Avoiding local minima in variational quantum eigensolvers with the natural gradient optimizer

We compare the BFGS optimizer, ADAM and Natural Gradient Descent (NatGrad) in the context of Variational Quantum Eigensolvers (VQEs). We systematically analyze their performance on the QAOA ansatz for the Transverse Field Ising Model (TFIM) as well as on overparametrized circuits with the ability to break the symmetry of the Hamiltonian. The BFGS algorithm is frequently unable to find a global minimum for systems beyond about 20 spins and ADAM easily gets trapped in local minima. On the other hand, NatGrad shows stable performance on all considered system sizes, albeit at a significantly higher cost per epoch. In sharp contrast to most classical gradient based learning, the performance of all optimizers is found to decrease upon seemingly benign overparametrization of the ansatz class, with BFGS and ADAM failing more often and more severely than NatGrad. Additional tests for the Heisenberg XXZ model corroborate the accuracy problems of BFGS in high dimensions, but they reveal some shortcomings of NatGrad as well. Our results suggest that great care needs to be taken in the choice of gradient based optimizers and the parametrization for VQEs.Comment: 16 pages, 6 figures, 1 tabl

Backpropagation scaling in parameterised quantum circuits

The discovery of the backpropagation algorithm ranks among one of the most important moments in the history of machine learning, and has made possible the training of large-scale neural networks through its ability to compute gradients at roughly the same computational cost as model evaluation. Despite its importance, a similar backpropagation-like scaling for gradient evaluation of parameterised quantum circuits has remained elusive. Currently, the best known method requires sampling from a number of circuits that scales with the number of circuit parameters, making training of large-scale quantum circuits prohibitively expensive in practice. Here we address this problem by introducing a class of structured circuits that admit gradient estimation with significantly fewer circuits. In the simplest case -- for which the parameters feed into commuting quantum gates -- these circuits allow for fast estimation of the gradient, higher order partial derivatives and the Fisher information matrix, and are not expected to suffer from the problem of vanishing gradients. Moreover, classes of parameterised circuits exist for which the scaling of gradient estimation is in line with classical backpropagation, and can thus be trained at scale. In a toy classification problem on 16 qubits, such circuits show competitive performance with other methods, while reducing the training cost by about two orders of magnitude.Comment: Comments welcom

Longevity of immediate rehabilitation with direct metal-wire reinforced composite fixed partial dentures.

OBJECTIVES This study aimed to analyze the longevity of direct metal-wire reinforced composite fixed partial dentures (MRC-FPD) and factors influencing their survival and success. METHODS Within one private practice 513 MRC-FPD were directly applied. The preparation of a proximal cavity in abutment teeth was not limited. MRC-FPD were reinforced by one to three metal-wires. At the last follow-up MRC-FPD were considered successful, if they were still in function without any need of therapy. MRC-FPD were considered as survived, if they were repaired or replaced. Multi-level Cox proportional hazard models were used to evaluate the association between clinical factors and time. RESULTS Mean follow-up period (range) was 59(2-249) months. Seventy-three bridges did not survive (cumulative survival rate(CSR):86%) and further 129 bridges had received a restorative follow-up treatment (CSR:61%). AFR was 2.2% for survival and 8.6% for success. In multivariate analysis MRC-FPD with> 1 wire showed a up to 2.3x higher failure rate than MRC-FPD with one wire(p ≤ 0.023). Dentist's experience in designing MRC-FDP (p ≤ 0.017), patient's caries risk (p ≤ 0.040) and bruxism (p = 0.033) significantly influenced the failure rate: the more experience, the lower caries risk and bruxism, the lower the failure rate. SIGNIFICANCE For directly prepared metal-wire reinforced composite bridges high survival and moderate success rates were observed. MRC-FPD might, thus, be an immediate, short- and medium-term solution for replacing missing teeth. However, several factors on the levels of practice (dentist's experience in designing MRC-FDP), patient (bruxism, caries risk) and restoration (number of wires) were identified as significant predictors for the failure rate. The study was registered in the German Clinical Trials Register (DRKS-ID: DRKS00021576)

Efficacy of nano-hydroxyapatite on caries prevention-a systematic review and meta-analysis.

Introduction/objectives: The review systematically explored in vivo or in situ studies investigating the efficacy of nano-hydroxyapatite (nHA) to reduce initiation of or to remineralize initial caries lesions. Data: Prospective controlled (non-)randomized clinical trials investigating the efficacy of a nHA compared to any other (placebo) treatment or untreated/standard control. Sources: Three electronic databases (Central Cochrane, PubMed-MEDLINE, Ovid EMBASE) were screened. Outcomes were, e.g., ICDAS score, laser fluorescence, enamel remineralization rate, mineral loss, and lesion depth. No language or time restrictions were applied. Risk of bias and level of evidence were graded using the Risk of Bias 2.0 tool and GRADE profiler. Study selection/results: Five in vivo (and 5 in situ) studies with at least 633 teeth (1031 specimens) being assessed in more than 420 (95) patients were included. No meta-analysis could be performed for in vivo studies due to the high heterogeneity of the study designs and the variety of outcomes. In situ studies indicate that under demineralization conditions, NaF was able to hinder demineralization, whereas nHA did not; simultaneously, nHA did not differ from the fluoride-free control. In contrast, under remineralizing conditions, nHA and NaF show the same remineralizing potential. However, the level of evidence was very low. Furthermore, six studies showed a high risk of bias, and six studies were funded/published by the manufacturers of the tested products. Conclusion: The low number of clinical studies, the relatively short follow-up periods, the high risks of bias, and the limiting grade of evidence do not allow for conclusive evidence on the efficacy of nHA. Clinical relevance: No conclusive evidence on the efficacy of nHA could be obtained based on the low number of clinical studies, the relatively short follow-up periods, the high risks of bias, the limiting grade of evidence, and study conditions that do not reflect the everyday conditions

Root canal morphology of the mandibular second premolar: a systematic review and meta- analysis

Background: The aim of this paper was to systematically review the root canal configuration (RCC) and morphology literature of the mandibular second premolar (Mn2P). Methods: Systematic research of five electronic databases was performed to identify published literature concerning the root canal configuration (RCC) of the Mn2P up through July 2020. Studies were selected according to predefined search terms and keywords inclusion criteria: “root canal configuration”, “root canal system”, “root canal morphology”, “mandibular second premolar”, “mandibular premolars”, “morphology” and “anatomy”. Further possible studies were identified by cross-referencing and screening the bibliographies of the selected articles. Results: From 1622 retrieved studies, 44 studies investigating the internal morphology of 17,839 Mn2Ps were included. Most examined Mn2Ps were single-rooted (89.5–100%); two-rooted (0.1–8%) and three-rooted (0.1–3.5%) Mn2Ps at lower frequency. Most frequent RCCs reported were 1–1–1/1 (55.3–99.6%) followed by 1–1–2/2 (0.5–57%) and 2–2–2/2 (0.6–18%). The meta-analysis of seven studies demonstrated that a significantly higher number of RCC type 1–2–1/1 (OR [95%CI] = 2.05 [1.27, 3.33]) and 2–2–2/2 (OR [95%CI] = 2.32 [0.65, 8.63]) were observed in male than in female patients. Conclusions: Different RCC research methods have been reported. Whereas clearing and radiographs were com- monly used in the past, CBCT has been prevalent in recent years. A globally high frequency of a 1–1–1/1 RCC in the Mn2P has been reported. Nevertheless, the probability that different, more complicated RCCs can appear in Mn2Ps should not be underestimated and, thus, should be taken into consideration when making decisions during an endo- dontic treatment

Systematic review and meta-analysis on physical barriers to prevent root dentin demineralization.

The present review systematically analyzed in vitro and in situ studies investigating physical diffusion barriers (sealants, desensitizer or adhesives) to prevent the development or the progression of root (dentin) demineralization. Three electronic databases (PubMed-Medline, CENTRAL, Ovid-EMBASE) were screened for studies from 1946 to 2022. Cross-referencing was used to identify further articles. Article selection and data abstraction were done in duplicate. Languages were not restricted. The type of outcome was not restricted, and their mean differences (MD) were calculated using fixed- or random-effects models. Risk of Bias was graded using Risk of Bias 2.0 tool. From 171 eligible studies, 34 were selected for full-text analysis evaluating 69 different materials, and 17 studies-still evaluating 36 different materials-were included (3 in situ and 14 in vitro). Ten studies evaluated desensitizers; 8 adhesives; and 1 infiltration. Meta-analyses were possible for all 17 studies. Meta-analyses revealed that lesion depth after no treatment was significantly higher than after the application of single-step adhesives (MD[95%CI] = - 49.82[- 69.34; - 30.30]) and multi-step adhesives (MD[95%CI]=-60.09 [-92.65, -27.54]). No significant differences in the lesion depth increase between single- and multi-step adhesives could be observed (MD[95%CI]=30.13 [-21.14, 81.39]). Furthermore, compared to no treatment the increase of the lesion depth was significantly hampered using desensitizers (MD[95%CI] = - 38.02[- 51.74; - 24.31]). Furthermore, the included studies presented unclear or high risk. A physical diffusion barrier can significantly hamper the increase of lesion depth under cariogenic conditions. Furthermore, multi-step adhesives seem not to be more effective than single-step adhesives. However, this conclusion is based on only few in vitro and in situ studies

Success and complication rates of non-precious alloy telescopic crowns in a general dental practice.

OBJECTIVES This retrospective, single-center, practice-based cohort study aimed to analyze factors associated with the success of removable partial dentures retained by telescopic crowns (TRPD). MATERIALS AND METHODS TRPD which were placed in a single practice of a practice-based research network were analyzed. Data from 139 patients (age (SD): 66 (11) years; 66 female) with 174 TRPD including 488 non-precious alloy telescopic crowns (TC) between 2004 and 2016 were included. TC without any technical complication were considered as successful, and as survived, if they were still in function at the last check-up. Multilevel Cox proportional hazard models were used to evaluate the association between clinical factors and time until failure. RESULTS Within a mean follow-up period (SD) of 4.2 (3.3) years (min-max: 1 day-12 years), 372 (76%) TC (AFR5years,TC-level: 5.0%) as well as 136 (87%) TRPD (AFR5years,TRPD-level: 5.1%) ("worst-case scenario") and 150 (86%) TRPD (AFR5years,TRPD-level: 3.4%) ("best-case scenario") were considered as successful. The main failure types were recementation (n = 39), endodontic treatment (n = 36), and extraction (n = 35). TC in male patients showed 1.6 times higher risk for failure than in female patients (95%CI: 1.1-2.4; p = 0.023). TC on premolars showed 2.2 times higher risk for failure than on incisors (95%CI: 1.1-5.0; p = 0.023) and TC in dentures with ≤ 3TC showed 2.1 times higher risk for failure than TC in dentures with > 3TC (1.3-3.4; p = 0.042). Furthermore, TC on the most distal tooth in an arch showed 2.4 times higher risk for failure than TC on a more mesial tooth (1.5-3.8; p < 0.001). CONCLUSION For removable partial dentures retained by telescopic crowns, high success rates could be found after up to 12 years. Patient-level and tooth-level factors were significantly associated with failure. CLINICAL RELEVANCE For removable partial dentures retained by telescopic crowns, high success rates could be found after up to 12 years. Patient-level and tooth-level factors were significantly associated with failure

Demineralization Inhibitory Effects of Highly Concentrated Fluoride Dentifrice and Fluoride Gels/Solutions on Sound Dentin and Artificial Dentin Caries Lesions in vitro

Objectives: The aim of this in vitro study was to compare the demineralization inhibitory effect of gels/solutions used in combination with either standard or highly fluoridated dentifrices on sound dentin as well as on artificial dentin carieslike lesions. Methods: Bovine dentin specimens (n = 240) with two different surfaces each (sound [ST] and artificial caries lesion [DT]) were prepared and randomly allocated to twelve groups. Weekly interventions during pH-cycling (28 days, 6 × 120 min demineralization/day) were: the application of gels/solutions containing amine fluoride/sodium fluoride (12,500 ppm F [ppm]; pH = 4.4; AmF); NaF (12,500 ppm; pH = 6.6; NaF1); NaF (12,500 ppm; pH = 6.3; NaF2); silver diamine fluoride (14,200 ppm; pH = 8.7; SDF); acidulated phosphate fluoride (12,500 ppm; pH = 3.8; APF), and no intervention (standard control; S). Furthermore, half of the specimens in each group were brushed (10 s; twice per day) with dentifrice slurries containing either 1,450 ppm (e.g., AmF1450) or 5,000 ppm (e.g., AmF5000). Differences in integrated mineral loss (ΔΔZ) and lesion depth (ΔLD) were calculated between values before and after pH-cycling using transversal microradiography. Results: After pH-cycling Ss showed significantly increased ΔZDT and LDDT values, indicating further demineralization. In contrast, except for one, all groups including fluoride gels/solutions showed significantly decreased ΔZDT values. Additional use of most fluoride gels/solutions significantly enhanced mineral gain, mainly in the surface area; however, acidic gels/solutions seemed to have negative effects on lesion depths. Significance: Under the present pH-cycling conditions the highly fluoridated dentifrice significantly reduced caries progression and additional application of nearly all of the fluoride gels/solutions resulted in remineralization. However, there was no difference in the remineralizing capacity of fluoride gels/solutions when used in combination with either standard or highly fluoridated dentifrices

Posterior ceramic versus metal restorations: A systematic review and meta-analysis.

OBJECTIVES The goal of this systemic review and meta-analysis was to evaluate the longevity of indirect adhesively-luted ceramic compared to conventionally cemented metal single tooth restorations. DATA Randomized controlled trials (RCT) investigating indirect adhesively-luted ceramic restorations compared to metal or metal-based cemented restorations in permanent posterior teeth. SOURCES Three electronic databases (PubMed, CENTRAL (Cochrane) and Embase) were screened. No language or time restrictions were applied. Study selection, data extraction and quality assessment were done in duplicate. Risk of Bias and level of evidence was graded using Risk of Bias 2.0 tool and Grade Profiler 3.6. RESULTS A total of 3056 articles were found by electronic databases. Finally, four RCTs were selected. Overall, 443 restorations of which 212 were adhesively-luted ceramic restorations and 231 conventionally cemented metal restorations have been placed in 314 patients (age: 22-72 years). The highest annual failure rates were found for ceramic restorations ranging from 2.1% to 5.6%. Lower annual failure rates were found for metal (gold) restorations ranging from 0% to 2.1%. Meta-analysis could be performed for adhesively-luted ceramic vs. conventionally cemented metal restorations. Conventionally cemented metal restoration showed a significantly lower failure rate than adhesively-luted ceramic ones (visual-tactile assessment: Risk Ratio (RR)[95%CI]=0.31[0.16,0.57], low level of evidence). Furthermore, all studies showed a high risk of bias. CONCLUSION Conventionally cemented metal restorations revealed significantly lower failure rates compared to adhesively-luted ceramic ones, although the selected sample was small and with medium follow-up periods with high risks of bias