arXiv subjects

Hemant Sharma

Publications and source records attributed to Hemant Sharma.

At least 19 recordsLinked to original sources

arXiv2026

Differentiable powder X-ray diffraction enables analysis of evolving structures

Operando and in-situ experiments extend powder X-ray diffraction (PXRD) to materials that evolve during experiments, producing series of hundreds or thousands of patterns. Such series are commonly refined one pattern at a time, so weak signals give noisy structural trajectories. Parametric refinement instead fits a shared model to all patterns, but with most existing programs, changing the model or fitting it efficiently remains challenging. Here, we introduce diffPXRD, a differentiable PXRD engine in PyTorch. diffPXRD calculates derivatives by automatic differentiation, so a shared model can be changed without new derivative code. Batched fitting is also more than seven times faster than serial fitting. In an operando cathode series, a shared lattice model can reduce lattice-parameter variability by 68.4% when 10% of the photon counts are retained. We also show shared models can describe the precipitation and dissolution of Li2S and reconstruct collective atomic displacements in Ca3Ti2O7.

cond-mat.mtrl-sci↗

arXiv2026

Iterated Lavrentiev regularization under random noise: variational source conditions and rates in expectation

The convergence theory of iterated Lavrentiev regularization for nonlinear monotone ill-posed equations is deterministic: the data error is bounded by a known level that the discrepancy principle uses explicitly. Under Gaussian noise no such bound exists. For a discretized two-dimensional nonlinear inverse source problem for the Poisson equation, we analyse convergence in a finite-energy Gaussian noise model, keeping the linearized and nonlinear cases apart. For the linearized iteration the noisy and noise-free iterates differ by one resolvent applied to the noise; this gives an exact singular-value variance formula, a priori rates in expectation, and the main result: for a family of discretizations whose distance functions are bounded uniformly in the mesh, the rate is governed by that decay, which relaxes the classical range condition. The rate degrades gracefully, down to logarithmic, as the underlying continuum error loses smoothness, and a balancing rule attains it without knowing the smoothness. For the full nonlinear iteration under the order-one source condition, a truncated discrepancy principle fed only the noise level attains $σ_E^{1/2}$ in expectation, in the energy noise level $σ_E\asympσ/h$, the rare event of large noise being controlled by concentration. The rough nonlinear regime and the general-exponent nonlinear rate are left open and supported numerically for kink and jump errors. We separate the deterministic worst-case, Gaussian, and white-noise settings, prove a worst-case lower bound, and describe where the method is statistically inefficient relative to spectral cut-off. Heterogeneous media and a cost comparison with an adjoint-based scheme are given as supplementary material.

math.NA↗

arXiv2026

A noise-level-free parameter-choice rule for iterated Lavrentiev regularization of nonlinear potential monotone ill-posed problems

We consider nonlinear ill-posed operator equations $F(x)=y$ in a Hilbert space, where $F$ is monotone with a Lipschitz continuous Fréchet derivative that is self-adjoint near the solution $x^\dg$ (a locally \emph{potential} operator), and only noisy data $y^δ$ with unknown noise norm $δ:=\|y-y^δ\|$ is available. For the nonstationary iterated Lavrentiev regularization \[ x_{k+1}^δ=x_k^δ-\bigl(F'(x_k^δ)+α_kI\bigr)^{-1}\bigl(F(x_k^δ)-y^δ+α_k(x_k^δ-x_0)\bigr), \] all classical stopping rules require $δ$. We analyze a \emph{noise-level-free} parameter-choice rule of retrospective type, selecting a minimizer $k_*$ of $θ(k,y^δ)=\|F(x_k^δ)-y^δ\|^2/α_k^2$ over a finite computed window. Under a standard noise condition (necessary in view of the Bakushinskii veto) the rule is well defined and $α_{k_*}^2\ge c\,δ/\|x_0-x^\dg\|$. If moreover $x_0-x^\dg\in\R(F'(x^\dg))$ and $k_*\ge1$, we prove $\|x_{k_*}^δ-x^\dg\|=O(\sqrt{δ_*}+\sqrtδ)$ with the computable $δ_*=\|F(x_{k_*}^δ)-y^δ\|$ satisfying $κδ\leδ_*\le C\sqrtδ$, yielding the baseline rate $O(δ^{1/4})$ along admissible growing-horizon families, and $O(\sqrtδ)$ whenever $δ_*=O(δ)$; no range-invariance or tangential cone conditions are imposed. Rates under Hölder source conditions with $p\ge1$ (including saturation) follow; the case $p<1$, the removal of the self-adjointness assumption, and a full oracle inequality are identified as open problems.

math.NA↗

arXiv2026

Logical information localisation in stabiliser codes via single-qubit measurements

Stabiliser path finding (SPF) has previously been introduced as a method to localise logical information in a stabiliser code undergoing loss onto a single pre-specified target qubit, using only one round of single-qubit measurements. When working with limited resources and flying qubits, this fast read-out of logical information is a helpful tool for fault-tolerant communication. In this work, we provide a broad analytical and computational study of localisation via SPF. We introduce $g$-SPF, where the task is to localise the logical information onto a set of at most $g$ unspecified target qubits. Through analytical arguments based on percolation theory and the disjointness of stabiliser codes, we prove that for i.i.d. qubit loss with probability $p<1/2$ and sufficiently large planar surface codes, localisation via $g$-SPF for constant $g$ succeeds with a probability converging to one, which establishes a localisation threshold. Furthermore, we propose and implement two algorithms to solve SPF. The first is exact and formulates SPF as an integer linear program, whereas the second is heuristic and formulates SPF as a decoding problem. We validate both algorithms by numerically reproducing the localisation threshold for the surface code and demonstrate that the heuristic algorithm is considerably faster. Our work significantly reduces the time required to solve SPF compared to current state-of-the-art algorithms, allowing us to study localisation in substantially larger stabiliser codes than previously considered in the literature. Together, these theoretical and computational results open the door to various applications, such as fault-tolerant teleportation and efficient logical fusion.

quant-ph↗

arXiv2026

Strategies for Deploying AI Agents in Production at Scientific User Facilities

Agentic artificial intelligence (AI) is moving beyond research demonstrations toward production use at scientific user facilities, including light sources, neutron sources, nanoscience centers, and autonomous laboratories. Its scientific value extends beyond increasing throughput. Agents can perform repeatable tasks in calibration, measurement execution, and quality control, as well as initial analyses that turn data into reviewable evidence, allowing scientists to focus on hypotheses, unexpected observations, and interpretation. Drawing on deployments of LLM-driven agents at the APS, this perspective distills practical strategies with an emphasis on elements that can be reused across instruments and facilities. We discuss agent harnesses for beamline control, facility knowledge retrieval, and data analysis while keeping the underlying design principles independent of any specific implementation. These principles cover inference endpoints, tool-server architectures, non-text data, computationally intensive services, reusable skills, and governed learning throughout an instrument's lifecycle. We also consider how network and Linux operations, governed shared memory, and deterministic orchestration can extend these patterns across facility services. Because LLM capabilities continue to evolve, these recommendations represent a snapshot of the technology as of the date on the cover.

cs.SE↗

arXiv2026

APEXA: Execution-Integrity Enforcement for Multi-Agent LLM Automation of Synchrotron Data Reduction

LLM agents can make expert scientific workflows accessible through natural language, but a plausible response does not establish that the requested computation ran. This matters at synchrotron facilities, where calibration and integration are multi-step operations over terabyte-scale datasets. We present APEXA, a deployed framework coordinating 61 tools for synchrotron data reduction. A deterministic execution-integrity guard prevents it from returning results for tool calls that did not execute, and the same tool layer enforces motor safety: across 50 adversarial scenarios and four models, it produced 0/200 violations against a simulated EPICS controller, versus 15/200 for a prompt-only baseline. We also introduce APEXA-Bench, 58 facility tasks organized by scientific correctness and physical consequence. On real APS beamline data, one prompt recovered detector geometry and integrated a full attenuation and exposure sweep. Trustworthy scientific agents need deterministic validation of execution, not model-side assurances. We release the framework, benchmark, and traces.

cs.AI↗

arXiv2026

An End-to-End Differentiable Forward Model for High-Energy Diffraction Microscopy

High-Energy Diffraction Microscopy (HEDM) recovers crystallographic orientation, strain, and grain position from rotating-crystal X-ray diffraction patterns. Existing forward models in far-field (FF), near-field (NF), and point-focused (pf) HEDM are not differentiable, which forecloses gradient-based joint parameter refinement, physics-informed regularisation, and Bayesian uncertainty quantification. We present the first end-to-end differentiable HEDM forward model covering all three geometries, implemented in PyTorch with pixel-exact agreement against the established MIDAS reference simulators (162/162 FF, 2304/2304 NF including a non-zero detector-tilt sweep, and 1088/1096 pf-HEDM spots matched). Three demonstrations validate the framework: joint orientation-strain-position recovery in NF-HEDM at ~6 nm precision; round-trip refinement on a real 214-grain alpha-Ti FF-HEDM dataset reaching 100% grain recovery from a 1.5 degree initial perturbation with residuals matching the production fit to 0.3%; and joint refinement of all per-detector geometry parameters and per-grain state on a synthetic four-panel FF-HEDM setup, recovering panel rotations about the beam axis to ~10 mu-rad and a global rotation-axis wedge to ~26 mu-rad. The framework is released as the open-source midas-diffract package (pip install midas-diffract).

cond-mat.mtrl-sci↗

arXiv2026

Sharp Spectral Bounds for Symmetric Positive Definite Tensors via Multiple Algebraic Invariants

We extend the trace--determinant framework of Nayak, Sharma, and Mishra~\cite{nayak2026} for bounding the H-eigenvalues of symmetric positive definite tensors. First, we replace the Arithmetic--Geometric Mean (AM--GM) relaxation underlying previous bounds by the exact solution of the associated constrained optimization problem, yielding sharp upper and lower bounds that are attained on the admissible spectral variety. Second, we incorporate higher-order power sums as additional spectral invariants and prove a structural theorem showing that any extremizer over a $K$-invariant feasibility region has at most $K$ distinct spectral values. This reduces the problem to a finite collection of low-dimensional polynomial systems and yields a hierarchy of increasingly tight bounds. For the four-invariant case $(T,S,p_3,D)$, we develop a complete theory including solution-count estimates, a multistart Newton algorithm, and sharpness conditions. We also derive closed-form bounds in small dimensions, establish perturbation estimates, and obtain refined Lyapunov region-of-attraction bounds. Numerical experiments for dimensions up to $d=100$ show that the sharp three-invariant bound reduces the median relative overestimation gap from $53\%$ to $6\%$ while maintaining low computational cost. The framework is validated on tensors with real H-spectrum.

math.OC↗

arXiv2026

Randomized Estimation of T-Eigenvalues of T-SPD Tensors: A Two-Sided Bracket

In earlier work \cite{sharma2025} we developed deterministic analytical bounds on the T-eigenvalues of symmetric positive definite (SPD) third-order tensors under the Kilmer--Martin T-product: the trace--determinant (TDet) bounds via the AM--GM inequality, and the trace-dependent (TDep) bounds generalizing Samuelson's inequality. While these bounds are cheap and guaranteed-valid, their relative gap grows as $\sqrt{d-1}$ in the tensor dimension $d = np$, limiting their usefulness for large tensors. This paper develops randomized estimators for the extreme T-eigenvalues of T-SPD tensors that complement the deterministic bounds. We adapt the Halko--Martinsson--Tropp framework \cite{halko2011} to the T-product setting and introduce four methods: (i) a randomized power method that produces a lower bound on $λ_1$ with exponential convergence; (ii) a randomized subspace iteration with a tensor-analogue HMT error bound; (iii) a two-sided rigorous bracket combining the randomized lower bound with the deterministic TDep upper bound; and (iv) a Hutchinson-based fully randomized TDep bound for matvec-only settings.

math.NA↗

arXiv2026

CVEvolve: Autonomous Algorithm Discovery for Unstructured Scientific Data Processing

Scientific data processing often requires task-specific algorithms or AI models, creating a barrier for domain scientists who need to analyze their data but may not have extensive computing or image-processing expertise. This barrier is especially pronounced when data are noisy, have a high dynamic range, are sparsely labeled, or are only loosely specified. We introduce CVEvolve, an autonomous agentic harness with a zero-code interface for scientific data-processing algorithm discovery. CVEvolve combines a multi-round search strategy with tools for code execution, evaluation implementation, history management, holdout testing, and optional inspection of scientific data and visual outputs. The search alternates between discovery and improvement actions, and uses lineage-aware stochastic candidate sampling to balance exploration and exploitation. We demonstrate CVEvolve on X-ray fluorescence microscopy image registration, Bragg peak detection, high-energy diffraction microscopy image segmentation, and hybrid analytical-learning-based affine registration. Across these tasks, CVEvolve discovers algorithms that improve over baseline methods, while holdout test tracking helps identify candidates that generalize better than later over-optimized alternatives. These results show that zero-code, autonomous LLM-powered algorithm development can help domain scientists turn unstructured scientific image data into practical algorithms and downstream scientific discoveries.

cs.AI↗

arXiv2026

Sharp Convergence Rates and Optimal Weights for Cimmino's Reflection Algorithm

In this paper, Cimmino's classical reflection algorithm for solving the $n\times n$ nonsingular linear system $A\bx=\bb$ is analysed through the lens of spectral theory. Reformulating the weighted iteration as $\e^{(ν+1)}=M_w\,\e^{(ν)}$, where $M_w = I - A^\top D_w A$, the error is shown to contract by the spectral radius $\sprad(M_w)$ at every step, with a sharp, asymptotically tight bound. For $n=2$, a closed-form expression for the contraction factor is derived, \[ \sprad(M_w) \;=\; |1-μ| + \tfrac{1}{2}\sqrt{(w_1-w_2)^2 + 4w_1w_2\cos^2\!θ}, \] where $μ=(w_1+w_2)/2$ and $θ$ denotes the angle between the hyperplane normals. A central result of this paper is that the standard unit weights $w_1^*=w_2^*=1$ are \emph{globally optimal} over all positive weight pairs, uniquely achieving the minimum contraction factor $\sprad^*=|\cosθ|$ -- a quantity determined solely by the geometry of the hyperplane normals. The inter-normal angle $θ$ thus emerges as the single diagnostic parameter governing both convergence speed and weight selection. Extensions to a single-step convergence criterion at $θ=π/2$ and to an exact spectral rate for general~$n$ are also established.

math.NA↗

arXiv2026

Catalytic entanglement transformations with noisy hardware

The availability of certain entangled resource states (catalyst states) can enhance the rate of converting several less entangled states into fewer highly entangled states in a process known as catalytic entanglement concentration (EC). Here, we extend catalytic EC from pure states to mixed states and numerically benchmark it against non-catalytic EC and distillation in the presence of state-preparation errors and operational errors. Furthermore, we analyse the re-usability of catalysts in the presence of such errors. To do this, we introduce a novel recipe for determining the positive-operator valued measurements (POVM) required for EC transformations, which allows for making tradeoffs between the number of communication rounds and the number of auxiliary qubits required. We find that in the presence of low operational errors and depolarising noise, catalytic EC can provide better rates than distillation and non-catalytic EC.

quant-ph↗

arXiv2026

Spectral Bounds for Tensors Derived from Trace Functionals and Wasserstein Distance in Tensor Spaces

This article introduces a trace-based metric on the space of positive semi-definite (PSD) tensors, offering a geometric perspective that connects their algebraic structure to their intrinsic geometric properties. It defines the Bures-Wasserstein distance on tensor spaces, establishing clear measurements between tensors. Moreover, the study derives trace-based eigenvalue bounds for PSD tensors and analyzes how these bounds depend on the PSD condition. The behavior of these bounds is further explored when the PSD requirement is relaxed, with illustrative examples provided to support the theoretical findings. In addition, a detailed complexity analysis is carried out for the methods proposed in this study.

math.NA↗

arXiv2026

Iterative Methods for Computing the T-Square Root of Third-Order Tensors

We develop and analyze iterative methods for computing the principal square root of third-order tensors under the T-product framework. Tensor extensions of the Newton iteration (quadratic convergence) and the Denman--Beavers iteration (geometric convergence with simultaneous computation of the inverse square root) are proposed, with rigorous convergence guarantees established via the Fourier-domain block-diagonalization of the T-product. We apply these methods to image processing, introducing Tensor Decorrelated Grayscale conversion, T-Whitening, and optimal color transfer under the T-product geometry. We also formulate the Tensor Bures--Wasserstein distance and prove it defines a valid metric on the space of T-positive definite tensors. Numerical experiments confirm rapid convergence and demonstrate that the proposed tensor-based techniques offer improved structural preservation and cross-channel decorrelation compared to classical methods.

math.NA↗

arXiv2026

Eigenbounds of symmetric positive definite tensors

This article introduces an algebraic framework for establishing eigenvalue bounds for symmetric positive definite tensors by leveraging intrinsic invariants, specifically the trace and determinant (resultant). We derive a hierarchy of inequalities via the Arithmetic Mean-Geometric Mean (AM-GM) inequality that yields progressively tighter upper and lower bounds for the tensor spectral radius and smallest eigenvalue. A comprehensive comparative analysis demonstrates that our invariant-based approach significantly outperforms classical coordinate-dependent methods such as the Gershgorin circle theorem. We explicitly show that our bounds remain robust and informative in scenarios where Gershgorin bounds fail, particularly for tensors with negative off-diagonal entries, where algebraic cancellations occur, and higher-order tensors, where combinatorial growth leads to loose estimates. Furthermore, we validate the practical utility of these bounds by applying them to certify the positive definiteness of Lyapunov functions in the stability analysis of nonlinear autonomous systems.

math.NA↗

arXiv2026

AlphaDiffract: Automated Crystallographic Analysis of Powder X-ray Diffraction Data

Materials identification and structural understanding from powder X-ray diffraction (PXRD) data is a long-standing challenge in materials science, fundamental to discovering and characterizing novel materials. A prerequisite for full structure solution is the accurate determination of the crystal lattice, including lattice parameters and crystallographic symmetries. Traditional methods for this are iterative and typically require expert input, and while existing deep learning approaches have shown promise, a robust, single-shot method for comprehensive lattice determination from experimental data remains a key goal. Here, we introduce AlphaDiffract, a deep learning framework that achieves state-of-the-art performance in predicting the crystal system, space group, and lattice parameters directly from PXRD patterns. AlphaDiffract utilizes a 1D adaptation of the ConvNeXt architecture, a modern convolutional neural network that integrates key design principles from transformers, coupled with dedicated prediction heads for each crystallographic property. The model is trained on the largest-to-date physics-based dataset of over 31 million simulated diffraction patterns, generated by augmenting 312,267 curated structures from the ICSD and Materials Project databases. Crucially, it demonstrates strong generalization to experimental data, achieving 81.7% crystal system accuracy and 66.2% space group accuracy on the RRUFF dataset while additionally predicting all six lattice parameters. By providing a unified model for rapid and accurate lattice determination from PXRD data, AlphaDiffract represents a significant step forward in leveraging deep learning for high-throughput materials discovery.

cond-mat.mtrl-sci↗

arXiv2026

Unsupervised Semantic Segmentation in Synchrotron Computed Tomography with Self-Correcting Pseudo Labels

X-ray computed tomography (CT) is a widely used imaging technique that provides detailed examinations into the internal structure of an object with synchrotron CT (SR-CT) enabling improved data quality by using higher energy, monochromatic X-rays. While SR-CT allows for improved resolution, time-resolved experimentation, and reduced imaging artifacts, it also produces significantly larger datasets than conventional CT. Accurate and efficient evaluation of these datasets is a critical component of these workflows; yet is often done manually representing a major bottleneck in the analysis phase. While deep learning has emerged as a powerful tool capable of providing a wide range of purely data-driven solutions, it requires a substantial amount of labeled data for training and manual annotation of SR-CT datasets is impractical in practice. In this paper, we introduce a novel framework that enables automatic segmentation of large, high-resolution SR-CT datasets by eliminating the need to hand label images for deep learning training. First, we generate pseudo labels by clustering on the voxel values identifying regions in the volume with similar attenuation coefficients producing an initial semantic map. Afterwards, we train a segmentation model on the pseudo labels before utilizing the Unbiased Teacher approach to self-correct them ensuring accurate final segmentations. We find our approach improves pixel-wise accuracy and mIoU by 13.31% and 15.94%, respectively, over the baseline pseudo labels when using a magnesium crystal SR-CT sample. Additionally, we extensively evaluate the different components of our workflow including segmentation model, loss function, pseudo labeling strategy, and input type. Finally, we evaluate our approach on to two additional samples highlighting our frameworks ability to produce segmentations that are considerably better than the original pseudo labels.

cs.CV↗

arXiv2026

Minimising the number of edges in LC-equivalent graph states

Graph states are a powerful class of entangled states with numerous applications in quantum communication and quantum computation. Local Clifford (LC) operations that map one graph state to another can alter the structure of the corresponding graphs, including changing the number of edges. Here, we tackle the associated edge-minimisation problem: finding graphs with the minimum number of edges in the LC-equivalence class of a given graph. Such graphs are called minimum edge representatives (MER) and are crucial for minimising the resources required to create a graph state. We leverage Bouchet's algebraic formulation of LC-equivalence to encode the edge-minimisation problem as an integer linear program (EDM-ILP). We further propose a simulated annealing (EDM-SA) approach guided by the local clustering coefficient for edge minimisation. We identify new MERs for graph states with up to 16 qubits by combining EDM-SA and EDM-ILP. We extend the ILP to weighted-edge minimisation, where each edge has an associated weight, and prove that this problem is NP-complete. Finally, we employ our tools to minimise the resources required to create all-photonic generalised repeater graph states using fusion operations.

quant-ph↗