arXiv subjects

Akash Kumar Singh

Publications and source records attributed to Akash Kumar Singh.

3 recordsLinked to original sources

arXiv2025

A Polylogarithmic-Time Quantum Algorithm for the Laplace Transform

We introduce a quantum algorithm to perform the Laplace transform on quantum computers. Already, the quantum Fourier transform (QFT) is the cornerstone of many quantum algorithms, but the Laplace transform or its discrete version has not seen any efficient implementation on quantum computers due to its dissipative nature and hence non-unitary dynamics. However, a recent work has shown an efficient implementation for certain cases on quantum computers using the Taylor series. Unlike previous work, our work provides a completely different algorithm for doing Laplace Transform using Quantum Eigenvalue Transformation and Lap-LCHS, very efficiently at points which form an arithmetic progression. Our algorithm can implement $N \times N$ discrete Laplace transform in gate complexity that grows as $O((log\,N)^3)$, ignoring the state preparation cost, where $N=2^n$ and $n$ is the number of qubits, which is a superpolynomial speedup in number of gates over the best classical counterpart that has complexity $O(N\cdot log\,N)$ for the same cases. Also, the circuit width grows as $O(log\,N)$. Quantum Laplace Transform (QLT) may enable new Quantum algorithms for cases like solving differential equations in the Laplace domain, developing an inverse Laplace transform algorithm on quantum computers, imaginary time evolution in the resolvent domain for calculating ground state energy, and spectral estimation of non-Hermitian matrices.

quant-ph↗

arXiv2023

DeepVAT: A Self-Supervised Technique for Cluster Assessment in Image Datasets

Estimating the number of clusters and cluster structures in unlabeled, complex, and high-dimensional datasets (like images) is challenging for traditional clustering algorithms. In recent years, a matrix reordering-based algorithm called Visual Assessment of Tendency (VAT), and its variants have attracted many researchers from various domains to estimate the number of clusters and inherent cluster structure present in the data. However, these algorithms face significant challenges when dealing with image data as they fail to effectively capture the crucial features inherent in images. To overcome these limitations, we propose a deep-learning-based framework that enables the assessment of cluster structure in complex image datasets. Our approach utilizes a self-supervised deep neural network to generate representative embeddings for the data. These embeddings are then reduced to 2-dimension using t-distributed Stochastic Neighbour Embedding (t-SNE) and inputted into VAT based algorithms to estimate the underlying cluster structure. Importantly, our framework does not rely on any prior knowledge of the number of clusters. Our proposed approach demonstrates superior performance compared to state-of-the-art VAT family algorithms and two other deep clustering algorithms on four benchmark image datasets, namely MNIST, FMNIST, CIFAR-10, and INTEL.

cs.LG↗

arXiv2019

Multi Modal Semantic Segmentation using Synthetic Data

Semantic understanding of scenes in three-dimensional space (3D) is a quintessential part of robotics oriented applications such as autonomous driving as it provides geometric cues such as size, orientation and true distance of separation to objects which are crucial for taking mission critical decisions. As a first step, in this work we investigate the possibility of semantically classifying different parts of a given scene in 3D by learning the underlying geometric context in addition to the texture cues BUT in the absence of labelled real-world datasets. To this end we generate a large number of synthetic scenes, their pixel-wise labels and corresponding 3D representations using CARLA software framework. We then build a deep neural network that learns underlying category specific 3D representation and texture cues from color information of the rendered synthetic scenes. Further on we apply the learned model on different real world datasets to evaluate its performance. Our preliminary investigation of results show that the neural network is able to learn the geometric context from synthetic scenes and effectively apply this knowledge to classify each point of a 3D representation of a scene in real-world.

cs.CV↗