Asir Abrar | Searcharxiv

arXiv2023

Minimum Trotterization Formulas for a Time-Dependent Hamiltonian

When a time propagator $e^{δt A}$ for duration $δt$ consists of two noncommuting parts $A=X+Y$, Trotterization approximately decomposes the propagator into a product of exponentials of $X$ and $Y$. Various Trotterization formulas have been utilized in quantum and classical computers, but much less is known for the Trotterization with the time-dependent generator $A(t)$. Here, for $A(t)$ given by the sum of two operators $X$ and $Y$ with time-dependent coefficients $A(t) = x(t) X + y(t) Y$, we develop a systematic approach to derive high-order Trotterization formulas with minimum possible exponentials. In particular, we obtain fourth-order and sixth-order Trotterization formulas involving seven and fifteen exponentials, respectively, which are no more than those for time-independent generators. We also construct another fourth-order formula consisting of nine exponentials having a smaller error coefficient. Finally, we numerically benchmark the fourth-order formulas in a Hamiltonian simulation for a quantum Ising chain, showing that the 9-exponential formula accompanies smaller errors per local quantum gate than the well-known Suzuki formula.

quant-ph↗

arXiv2022

Patients' Severity States Classification based on Electronic Health Record (EHR) Data using Multiple Machine Learning and Deep Learning Approaches

This research presents an examination of categorizing the severity states of patients based on their electronic health records during a certain time range using multiple machine learning and deep learning approaches. The suggested method uses an EHR dataset collected from an open-source platform to categorize severity. Some tools were used in this research, such as openRefine was used to pre-process, RapidMiner was used for implementing three algorithms (Fast Large Margin, Generalized Linear Model, Multi-layer Feed-forward Neural Network) and Tableau was used to visualize the data, for implementation of algorithms we used Google Colab. Here we implemented several supervised and unsupervised algorithms along with semi-supervised and deep learning algorithms. The experimental results reveal that hyperparameter-tuned Random Forest outperformed all the other supervised machine learning algorithms with 76% accuracy as well as Generalized Linear algorithm achieved the highest precision score 78%, whereas the hyperparameter-tuned Hierarchical Clustering with 86% precision score and Gaussian Mixture Model with 61% accuracy outperformed other unsupervised approaches. Dimensionality Reduction improved results a lot for most unsupervised techniques. For implementing Deep Learning we employed a feed-forward neural network (multi-layer) and the Fast Large Margin approach for semi-supervised learning. The Fast Large Margin performed really well with a recall score of 84% and an F1 score of 78%. Finally, the Multi-layer Feed-forward Neural Network performed admirably with 75% accuracy, 75% precision, 87% recall, 81% F1 score.

cs.LG↗