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We introduce a novel, \textit{fully} quantum hash (FQH) function within the quantum walk on a cycle framework. We incorporate deterministic quantum computation with a single qubit to replace classical post-processing, thus increasing the inherent security. Further, our proposed hash function exhibits zero collision rate and high reliability. We further show that it provides $ > 50\%$ avalanche on average, and is highly sensitive to the initial conditions. We show comparisons of several performance metrics for the proposed FQH with different settings as well as with existing protocols to prove its efficacy. FQH requires minimal quantum resources to produce a large hash value, providing security against the birthday attack. This innovative approach thus serves as an efficient hash function and lays the foundation for potential advancements in quantum cryptography by integrating the fully quantum hash generation protocol.

The power graph $\mathscr{P}(G)$ of a group $G$ is defined as the simple graph with vertex set $G$, and where two distinct vertices $x$ and $y$ are joined by an edge if and only if either $x= y^k$ or $y= x^k$, $k \in \mathbb{N}$. Here we determine the characteristic polynomial of $\mathscr{P}(\mathbb{Z}_m \times \mathbb{Z}_{n})$ for any positive integers $m$ and $n$. Additionally, for some particular values of $m$ and $n$, we simplify the above characteristic polynomials and provide the full spectrum in a few cases.

Spin chirality in electron gases is mandated by symmetry to be nonzero whenever time reversal symmetry (TRS) is broken. In metals, both normal and superconducting, spin chirality is generated by orbital currents present in the ground state as a result of TRS breaking. Nonzero chirality is found to emerge in the absence of any spin-dependent interactions, even when the ground state remains spin-unpolarized. We present a diagrammatic derivation of the chirality effect and illustrate its generality for problems such as valley magnetism and topological superconductivity. Spin chirality results in a chiral three-spin RKKY interaction between localized spins coupled to carriers by s-d interaction, an effect that can be detected by local probes such as spin-sensitive STM. In systems where detecting TRS breaking by macroscopic measurements is challenging, such as topological superconductors, local detection of spin chirality can serve as a reliable diagnostic of broken time reversal symmetry., Comment: 7pgs 2fgs

Magnetism typically arises from the effect of exchange interactions on highly localized fermionic wave functions in f- and d-atomic orbitals. In rhombohedral graphene multilayers, in contrast, magnetism -- manifesting as spontaneous polarization into one or more spin and valley flavors[1-7]-originates from fully itinerant electrons near a Van Hove singularity. Here, we show that despite the absence of localized electronic orbitals on the scale of the interparticle separation, rhombohedral graphene bi- and trilayers show thermodynamic signatures typically associated with disordered local magnetic moments. Specifically, while long range valley order vanishes at temperatures of a few Kelvin, thermodynamic characteristics of fluctuating moments, probed via both electronic compressibility[2-4] and exciton sensing measurements[8], survive to temperatures an order of magnitude higher. Measurements of the electronic entropy in this regime reveal a contribution of $\Delta S \approx 1k_B$/charge carrier, onsetting at the Curie temperature, while first order phase transitions show an isospin "Pomeranchuk effect" in which the fluctuating moment phase is entropically favored over the nearby symmetric Fermi liquid[9, 10]. Our results imply that despite the itinerant nature of the electron wave functions, the spin- and valley polarization of individual electrons are decoupled, a phenomenon typically associated with localized moments, as happens, for example, in solid 3He[11]. Transport measurements, surprisingly, show a finite temperature resistance minimum within the fluctuating moment regime, which we attribute to the interplay of fluctuating magnetic moments and electron phonon scattering. Our results highlight the universality of soft isospin modes to two dimensional flat band systems and their possible relevance both to low-temperature ground states and high temperature transport anomalies.

In this study, we highlight the potential of strain engineering in graphene/hBN (hexagonal Boron nitride) 2D heterostructures, enabling their use as wide-range light absorbers with significant implications for optoelectronic applications. We systematically investigate the electronic and optical properties of graphene/hBN under the application of strain, considering various stacking geometries within the framework of density-functional theory. The semimetallic graphene layer upon aligning on the insulating hexagonal boron nitride sheet opens a few tens of meV band gap at the Dirac point due to the induced on-site energy differences on the two sublattices of graphene. Here, we demonstrate that by simultaneously tuning the interlayer distance and lattice constant, this band gap can be significantly increased to 1 eV. Interestingly, in both scenarios (small and large band gaps), the material undergoes a transition from a semiconductor to a semimetallic state. Importantly, the tunability of this band gap is strongly influenced by the specific stacking configuration. We further explored the optical properties across a broad spectrum, revealing that the presence of a strain-induced band gap fundamentally alters how light interacts with the system., Comment: 12 pages, 17 figures

Transformer-based chatbots can conduct fluent, natural-sounding conversations, but we have limited understanding of the mechanisms underlying their behavior. Prior work has taken a bottom-up approach to understanding Transformers by constructing Transformers for various synthetic and formal language tasks, such as regular expressions and Dyck languages. However, it is not obvious how to extend this approach to understand more naturalistic conversational agents. In this work, we take a step in this direction by constructing a Transformer that implements the ELIZA program, a classic, rule-based chatbot. ELIZA illustrates some of the distinctive challenges of the conversational setting, including both local pattern matching and long-term dialog state tracking. We build on constructions from prior work -- in particular, for simulating finite-state automata -- showing how simpler constructions can be composed and extended to give rise to more sophisticated behavior. Next, we train Transformers on a dataset of synthetically generated ELIZA conversations and investigate the mechanisms the models learn. Our analysis illustrates the kinds of mechanisms these models tend to prefer -- for example, models favor an induction head mechanism over a more precise, position based copying mechanism; and using intermediate generations to simulate recurrent data structures, like ELIZA's memory mechanisms. Overall, by drawing an explicit connection between neural chatbots and interpretable, symbolic mechanisms, our results offer a new setting for mechanistic analysis of conversational agents., Comment: Code and data are available at https://github.com/princeton-nlp/ELIZA-Transformer

We present an analysis of the half-filled CPT model, an analytically tractable Kondo lattice model with Yao-Lee spin-spin interactions on a 3D hyperoctagon lattice, proposed by Coleman, Panigrahi, and Tsvelik. Previous studies have established that the CPT model exhibits odd-frequency triplet superconductivity and order fractionalization. Through asymptotic analyses in the small $J$ and large $J$ Kondo coupling limits, we identify a quantum critical point at $J_c$, marking a transition from a superconductor to a Kondo insulator. By estimating the vison gap energy to account for thermal gauge fluctuations, we determine the energy scales governing the thermal breakdown of order fractionalization. Moreover, at large $J$ the Kondo insulator undergoes orbital decoupling, leading to the formation of a decoupled Kitaev orbital liquid. These findings and analogies with the $\mathbb{Z}_2$-gauged $XY$ model lead us to propose a tentative phase diagram for the CPT model at half-filling., Comment: 10 pages, 7 figures

Recently, neutral atoms have emerged as a promising platform for quantum computing, offering scalability. In this study, we showcase the realization of atomic qubits in atom-molecular Bose-Einstein condensate, belonging to three distinct classes. In the first case, the condensed molecules form a droplet platform with a flat-top configuration, facilitating effective isolation from both external environments and neighbouring molecules. The second atomic qubits have wavefunctions in the ``pulse" form, exhibiting power law behaviour, whereas the third one has ground and excited state wavefunctions in their respective composite forms, $\sech^2{\beta x}$ and $\sech{\beta x}\tanh{\beta x}$. The localization of the qubits depends on the chemical potential, which is governed by the photo association, providing effective control for qubit manipulation. The relevant parameters, such as energy level separation, healing length, and atom numbers, are found to be influenced by the non-linearity and strength of photo associations governing the behaviour of macroscopic qubits and molecular droplets.

This article investigates the existence of an $r$-primitive $k$-normal polynomial, defined as the minimal polynomial of an $r$-primitive $k$-normal element in $\mathbb{F}_{q^n}$, with a specified degree $n$ and two given coefficients over the finite field $\mathbb{F}_{q}$. Here, $q$ represents an odd prime power, and $n$ is an integer. The article establishes a sufficient condition to ensure the existence of such a polynomial. Using this condition, it is demonstrated that a $2$-primitive $2$-normal polynomial of degree $n$ always exists over $\mathbb{F}_{q}$ when both $q\geq 11$ and $n\geq 15$. However, for the range $10\leq n\leq 14$, uncertainty remains regarding the existence of such a polynomial for $71$ specific pairs of $(q,n)$. Moreover, when $q<11$, the number of uncertain pairs reduces to $16$. Furthermore, for the case of $n=9$, extensive computational power is employed using SageMath software, and it is found that the count of such uncertain pairs is reduced to $3988$., Comment: 27 pages, 3 Tables

This work introduces a novel approach to achieving architecture-agnostic equivariance in deep learning, particularly addressing the limitations of traditional equivariant architectures and the inefficiencies of the existing architecture-agnostic methods. Building equivariant models using traditional methods requires designing equivariant versions of existing models and training them from scratch, a process that is both impractical and resource-intensive. Canonicalization has emerged as a promising alternative for inducing equivariance without altering model architecture, but it suffers from the need for highly expressive and expensive equivariant networks to learn canonical orientations accurately. We propose a new method that employs any non-equivariant network for canonicalization. Our method uses contrastive learning to efficiently learn a unique canonical orientation and offers more flexibility for the choice of canonicalization network. We empirically demonstrate that this approach outperforms existing methods in achieving equivariance for large pretrained models and significantly speeds up the canonicalization process, making it up to 2 times faster., Comment: Accepted to EquiVision workshop, CVPR 2024. 7 pages, 1 figure

The centrality measure (CM) is one of the most fundamental metrics for evaluating the efficiency and vulnerability analysis of complex power grids (CPGs). Despite an abundance of different CMs for individual nodes, there are only a few metrics available in the literature to measure the centrality of individual lines. We propose here the current-flow (CF) line CMs to identify the ranking of lines, where each set of lines is associated with a different level of importance. We then find the CMs using effective resistance and apply it to identify the important lines in a commonly used IEEE 118-bus network. Finally, the efficiency and vulnerability of CPG are analyzed to validate the proposed concepts., Comment: None

When analyzing large datasets, it is common to select a model prior to making inferences. For reliable inferences, it is important to make adjustments that account for the model selection process, resulting in selective inferences. Our paper introduces an asymptotic pivot to infer about the effects of selected variables on conditional quantile functions. Utilizing estimators from smoothed quantile regression, our proposed pivot is easy to compute and ensures asymptotically-exact selective inferences without making strict distributional assumptions about the response variable. At the core of the pivot is the use of external randomization, which enables us to utilize the full sample for both selection and inference without the need to partition the data into independent data subsets or discard data at either step. On simulated data, we find that: (i) the asymptotic confidence intervals based on our pivot achieve the desired coverage rates, even in cases where sample splitting fails due to insufficient sample size for inference; (ii) our intervals are consistently shorter than those produced by sample splitting across various models and signal settings. We report similar findings when we apply our approach to study risk factors for low birth weights in a publicly accessible dataset of US birth records from 2022.

Recently, a wide family of electronic orders was unveiled in graphene flat bands, such as spin- and valley-polarized phases as well as nematic momentum-polarized phases, stabilized by exchange interactions via a generalized Stoner mechanism. Momentum polarization involves orbital degrees of freedom and is therefore expected to impact resistivity in a way that is uniquely sensitive to the ordering type. Under pocket polarization, carrier distribution shifts in $k$ space and samples the band mass in regions defined by the displaced momentum distribution. This makes transport coefficients sensitive to pocket polarization, resulting in the Ohmic resistivity decreasing with temperature. In addition, it leads to current switching and hysteresis under strong $E$ field. Being robust in the presence of electron-phonon scattering, this behavior can serve as a telltale sign of pocket polarization order. The fast timescale and low dissipation of the switching cycle may be advantageous for highly applicable memory-dependent resistors, i.e., memristors., Comment: 13 pages, 4 figures

The hypergraph unreliability problem asks for the probability that a hypergraph gets disconnected when every hyperedge fails independently with a given probability. For graphs, the unreliability problem has been studied over many decades, and multiple fully polynomial-time approximation schemes are known starting with the work of Karger (STOC 1995). In contrast, prior to this work, no non-trivial result was known for hypergraphs (of arbitrary rank). In this paper, we give quasi-polynomial time approximation schemes for the hypergraph unreliability problem. For any fixed $\varepsilon \in (0, 1)$, we first give a $(1+\varepsilon)$-approximation algorithm that runs in $m^{O(\log n)}$ time on an $m$-hyperedge, $n$-vertex hypergraph. Then, we improve the running time to $m\cdot n^{O(\log^2 n)}$ with an additional exponentially small additive term in the approximation., Comment: To appear in STOC 2024

Van der Waals heterostructures provide a versatile platform for tailoring electronic properties through the integration of two-dimensional materials. Among these combinations, the interaction between bilayer graphene and transition metal dichalcogenides (TMDs) stands out due to its potential for inducing spin-orbit coupling (SOC) in graphene. Future devices concepts require the understanding the precise nature of SOC in TMD/bilayer graphene heterostructures and its influence on electronic transport phenomena. Here, we experimentally confirm the presence of two distinct types of SOC, Ising (1.55 meV) and Rashba (2.5 meV), in bilayer graphene when interfaced with molybdenum disulphide, recognized as one of the most stable TMDs. Furthermore, we reveal a non-monotonic trend in conductivity with respect to the electric displacement field at charge neutrality. This phenomenon is ascribed to the existence of single-particle gaps induced by the Ising SOC, which can be closed by a critical displacement field. Remarkably, our findings also unveil sharp peaks in the magnetoconductivity around the critical displacement field, challenging existing theoretical models.

Applications of an efficient emotion recognition system can be found in several domains such as medicine, driver fatigue surveillance, social robotics, and human-computer interaction. Appraising human emotional states, behaviors, and reactions displayed in real-world settings can be accomplished using latent continuous dimensions. Continuous dimensional models of human affect, such as those based on valence and arousal are more accurate in describing a broad range of spontaneous everyday emotions than more traditional models of discrete stereotypical emotion categories (e.g. happiness, surprise). Most of the prior work on estimating valence and arousal considers laboratory settings and acted data. But, for emotion recognition systems to be deployed and integrated into real-world mobile and computing devices, we need to consider data collected in the world. Action recognition is a domain of Computer Vision that involves capturing complementary information on appearance from still frames and motion between frames. In this paper, we treat emotion recognition from the perspective of action recognition by exploring the application of deep learning architectures specifically designed for action recognition, for continuous affect recognition. We propose a novel three-stream end-to-end deep learning regression pipeline with an attention mechanism, which is an ensemble design based on sub-modules of multiple state-of-the-art action recognition systems. The pipeline constitutes a novel data pre-processing approach with a spatial self-attention mechanism to extract keyframes. The optical flow of high-attention regions of the face is extracted to capture temporal context. AFEW-VA in-the-wild dataset has been used to conduct comparative experiments. Quantitative analysis shows that the proposed model outperforms multiple standard baselines of both emotion recognition and action recognition models.

We report the close form expressions of the photon number statistics for a generalized coherent state and a generalized photon-added coherent state, which are shown to be crucial for proposing a variety of quantum scissor operations. The analytically obtained distributions are also capable of predicting the precise laser intensity windows for realizing a variety of quantum scissors. Truncating a photon added state overcomes the selection rule of obtaining the lower order Fock states. Photon addition also enables us to obtain a higher order Fock state in a lower order superposition. The importance of circular geometry is also demonstrated for engineering such quantum scissors., Comment: Accepted

We study the approximability of the MaxCut problem in the presence of predictions. Specifically, we consider two models: in the noisy predictions model, for each vertex we are given its correct label in $\{-1,+1\}$ with some unknown probability $1/2 + \epsilon$, and the other (incorrect) label otherwise. In the more-informative partial predictions model, for each vertex we are given its correct label with probability $\epsilon$ and no label otherwise. We assume only pairwise independence between vertices in both models. We show how these predictions can be used to improve on the worst-case approximation ratios for this problem. Specifically, we give an algorithm that achieves an $\alpha + \widetilde{\Omega}(\epsilon^4)$-approximation for the noisy predictions model, where $\alpha \approx 0.878$ is the MaxCut threshold. While this result also holds for the partial predictions model, we can also give a $\beta + \Omega(\epsilon)$-approximation, where $\beta \approx 0.858$ is the approximation ratio for MaxBisection given by Raghavendra and Tan. This answers a question posed by Ola Svensson in his plenary session talk at SODA'23., Comment: 18 pages

Most state-of-the-art computer vision models heavily depend on data. However, many datasets exhibit extreme class imbalance which has been shown to negatively impact model performance. Among the training-time and data-generation solutions that have been explored, one subset that leverages existing data is importance sampling. A good deal of this work focuses primarily on the CIFAR-10 and CIFAR-100 datasets which fail to be representative of the scale, composition, and complexity of current state-of-the-art datasets. In this work, we explore and compare three techniques that derive from importance sampling: loss reweighting, undersampling, and oversampling. Specifically, we compare the effect of these techniques on the performance of two encoders on an impactful satellite imagery dataset, Planet's Amazon Rainforest dataset, in preparation for another work. Furthermore, we perform supplemental experimentation on a scene classification dataset, ADE20K, to test on a contrasting domain and clarify our results. Across both types of encoders, we find that up-weighting the loss for and undersampling has a negigible effect on the performance on underrepresented classes. Additionally, our results suggest oversampling generally improves performance for the same underrepresented classes. Interestingly, our findings also indicate that there may exist some redundancy in data in the Planet dataset. Our work aims to provide a foundation for further work on the Planet dataset and similar domain-specific datasets. We open-source our code at https://github.com/RichardZhu123/514-class-imbalance for future work on other satellite imagery datasets as well., Comment: Preprint

Principal component analysis (PCA) is a longstanding and well-studied approach for dimension reduction. It rests upon the assumption that the underlying signal in the data has low rank, and thus can be well-summarized using a small number of dimensions. The output of PCA is typically represented using a scree plot, which displays the proportion of variance explained (PVE) by each principal component. While the PVE is extensively reported in routine data analyses, to the best of our knowledge the notion of inference on the PVE remains unexplored. In this paper, we consider inference on the PVE. We first introduce a new population quantity for the PVE with respect to an unknown matrix mean. Critically, our interest lies in the PVE of the sample principal components (as opposed to unobserved population principal components); thus, the population PVE that we introduce is defined conditional on the sample singular vectors. We show that it is possible to conduct inference, in the sense of confidence intervals, p-values, and point estimates, on this population quantity. Furthermore, we can conduct valid inference on the PVE of a subset of the principal components, even when the subset is selected using a data-driven approach such as the elbow rule. We demonstrate the proposed approach in simulation and in an application to a gene expression dataset.

This paper explores the fundamental relationship between the geometry of entanglement and von Neumann entropy, shedding light on the intricate nature of quantum correlations. We provide a comprehensive overview of entanglement, highlighting its crucial role in quantum mechanics. Our focus centers on the connection between entanglement, von Neumann entropy, a measure of the information content within quantum systems and the geometry of composite Hilbert spaces. We discuss various methods for quantifying and characterizing entanglement through a geometric perspective and elucidate how this connection unveils the nature of quantum entanglement, offering valuable insights into the underlying structure of quantum systems. This study underscores the significance of geometry as a key tool for understanding the rich landscape of quantum correlations and their implications across various domains of physics and information theory. An example of entanglement as an indispensable resource for the task of state teleportation is presented at the end.

Power electronic systems (PES) face significant threats from various data availability and integrity attacks, significantly affecting the performance of communication networks and power system operation. As a result, several attack detection and reconstruction techniques are deployed, which makes it a costly \& complex cybersecurity operational platform with significant room for incremental extensions for mitigation against future threats. Unlike the said traditional arrangements, our paper introduces a foundational approach by establishing a monolithic cybersecurity architecture (MCA) via incorporating semantic principles into the sampling process for distributed energy resources (DERs). This unified approach concurrently compensates for the intrusion challenges posed by cyber attacks by reconstructing signals using the dynamics of the inner control layer. This reconstruction considers essential semantic attributes, like Priority, Freshness, and Relevance to ensure resilient dynamic performance. Hence, the proposed scheme promises a generalized route to concurrently tackle a global set of cyber attacks in elevating the resilience of PES. Finally, rigorous validation on a modified IEEE 69-bus distribution system and a real-world South California Edison (SCE) 47-bus network, using OPAL-RT under diverse operating conditions, underscores its robustness, model-free design capability, scalability, and adaptability to dynamic cyber graphs and system reconfiguration., Comment: This paper has been accepted for publication in IEEE Transactions on Smart Grid

In power electronic systems (PES), attacks on data availability such as latency attacks, data dropouts, and time-synchronization attacks (TSAs) continue to pose significant threats to both the communication network and the control system performance. As per the conventional norms of communication engineering, PES still rely on time synchronized sampling, which translates every received message with equal importance. In this paper, we go beyond event-triggered sampling/estimation to integrate semantic principles into the sampling process for each distributed energy resource (DER), which not only compensates for delayed communicated signals by reconstruction of a new signal from the inner control layer dynamics, but also evaluates the reconstruction stage using key semantic requirements, namely Freshness, Relevance and Priority for good dynamic performance. As a result, the sparsity provided by event-driven sampling of internal control loop dynamics translates as semantics in PES. The proposed scheme has been extensively tested and validated on a modified IEEE 37-bus AC distribution system, under many operating conditions and noisy environment in OPAL-RT environment to establish its robustness, model-free design ability and adaptive behavior to dynamic cyber graph topologies., Comment: This paper has been accepted for publication in IEEE Transactions on Smart Grid

Recent developments in large language models have sparked interest in efficient pretraining methods. A recent effective paradigm is to perform stage-wise training, where the size of the model is gradually increased over the course of training (e.g. gradual stacking (Reddi et al., 2023)). While the resource and wall-time savings are appealing, it has limitations, particularly the inability to evaluate the full model during earlier stages, and degradation in model quality due to smaller model capacity in the initial stages. In this work, we propose an alternative framework, progressive subnetwork training, that maintains the full model throughout training, but only trains subnetworks within the model in each step. We focus on a simple instantiation of this framework, Random Path Training (RaPTr) that only trains a sub-path of layers in each step, progressively increasing the path lengths in stages. RaPTr achieves better pre-training loss for BERT and UL2 language models while requiring 20-33% fewer FLOPs compared to standard training, and is competitive or better than other efficient training methods. Furthermore, RaPTr shows better downstream performance on UL2, improving QA tasks and SuperGLUE by 1-5% compared to standard training and stacking. Finally, we provide a theoretical basis for RaPTr to justify (a) the increasing complexity of subnetworks in stages, and (b) the stability in loss across stage transitions due to residual connections and layer norm.

We investigate the temperature effects in an imbalanced superfluid atomic Fermi gas. We consider a bilayer system of two-component dipolar fermionic atoms with one layer containing atoms of one component and the other layer the atoms of other component with an imbalance between the populations of the two components. This imbalance results in uniform and nonuniform superfluid phases such as phase-separated BCS, Fulde-Ferrel-Larkin-Ovchinnikov (FFLO), Sarma and normal Fermi liquid phases for different system parameters. Using the mean-field BCS theory together with the superfluid mass-density criterion we classify different phases in thermodynamic phase diagram. Our results indicate that for a dipolar Fermi system the Sarma phase is stable for large imbalance at finite temperature below the critical temperature, and the FFLO phase is stable for intermediate imbalance on the BCS side of a BCS-BCE crossover. The phase diagram in the temperature and population imbalance plane indicate three Lifshitz points: one corresponding to coexistance of BCS, FFLO and normal Fermi liquid phase while the other two correspond to the coexistance of the Sarma phase, FFLO phase and normal Fermi phase for dipolar interactions., Comment: 11 pages, 9 figures

Neighborhood selection is a widely used method used for estimating the support set of sparse precision matrices, which helps determine the conditional dependence structure in undirected graphical models. However, reporting only point estimates for the estimated graph can result in poor replicability without accompanying uncertainty estimates. In fields such as psychology, where the lack of replicability is a major concern, there is a growing need for methods that can address this issue. In this paper, we focus on the Gaussian graphical model. We introduce a selective inference method to attach uncertainty estimates to the selected (nonzero) entries of the precision matrix and decide which of the estimated edges must be included in the graph. Our method provides an exact adjustment for the selection of edges, which when multiplied with the Wishart density of the random matrix, results in valid selective inferences. Through the use of externally added randomization variables, our adjustment is easy to compute, requiring us to calculate the probability of a selection event, that is equivalent to a few sign constraints and that decouples across the nodewise regressions. Through simulations and an application to a mobile health trial designed to study mental health, we demonstrate that our selective inference method results in higher power and improved estimation accuracy., Comment: 44 pages, 6 figures, 3 tables

In this work, we have introduced two innovative quantum algorithms: the Direct Column Algorithm and the Quantum Backtracking Algorithm to solve N-Queens problem, which involves the arrangement of $N$ queens on an $N \times N$ chessboard such that they are not under attack from each other on the same row, column and diagonal. These algorithms utilizes Controlled W-states and dynamic circuits, to efficiently address this NP-Complete computational problem. The Direct Column Algorithm strategically reduces the search space, simplifying the solution process, even with exponential circuit complexity as the problem size grows, while Quantum Backtracking Algorithm emulates classical backtracking techniques within a quantum framework which allows the possibility of solving complex problems like satellite communication, routing and VLSI testing., Comment: Accepted in Conference on COMSNETS 2024

We investigate the benefits of probabilistic non-Gaussian operations in phase estimation using difference-intensity and parity detection-based Mach-Zehnder interferometers (MZI). We consider an experimentally implementable model to perform three different non-Gaussian operations, namely photon subtraction (PS), photon addition (PA), and photon catalysis (PC) on a single-mode squeezed vacuum (SSV) state. In difference-intensity detection-based MZI, two PC operation is found to be the most optimal, while for parity detection-based MZI, two PA operation emerges as the most optimal process. We have also provided the corresponding squeezing and transmissivity parameters at best performance, making our study relevant for experimentalists. Further, we have derived the general expression of moment-generating function, which shall be useful in exploring other detection schemes such as homodyne detection and quadratic homodyne detection., Comment: 13 pages, 11 figures. Comments are most welcome!!!

The geometrical representation of two-flavor neutrino oscillation represents the neutrino's flavor eigenstate as a magnetic moment-like vector that evolves around a magnetic field-like vector that depicts the Hamiltonian of the system. In the present work, we demonstrate the geometrical interpretation of neutrino in a vacuum in the presence of decay, which transforms this circular trajectory of neutrino into a helical track that effectively makes the neutrino system mimic a classical damped driven oscillator. We show that in the absence of the phase factor $\xi$ in the decay Hamiltonian, the neutrino exactly behaves like the system of nuclear magnetic resonance(NMR); however, the inclusion of the phase part introduces a $CP$ violation, which makes the system deviate from NMR. Finally, we make a qualitative discussion on under-damped, critically-damped, and over-damped scenarios geometrically by three different diagrams. In the end, we make a comparative study of geometrical picturization in vacuum, matter, and decay, which extrapolates the understanding of the geometrical representation of neutrino oscillation in a more straightforward way., Comment: 16 pages, 7 figures, regular article

Social media platforms serve as accessible outlets for individuals to express their thoughts and experiences, resulting in an influx of user-generated data spanning all age groups. While these platforms enable free expression, they also present significant challenges, including the proliferation of hate speech and offensive content. Such objectionable language disrupts objective discourse and can lead to radicalization of debates, ultimately threatening democratic values. Consequently, organizations have taken steps to monitor and curb abusive behavior, necessitating automated methods for identifying suspicious posts. This paper contributes to Hate Speech and Offensive Content Identification in English and Indo-Aryan Languages (HASOC) 2023 shared tasks track. We, team Z-AGI Labs, conduct a comprehensive comparative analysis of hate speech classification across five distinct languages: Bengali, Assamese, Bodo, Sinhala, and Gujarati. Our study encompasses a wide range of pre-trained models, including Bert variants, XLM-R, and LSTM models, to assess their performance in identifying hate speech across these languages. Results reveal intriguing variations in model performance. Notably, Bert Base Multilingual Cased emerges as a strong performer across languages, achieving an F1 score of 0.67027 for Bengali and 0.70525 for Assamese. At the same time, it significantly outperforms other models with an impressive F1 score of 0.83009 for Bodo. In Sinhala, XLM-R stands out with an F1 score of 0.83493, whereas for Gujarati, a custom LSTM-based model outshined with an F1 score of 0.76601. This study offers valuable insights into the suitability of various pre-trained models for hate speech detection in multilingual settings. By considering the nuances of each, our research contributes to an informed model selection for building robust hate speech detection systems., Comment: 14 pages, 3 figures. Accepted Working Notes at HASOC-FIRE 2023, to be published in CEUR Working Notes of FIRE