Trainability Analysis of Quantum Optimization Algorithms from a Bayesian Lens

The Quantum Approximate Optimization Algorithm (QAOA) is an extensively studied variational quantum algorithm utilized for solving optimization problems on near-term quantum devices. A significant focus is placed on determining the effectiveness of training the $n$-qubit QAOA circuit, i.e., whether the optimization error can converge to a constant level as the number of optimization iterations scales polynomially with the number of qubits. In realistic scenarios, the landscape of the corresponding QAOA objective function is generally non-convex and contains numerous local optima. In this work, motivated by the favorable performance of Bayesian optimization in handling non-convex functions, we theoretically investigate the trainability of the QAOA circuit through the lens of the Bayesian approach. This lens considers the corresponding QAOA objective function as a sample drawn from a specific Gaussian process. Specifically, we focus on two scenarios: the noiseless QAOA circuit and the noisy QAOA circuit subjected to local Pauli channels. Our first result demonstrates that the noiseless QAOA circuit with a depth of $\tilde{\mathcal{O}}\left(\sqrt{\log n}\right)$ can be trained efficiently, based on the widely accepted assumption that either the left or right slice of each block in the circuit forms a local 1-design. Furthermore, we show that if each quantum gate is affected by a $q$-strength local Pauli channel with the noise strength range of $1/{\rm poly} (n)$ to 0.1, the noisy QAOA circuit with a depth of $\mathcal{O}\left(\log n/\log(1/q)\right)$ can also be trained efficiently. Our results offer valuable insights into the theoretical performance of quantum optimization algorithms in the noisy intermediate-scale quantum era

Association between exposure to noise and risk of hypertension: A meta-analysis of observational epidemiological studies

Background and Objective: An increasing amount of original studies suggested that exposure to noise could be associated with the risk of hypertension, but the results remain inconsistent and inconclusive. We aimed to synthesize available epidemiological evidence about the relationship between various types of noise and hypertension, and to explore the potential dose-response relationship between them in an up-to-date meta-analysis. Methods: We conducted a literature search of PubMed and Embase from these databases’ inception through December 2016 to identify observational epidemiological studies examining the association between noise and risk of hypertension. A Random-effects model was used to combine the results of included studies. Dose-response meta-analysis was conducted to examine the potential dose-response relationship. Results: Thirty-two studies (five cohort studies, one case-control study, and twenty-six cross-section Studies) involving 264,678 participants were eligible for inclusion. Pooled result showed that living or working in environment with noise exposure was significantly associated with increase risk of hypertension (OR 1.62; 95% CI: 1.40 to 1.88). We found no evidence of a curve linear association between noise and risk of hypertension. Dose-response analysis suggested that, for an increment of per 10 dB(A) of noise, the combined odds ratio of hypertension was 1.06 (95% CI: 1.04 to 1.08). Conclusions: Integrated epidemiological evidence supports the hypothesis that exposure to noise may be a risk factor of hypertension, and there is a positive dose-response association between them

Enhanced mechanical properties in β-Ti alloy aged from recrystallized ultrafine β grains

Ultrafine β grain structures with recrystallized morphologies were fabricated by severe plastic deformation and subsequent annealing in Ti-10Mo-8 V-1Fe-3.5Al alloy. The minimum mean β grain size of 480 nm was obtained for the first time as a recrystallized structure in Ti alloys. Precipitation behavior of α in subsequent aging significantly changed with decreasing the recrystallized β grain size. Both tensile strength and total ductility of the aged Ti-alloy were increased by the β grain refinement. Tensile strength of 1.6 GPa and total elongation of 9.1% were achieved in the aged specimen having the prior β grain size of 480 nm, which was attributed to its finer and more homogeneous precipitated microstructure having a mixture of nanoscale thin-plate α and globular α without side α plates along β grain boundaries

Achieving large super-elasticity through changing relative easiness of deformation modes in Ti-Nb-Mo alloy by ultra-grain refinement

Large super-elasticity approaching its theoretically expected value was achieved in Ti-13.3Nb-4.6Mo alloy having an ultrafine-grained β-phase. In-situ synchrotron radiation X-ray diffraction analysis revealed that the dominant yielding mechanism changed from dislocation slip to martensitic transformation by decreasing the β-grain size down to sub-micrometer. Different grain size dependence of the critical stress to initiate dislocation slip and martensitic transformation, which was reflected by the transition of yielding behavior, was considered to be the main reason for the large super-elasticity in the ultrafine-grained specimen. The present study clarified that ultra-grain refinement down to sub-mirometer scale made dislocation slips more difficult than martensitic transformation, leading to an excellent super-elasticity close to the theoretical limit in the β-Ti alloy

Preparation, Properties and Applications of Pre-gelatinized Starch on Starch Based Foods

With the continuous development of modified starch, people's demand for the functional characteristics, safety, and convenience of modified starch has increased significantly. Pre-gelatinized starch (PGS) is a type of starch modified by physical methods, which is a modified starch particle without obvious crystallization obtained by rapid dehydration and drying after starch gelatinization. PGS has a porous and hydrogen-bonded fracture structure, which has the advantages of good cold water solubility, strong water retention ability and high viscoelasticity. Cold water can be mixed into paste during application, eliminating the step of heating and gelatinization. Therefore, as a biodegradable raw material with excellent performance, PGS has important application value in the fields of flour products, low-temperature meat products, condiments and other leisure starch-based foods. This paper briefly introduces the definition, preparation methods, properties, and influencing factors of PGS performance, focuses on the current application status of PGS in starch-based foods, and points out the future research direction of PGS in the field of food, aiming to provide some references for promoting the application of PGS in the food industry

Research Progress on Starch Digestibility Regulated by Multi-scale Structure and Physical Modification

Starch provides essential calories for the body's vital activities, but it usually has a high glycemic index. The digestion of starch tends to lead to a steep increase in blood sugar levels, insulin resistance and health risk. The digestibility of starch is related to its multi-scale structure. The regulations of starch digestibility can be achieved by altering its multi-scale structure through the modifications. However, the physical modification has received more and more attention due to its safety, simplicity and environmental friendliness. Based on this, the digestibility of starch is outlined. The relationship between the multi-scale structure and digestive properties of starch is analyzed. The digestive properties of starch regulated by physical modifications, such as hydrothermal treatment, microwave, extrusion, high-pressure homogenization, ultrasonic, cold plasma and physical encapsulation are reviewed. The future research directions on starch digestibility are also provided

Comparative Effects of Er-Xian Decoction, Epimedium

Er-Xian Decoction (EXD), Epimedium herbs (herbs of Epimedium brevicornum Maxim, EBH), and icariin (ICA) have been proven to have estrogen-like and antiosteoporotic activity and are used for the treatment of osteoporosis, menopausal syndrome, and age-associated diseases. The present study found that EXD, EBH, and ICA treatments, emulating estrogen, significantly contributed to bone density and architecture in OVX rats and that EXD is similar to estrogen and exerts a concomitant effect on bone formation and bone resorption at the tissue level, while EBH and ICA produced bone-protective effects mainly by inhibiting bone resorption. Nevertheless, EXD, EBH, and ICA treatments manifested a fewer adverse effects on the uterus, mammary gland, and vagina compared to estrogen administrations. Among the EXD, EBH, and ICA, EXD was found to have superior efficacy and safety profile

Rotatable precipitates change the scale-free to scale dependent statistics in compressed Ti nano-pillars.

Compressed nano-pillars crackle from moving dislocations, which reduces plastic stability. Crackling noise is characterized by stress drops or strain bursts, which scale over a large region of sizes leading to power law statistics. Here we report that this "classic" behaviour is not valid in Ti-based nanopillars for a counterintuitive reason: we tailor precipitates inside the nano-pillar, which "regulate" the flux of dislocations. It is not because the nano-pillars become too small to sustain large dislocation movements, the effect is hence independent of size. Our precipitates act as "rotors": local stress initiates the rotation of inclusions, which reduces the stress amplitudes dramatically. The size distribution of stress drops simultaneously changes from power law to exponential. Rotors act like revolving doors limiting the number of passing dislocations. Hence each collapse becomes weak. We present experimental evidence for Ti-based nano-pillars (diameters between 300 nm and 2 μm) with power law distributions of crackling noise P(s) ∼ s-τ with τ ∼ 2 in the defect free or non-rotatable precipitate states. Rotors change the size distribution to P(s) ∼ exp(-s/s0). Rotors are inclusions of ω-phase that aligns under stress along slip planes and limit dislocation glide to small distances with high nucleation rates. This opens new ways to make nano-pillars more stable