Variational data encoding and correlations in quantum-enhanced machine learning

Leveraging the extraordinary phenomena of quantum superposition and quantum correlation,quantum computing offers unprecedented potential for addressing challenges beyond the reach of classical computers.This paper tackles two pivotal challenges in the realm of quantum computing:firstly,the development of an effective encoding protocol for translating classical data into quantum states,a critical step for any quantum computation.Different encoding strategies can significantly influence quantum computer performance.Secondly,we address the need to counteract the inevitable noise that can hinder quantum acceleration.Our primary contribution is the introduction of a novel variational data encoding method,grounded in quantum regression algorithm models.By adapting the learning concept from machine learning,we render data encoding a learnable process.This allowed us to study the role of quantum correlation in data encoding.Through numerical simulations of various regression tasks,we demonstrate the efficacy of our variational data encoding,particularly post-learning from instructional data.Moreover,we delve into the role of quantum correlation in enhancing task performance,especially in noisy environments.Our findings underscore the critical role of quantum correlation in not only bolstering performance but also in mitigating noise interference,thus advancing the frontier of quantum computing.

Study of baryon number transport dynamics and strangeness conservation effects using Ω-hadron correlations

In nuclear collisions at RHIC energies, an excess of Ω hyperons over ■ is observed, indicating that Ω has a net baryon number despite s and s quarks being produced in pairs. The baryon number in Ω may have been transported from the incident nuclei and/or produced in the baryon-pair production of Ω with other types of anti-hyperons such as Ξ. To investigate these two scenarios, we propose to measure the correlations between Ω and K and between Ω and anti-hyperons. We use two versions, the default and string-melting, of a multiphase transport(AMPT) model to illustrate the method for measuring the correlation and to demonstrate the general shape of the correlation. We present the Ω-hadron correlations from simulated Au+Au collisions at ■ =7.7 and 14.6 Ge V and discuss the dependence on the collision energy and on the hadronization scheme in these two AMPT versions. These correlations can be used to explore the mechanism of baryon number transport and the effects of baryon number and strangeness conservation on nuclear collisions.

Dynamics of Non-Markovianity, Quantum Correlations and Information Scrambling of Three Qubits Systems Interacting via Rashba Interaction

The behavior of the quantum correlations, information scrambling and the non-Markovianity of three entangling qubits systems via Rashba is discussed. The results showed that, the three physical quantities oscillate between their upper and lower bounds, where the number of oscillations increases as the Rashba interaction strength increases. The exchanging rate of these three quantities depends on the Rashba strength, and whether the entangled state is generated via direct/indirect interaction. Moreover, the coherence parameter can be used as a control parameter to maximize or minimize the three physical quantities.

Evaluation of frictional pressure drop correlations for air-water and air-oil two-phase flow in pipeline-riser system

Accurate prediction of the frictional pressure drop is important for the design and operation of subsea oil and gas transporting system considering the length of the pipeline. The applicability of the correlations to pipeline-riser flow needs evaluation since the flow condition in pipeline-riser is quite different from the original data where they were derived from. In the present study, a comprehensive evaluation of 24prevailing correlation in predicting frictional pressure drop is carried out based on experimentally measured data of air-water and air-oil two-phase flows in pipeline-riser. Experiments are performed in a system having different configuration of pipeline-riser with the inclination of the downcomer varied from-2°to-5°to investigated the effect of the elbow on the frictional pressure drop in the riser. The inlet gas velocity ranges from 0.03 to 6.2 m/s, and liquid velocity varies from 0.02 to 1.3 m/s. A total of885 experimental data points including 782 on air-water flows and 103 on air-oil flows are obtained and used to access the prediction ability of the correlations. Comparison of the predicted results with the measured data indicate that a majority of the investigated correlations under-predict the pressure drop on severe slugging. The result of this study highlights the requirement of new method considering the effect of pipe layout on the frictional pressure drop.

Quantum correlations and entanglement in coupled optomechanical resonators with photon hopping via Gaussian interferometric power analysis

Quantum correlations that surpass entanglement are of great importance in the realms of quantum information processing and quantum computation.Essentially,for quantum systems prepared in pure states,it is difficult to differentiate between quantum entanglement and quantum correlation.Nonetheless,this indistinguishability is no longer holds for mixed states.To contribute to a better understanding of this differentiation,we have explored a simple model for both generating and measuring these quantum correlations.Our study concerns two macroscopic mechanical resonators placed in separate Fabry–Pérot cavities,coupled through the photon hopping process.this system offers a comprehensively way to investigate and quantify quantum correlations beyond entanglement between these mechanical modes.The key ingredient in analyzing quantum correlation in this system is the global covariance matrix.It forms the basis for computing two essential metrics:the logarithmic negativity(E_(N)^(m))and the Gaussian interferometric power(P_(G)^(m)).These metrics provide the tools to measure the degree of quantum entanglement and quantum correlations,respectively.Our study reveals that the Gaussian interferometric power(P_(G)^(m))proves to be a more suitable metric for characterizing quantum correlations among the mechanical modes in an optomechanical quantum system,particularly in scenarios featuring resilient photon hopping.

Spatial correlations in time and frequency domains between chlorophyll-a concentration and environmental factors in the Bohai Sea

Based on the reconstructed MODIS data and ECMWF reanalysis data from 2003 to 2021,spatial correlations between chlorophyll a(Chl a)and sea surface temperature(SST),photosynthetically available radiation(PAR),aerosol optical thickness(AOT),and wind speed(WS)in the Bohai Sea were analyzed from the perspective of time domain and frequency domain.Results indicate that the frequency domain analysis was more conducive to revealing the correlations between Chl a and environmental factors.The spatial pattern of time-domain correlations was similar to the isobaths of the Bohai Sea,which was positive in shallow waters and negative in deep waters for SST,PAR,and AOT,and was reversed for WS.Frequency-domain correlations were obtained by performing Fourier Transform and were higher than correlations in time domain.The spatial distributions indicated that the effects of SST and PAR on Chl a were greater than AOT and WS in the Bohai Sea.Additionally,cross-spectrum analysis was applied to explore the response relationships.A depth-dependent pattern was shown in correlations and time lags,indicating that the influential mechanism of environmental factors on Chl-a concentration is related to seawater depth.

Spatial correlations in ground motion intensity measuring from the 2023 Türkiye earthquake

When evaluating an area's seismic risk or resilience,it is necessary to use the spatial correlation to analyze the ground motion parameters of multiple sites together in an earthquake.These two large earthquakes in Türkiye provided the possibility for spatial correlation analysis of ground motion intensity measurements in this area.Based on the strong motion records provided by The Disaster and Emergency Management Authority of Türkiye(AFAD),this study uses the local ground motion prediction equation in Türkiye to give spatial correlation analysis of Intensity Measurements.This study gives an exponential model based on a semivariogram and compares it with the correlation model obtained from previous studies.

Classical Correlations vs Quantum Correlations—Similarities, Differences, Opportunities

Classical Correlations were founded in 1900 by Karl Pearson and have since been applied as a statistical tool in virtually all sciences. Quantum correlations go back to Albert Einstein et al. in 1935 and Erwin Schrödinger’s responses shortly after. In this paper, we contrast classical with quantum correlations. We find that classical correlations are weaker than quantum correlations in the CHSH framework. With respect to correlation matrices, the trace of classical correlation matrices is dissimilar to quantum density matrices. However, the off-diagonal terms have equivalent interpretations. We contrast classical dynamic (i.e., time evolving) stochastic correlation with dynamic quantum density matrices and find that the off-diagonal elements, while different in nature, have similar interpretations. So far, due to the laws of quantum physics, no classical correlations are applied to the quantum spectrum. However, conversely, quantum correlations are applied in classical environments such as quantum computing, cryptography, metrology, teleportation, medical imaging, laser technology, the quantum Internet and more.

An event mixing technique for Bose-Einstein correlations of two pions in photoproduction around 1 GeV

We have developed an event mixing technique to observe Bose-Einstein correlations （BEC） between two identical neutral pions produced in photo-induced reactions in the non-perturbative QCD energy region. It is found that the missing-mass consistency cut and the pion-energy cut are essential for the event mixing method to effectively extract BEC observables. A Monte Carlo （MC） simulation is used to validate these constraints and confirms the efficiency of this method. Our work paves the way for similar BEC studies at lower energies where the multiplicity of emitted bosons is limited.

An energy sum constraint of event mixing for Bose-Einstein correlations in reactions with ππX final states around 1 GeV

We present a new event mixing technique for measuring two-pion Bose-Einstein correlations （BEC） in reactions with only two identical bosons among three final state particles. This new mixing method contains a missing mass consistency （MMC） cut and an energy sum order （ESO） cut. Unlike the previous proposed pion energy cut, which abandons nearly half the original events, the ESO cut does not eliminate any original events and hence improves the statistics of both original events and mixed events. Numerical tests using the γp→π0π0p events around 1 GeV are carried out to verify the validity of the ESO cut. This cut is able to reproduce the relative momentum distribution of the original events in the absence of BEC effects. In addition, its ability to observe BEC effects is tested by an event sample in the presence of BEC effects. Simulation results show the BEC effects can be observed clearly as an enhancement in the correlation function, and the BEC parameters extracted by this event mixing cut are consistent with the input BEC parameters.

Correlations among core species corresponding to the clinical staging of periodontitis

The correlation between microbiota plays a vital role in the progression of periodontal disease.This study investigated the in situ interaction networks between periodontal pathogens in periodontal and peri-implant disease.We used quantitative real-time polymerase chain reaction and Pearson’s correlation coefficients to quantify the copy numbers and correlations of four oral core species—Fusobacterium nucleatum,Porphyromonas gingivalis,Prevotella intermedia,and Streptococcus gordonii—from 80 subgingival sites(healthy and with periodontitis or gingivitis)in patients with periodontitis,and 68 subgingival sites(healthy and with periodontitis,gingivitis,peri-implantitis,or peri-implant mucositis)in patients with implants.The highest bacterial counts were observed for Porphyromonas gingivalis and Prevotella intermedia at all the sites.Within the same cohorts,the bacterial loads were greater at diseased sites than at healthy sites.Bacterial counts did not differ among clinical sites in the same group(P>0.05)but differed between periodontitis and peri-implant mucositis sites in the two groups.Porphyromonas gingivalis,F.nucleatum,and Prevotella intermedia had strong correlations at gingivitis and healthy sites and moderate correlations at periodontitis sites in patients with periodontitis.In patients with implants,Prevotella intermedia,F.nucleatum,and S.gordonii had strong correlations only at peri-implantitis sites.Also,based on metagenomic analysis,F.nucleatum and Prevotella intermedia were significantly correlated at the subgingival plaque in peri-implantitis and periodontitis samples.Our results suggest that variations in microbe-microbe interactions in subgingival plaque reflect changes in the progression of periodontal disease,providing a new perspective for understanding the mechanisms of periodontitis and peri-implantitis.

Effects of source opacity and expansion on two-pion Bose-Einstein correlations

We examine two-pion Bose-Einstein correlations for partially coherent particle-emitting sources within quantum statistical formal- ism, where the sources are treated as classical currents with chaotic and coherent components. The two-pion correlation functions of the partially coherent sources contain a phase which is sensitive to the asymmetry of the source emission function. We investigate the influence of source opacity and expansion in high energy heavy ion collisions on the phase by Monte Carlo calculations. We find that these two physical effects shift the phase from zero. The Gaussian-formula fit results to the simulated two-pion correlation functions indicate that the opaque and expansion effects lead to a smaller interferometry radius Rout and a larger 2 parameter.

Channel Correlation Based User Grouping Algorithm for Nonlinear Precoding Satellite Communication System

Low Earth Orbit(LEO)multibeam satellites will be widely used in the next generation of satellite communication systems,whose inter-beam interference will inevitably limit the performance of the whole system.Nonlinear precoding such as Tomlinson-Harashima precoding(THP)algorithm has been proved to be a promising technology to solve this problem,which has smaller noise amplification effect compared with linear precoding.However,the similarity of different user channels(defined as channel correlation)will degrade the performance of THP algorithm.In this paper,we qualitatively analyze the inter-beam interference in the whole process of LEO satellite over a specific coverage area,and the impact of channel correlation on Signal-to-Noise Ratio(SNR)of receivers when THP is applied.One user grouping algorithm is proposed based on the analysis of channel correlation,which could decrease the number of users with high channel correlation in each precoding group,thus improve the performance of THP.Furthermore,our algorithm is designed under the premise of co-frequency deployment and orthogonal frequency division multiplexing(OFDM),which leads to more users under severe inter-beam interference compared to the existing research on geostationary orbit satellites broadcasting systems.Simulation results show that the proposed user grouping algorithm possesses higher channel capacity and better bit error rate(BER)performance in high SNR conditions relative to existing works.

Space-time correlations of passive scalar in Kraichnan model

We consider the two-point,two-time(space-time)correlation of passive scalar R(r,τ)in the Kraichnan model under the assumption of homogeneity and isotropy.Using the fine-gird PDF method,we find that R(r,τ)satisfies a diffusion equation with constant diffusion coefficient determined by velocity variance and molecular diffusion.Itssolution can be expressed in terms of the two-point,one time correlation of passive scalar,i.e.,R(r,0).Moreover,the decorrelation o R(k,τ),which is the Fourier transform of R(r,τ),is determined byR(k,0)and a diffusion kernal.

Emergence of correlations in twisted monolayer-trilayer graphene heterostructures

Twisted bilayer graphene heterostructures have recently emerged as a well-established platform for studying strongly correlated phases,such as correlated insulating,superconducting,and topological states.Extending this notion to twisted multilayer graphene heterostructures has exhibited more diverse correlated phases,as some fundamental properties related to symmetry and band structures are correspondingly modified.Here,we report the observations of correlated states in twisted monolayer-trilayer(Bernal stacked)graphene heterostructures.Correlated phases at integer fillings of the moire unit cell are revealed at a high displacement field and stabilized with a moderate magnetic field on the electron-doping side at a twist angle of 1.45°,where the lift of degeneracy at the integer fillings is observed in the Landau fan diagram.Our results demonstrate the effectiveness of moire engineering in an extended structure and provide insights into electric-field tunable correlated phases.

Dominant factors in MiniCone, CPT and pile correlations: A data‐based approach

The cone penetration test(CPT)contributes to the design and analysis of piles regarding geometry,installation effect,and pile capacity(shaft and toe resistance).MiniCone,as an alternative to CPT sounding,has been used to carry outfield and laboratory investigations by physical modeling.More tests can be practically carried out through light equipment and small soil mass,involving fewer errors caused by boundary conditions.Furthermore,it can be used for in situ testing,such as quality control,assessment of ground improvement,and subgrade characterization.A database comprising MiniCone and CPT records infield and physical modeling is proposed with a variety of cone diameters.The case study records in the database have been obtained from 140 tests compiled from data from 26 sources.The sources include the results of 20 physical modelings andfield data from six sites in 10 countries.The data comprise MiniCone and CPT cone tip resistance(qc),and sleeve friction(fs).The different cones are used in sandy,silty sand,and clayey soils via simple chambers(1 g),calibration chambers,and frustum confining vessels.In addition,correlations were found in penetration records in terms of physical modeling types,cone diameters,penetration rates,and soil densities.Moreover,qc and fs are related to capacities of pile toes and shafts using proper correlation coefficients less than unity,respectively.Correlations and dominant factors in geotechnical practice between MiniCone,CPT,and pile have been reviewed and discussed.

Pressure drop of structured packing in pilot column and comparison to common correlations

Packed columns are widely used in the chemical industry such as absorption,stripping,distillation,and extraction in the production of e.g.organic chemicals,and pharmaceuticals.Pressure loss and pressure drop correlations are of special interest when it comes to the hydrodynamic properties of a column.The pressure loss across the column is of interest in the design phase when the size of the blower to drive the gas stream through the column has to be decided.The loading point and flooding point are also influenced by the pressure loss and the area of operation is determined from these points.This work examines four different correlations on pressure drop.The correlations are(i)Ergun’s equation(1952),(ii)an improved version of Ergun’s equation by Stichlmair,Bravo,and Fair(1989),(iii)an equation developed by Billet and Schultes(1999),and(iv)an equation by Rocha,Bravo,and Fair(1993).The complexity of the correlations is increasing in the mentioned order,Ergun’s equation being the simplest one.This study investigates if the more complicated correlations give better predictions to pressure drop in packed columns.This is determined by comparing the correlations to experimental data for pressure drop in a packed column with 8.2 m of structured packing using water as the liquid and atmospheric air as the gas.Seven experiments were carried out for determining the pressure drop in the column with liquid flows varying from 0 to 500 kg·h^(-1).At constant liquid flow,the gas flow was varied from approximately 10 to 70 kg·h^(-1).The pressure drop across the non-wetted column was best described by the correlation by Rocha et al.while the pressure drop for liquid flows from 100 to 500 kg·h^(-1)was,in general,best described by Stichlmair’s equation.For an irrigated column,the highest deviation was a predicted pressure drop 69.6%lower than measured.The best prediction was 0.1%higher than the measured.This study shows,surprisingly,that for a system of water and atmospheric air,complicated correlations on pressure drop determination do not provide better estimates than simple equations.

Assessment of Dependent Performance Shaping Factors in SPAR-H Based on Pearson Correlation Coefficient

With the improvement of equipment reliability,human factors have become the most uncertain part in the system.The standardized Plant Analysis of Risk-Human Reliability Analysis(SPAR-H)method is a reliable method in the field of human reliability analysis(HRA)to evaluate human reliability and assess risk in large complex systems.However,the classical SPAR-H method does not consider the dependencies among performance shaping factors(PSFs),whichmay cause overestimation or underestimation of the risk of the actual situation.To address this issue,this paper proposes a new method to deal with the dependencies among PSFs in SPAR-H based on the Pearson correlation coefficient.First,the dependence between every two PSFs is measured by the Pearson correlation coefficient.Second,the weights of the PSFs are obtained by considering the total dependence degree.Finally,PSFs’multipliers are modified based on the weights of corresponding PSFs,and then used in the calculating of human error probability(HEP).A case study is used to illustrate the procedure and effectiveness of the proposed method.

Site selective 5f electronic correlations inβ-uranium

We investigate the electronic structure ofβ-uranium,which has five nonequivalent atomic sites in its unit cell,by means of the density functional theory plus Hubbard-U correction with U from linear response calculation.It is found that the 5f electronic correlations inβ-uranium are moderate.More interestingly,their strengths are site selective,depending on the local atomic environment of the present uranium atom.As a consequence,the occupation matrices and partial 5f density of states ofβ-uranium manifest site dependence.In addition,the complicate experimental structure ofβ-uranium could be well reproduced within this theoretical framework.

Maintenance Optimization for EMU Trains Considering Environmental Impacts and Correlations

The complexity of the actual operating environment of EMU trains and the interaction between the reliability of system components have become a huge challenge for the maintenance scheduling of EMU trains. In response to these problems, the evolution of reliability and failure rate under the influence of environmental factors, failure correlations and economy correlations is analyzed. We assume bogie systems form the EMU train in series. The failure correlation matrix of the bogie systems is modeled. With the lowest total maintenance cost as the optimization objective, a decision-making model for EMU train maintenance is established. A dynamic maintenance strategy is proposed for the model, which can improve maintenance plans efficiently. Artificial bee colony algorithm is applied to further iteratively optimize the threshold parameters in the strategy. The results are calculated and verified by a numerical example. The results show the effectiveness of the maintenance decision model. The dynamic maintenance strategy in this paper is compared with the traditional opportunistic maintenance strategy. The proposed maintenance strategy outperforms the traditional opportunistic maintenance strategy in the numerical example.