examples include linear cross-entropy benchmarking, character benchmarking, Pauli-noise tomography and variants of simultaneous RB. Building upon recent results for random circuits, we show that many relevant filtered RB schemes can be realized with random quantum circuits in linear depth, and we provide explicit small constants for common instances. We further derive general sample complexity bounds for filtered RB. We show filtered RB to be sample-efficient for several relevant groups, including protocols addressing higher-order cross-talk. Our theory for non-uniform filtered RB is, in principle, flexible enough to design new protocols for non-universal and analog quantum simulators.Comment: 77 pages, 3 figures. Accepted for a talk at QIP 202

The Bigflower Tellima (Tellima grandiflora), naturalized in the Ruhr Area

Tellima grandiflora, die Falsche Alraunwurzel, eine Zierpflanze aus Nordamerika, wird in Gärten als Bodendecker in schattigen Bereichen gepflanzt. Aus solchen Anpflanzungen heraus verwildert die Art und ist in der Lage, sich bevorzugt an feuchten und schattigen Standorten einzubürgern, wie dies an einigen Stellen im Ruhrgebiet geschehen ist.Tellima grandiflora (Fringecups, Bigflower Tellima) is a widely grown garden plant originating from North America.This species is considered to be a potential garden escape and can become naturalized in moist and shady environments, which has happened for some locations in the Ruhr Area

Closed-form analytic expressions for shadow estimation with brickwork circuits

Properties of quantum systems can be estimated using classical shadows, which implement measurements based on random ensembles of unitaries. Originally derived for global Clifford unitaries and products of single-qubit Clifford gates, practical implementations are limited to the latter scheme for moderate numbers of qubits. Beyond local gates, the accurate implementation of very short random circuits with two-local gates is still experimentally feasible and, therefore, interesting for implementing measurements in near-term applications. In this work, we derive closed-form analytical expressions for shadow estimation using brickwork circuits with two layers of parallel two-local Haar-random (or Clifford) unitaries. Besides the construction of the classical shadow, our results give rise to sample-complexity guarantees for estimating Pauli observables. We then compare the performance of shadow estimation with brickwork circuits to the established approach using local Clifford unitaries and find improved sample complexity in the estimation of observables supported on sufficiently many qubits.Comment: 15+12 pages, several figures; v2: small improvements and new examples. Close to published versio

Seismotectonics of the Horseshoe Abyssal Plain and Gorringe Bank, eastern Atlantic Ocean - constraints from ocean-bottom seismometer data

At the eastern end of the Azores-Gloria transform fault system to the southwest of Portugal, the plate boundary between Africa and Iberia is a region where deformation is accommodated over a wide tectonically-active area. The region has unleashed large earthquakes and tsunamis, including the Mw ~ 8.5 Great Lisbon earthquake of 1755. Although the source region of the 1755 earthquake is still disputed, most proposals include a source location in the vicinity of the Horseshoe Abyssal Plain (HAP), which is bounded by the 5000 m high Gorringe Bank (GB). In this study we characterise seismic activity in the region using data recorded by two local networks of ocean-bottom seismometers (OBS). The networks were deployed in the eastern HAP and at the GB. The dataset allowed the detection of 160 local earthquakes. These earthquakes cluster around the GB, to the SW of Cabo Sao Vicente, and in the HAP. Focal depths indicate deep-seated earthquakes, with depths increasing from 20-35 km (mean of 26.1 ± 7.2 km) at the GB to 15-45 km (mean 31.5 km ± 10.5 km) under the HAP. Seismic activity thus extends down to levels that are deeper than those mapped by active seismic profiling, with the majority of events occurring within the mantle. Thermal modelling suggests that temperatures of approximately 600 °C characterise the base of the seismogenic brittle lithosphere at ~45 km depth. The large source depth and thermal structure supports previous suggestions that catastrophic seismic rupture through the lithospheric mantle may indeed occur in the area

Efficient Unitary Designs with a System-Size Independent Number of Non-Clifford Gates

Many quantum information protocols require the implementation of random unitaries. Because it takes exponential resources to produce Haar-random unitaries drawn from the full n-qubit group, one often resorts to t-designs. Unitary t-designs mimic the Haar-measure up to t-th moments. It is known that Clifford operations can implement at most 3-designs. In this work, we quantify the non-Clifford resources required to break this barrier. We find that it suffices to inject O(t4log2(t)log(1/ε)) many non-Clifford gates into a polynomial-depth random Clifford circuit to obtain an ε-approximate t-design. Strikingly, the number of non-Clifford gates required is independent of the system size – asymptotically, the density of non-Clifford gates is allowed to tend to zero. We also derive novel bounds on the convergence time of random Clifford circuits to the t-th moment of the uniform distribution on the Clifford group. Our proofs exploit a recently developed variant of Schur-Weyl duality for the Clifford group, as well as bounds on restricted spectral gaps of averaging operators

The German version of the Posttraumatic Stress Disorder Checklist for DSM-5 (PCL-5): psychometric properties and diagnostic utility

Background: The Posttraumatic Stress Disorder (PTSD) Checklist (PCL, now PCL-5) has recently been revised to reflect the new diagnostic criteria of the disorder. Methods: A clinical sample of trauma-exposed individuals (N = 352) was assessed with the Clinician Administered PTSD Scale for DSM-5 (CAPS-5) and the PCL-5. Internal consistencies and test-retest reliability were computed. To investigate diagnostic accuracy, we calculated receiver operating curves. Confirmatory factor analyses (CFA) were performed to analyze the structural validity. Results: Results showed high internal consistency (α = .95), high test-retest reliability (r = .91) and a high correlation with the total severity score of the CAPS-5, r = .77. In addition, the recommended cutoff of 33 on the PCL-5 showed high diagnostic accuracy when compared to the diagnosis established by the CAPS-5. CFAs comparing the DSM-5 model with alternative models (the three-factor solution, the dysphoria, anhedonia, externalizing behavior and hybrid model) to account for the structural validity of the PCL-5 remained inconclusive. Conclusions: Overall, the findings show that the German PCL-5 is a reliable instrument with good diagnostic accuracy. However, more research evaluating the underlying factor structure is needed

Роль метода электрофоретического осаждения в создании биокомпозита на основе слоев гидроксиапатити и наночастиц серебра

Работа посвящена созданию многофункционального биокомпозита, состоящего из покрытия на основе гидроксиапатита (ГА) и наночастиц серебра с использованием высокотехнологичных методов обработки поверхности. Высокочастотное магнетронное распыление использовалось для получения слоев ГА покрытия с различной толщиной и структурой на титане и наночастицах серебра. Для получения антибактериального слоя наночастиц серебра использовался метод электрофоретического осаждения. Наночастицы серебра имели сферическую форму с диаметром 70±20 нм и[zeta] -потенциалом -20 мВ. Дифракционные картины биокомпозитов выявили пики кристаллического ГА и серебра (Ag). Так же установлено, что наночастицы серебра являются кристаллическими с размером кристаллитов 14 нм

factor structure and symptom profiles

Background: The proposed ICD-11 criteria for trauma-related disorders define posttraumatic stress disorder (PTSD) and complex posttraumatic stress disorder (cPTSD) as separate disorders. Results of previous studies support the validity of this concept. However, due to limitations of existing studies (e.g. homogeneity of the samples), the present study aimed to test the construct validity and factor structure of cPTSD and its distinction from PTSD using a heterogeneous trauma-exposed sample. Method: Confirmatory factor analyses (CFAs) were conducted to explore the factor structure of the proposed ICD-11 cPTSD diagnosis in a sample of 341 trauma-exposed adults (n = 191 female, M = 37.42 years, SD = 12.04). In a next step, latent profile analyses (LPAs) were employed to evaluate predominant symptom profiles of cPTSD symptoms. Results: The results of the CFA showed that a six-factor structure (i.e. symptoms of intrusion, avoidance, hyperarousal and symptoms of affective dysregulation, negative self-concept, and interpersonal problems) fits the data best. According to LPA, a four-class solution optimally characterizes the data. Class 1 represents moderate PTSD and low symptoms in the specific cPTSD clusters (PTSD group, 30.4%). Class 2 showed low symptom severity in all six clusters (low symptoms group, 24.1%). Classes 3 and 4 both exhibited cPTSD symptoms but differed with respect to the symptom severity (Class 3: cPTSD, 34.9% and Class 4: severe cPTSD, 10.6%). Conclusions: The findings replicate previous studies supporting the proposed factor structure of cPTSD in ICD-11. Additionally, the results support the validity and usefulness of conceptualizing PTSD and cPTSD as discrete mental disorders

Using the dendro-climatological signal of urban trees as a measure of urbanization and urban heat island

Using dendroclimatological techniques this study investigates whether inner city tree-ring width (TRW) chronologies from eight tree species (ash, beech, fir, larch, lime, sessile and pedunculate oak, and pine) are suitable to examine the urban heat island of Berlin, Germany. Climate-growth relationships were analyzed for 18 sites along a gradient of increasing urbanization covering Berlin and surrounding rural areas. As a proxy for defining urban heat island intensities at each site, we applied urbanization parameters such as building fraction, impervious surfaces, and green areas. The response of TRW to monthly and seasonal air temperature, precipitation, aridity, and daily air-temperature ranges were used to identify climate-growth relationships. Trees from urban sites were found to be more sensitive to climate compared to trees in the surrounding hinterland. Ring width of the deciduous species, especially ash, beech, and oak, showed a high sensitivity to summer heat and drought at urban locations (summer signal), whereas conifer species were found suitable for the analysis of the urban heat island in late winter and early spring (winter signal). The summer and winter signals were strongest in tree-ring chronologies when the urban heat island intensities were based on an area of about 200 m to 3000 m centered over the tree locations, and thus reflect the urban climate at the scale of city quarters. For the summer signal, the sensitivity of deciduous tree species to climate increased with urbanity. These results indicate that urban trees can be used for climate response analyses and open new pathways to trace the evolution of urban climate change and more specifically the urban heat island, both in time and space

Confirmatory factor analysis of the Clinician-Administered PTSD Scale (CAPS-5) based on DSM-5 vs. ICD-11 criteria

Introduction Many studies have investigated the latent structure of the DSM-5 criteria for posttraumatic stress disorder (PTSD). However, most research on this topic was based on self-report data. We aimed to investigate the latent structure of PTSD based on a clinical interview, the Clinician-Administered PTSD Scale (CAPS-5). Method A clinical sample of 345 participants took part in this multi-centre study. Participants were assessed with the CAPS-5 and the Posttraumatic Stress Disorder Checklist (PCL-5). We evaluated eight competing models of DSM-5 PTSD symptoms and three competing models of ICD-11 PTSD symptoms. Results The internal consistency of the CAPS-5 was replicated. In CFAs, the Anhedonia model emerged as the best fitting model within all tested DSM-5 models. However, when compared with the Anhedonia model, the non-nested ICD-11 model as a less complex three-factor solution showed better model fit indices. Discussion We discuss the findings in the context of earlier empirical findings as well as theoretical models of PTSD