23 papers
Hybrid quantum-classical framework for Betti number estimation with applications to topological data analysis
Nhat A. Nghiem, Tzu-Chieh Wei
Topological data analysis (TDA) is a rapidly growing area that applies techniques from algebraic topology to extract robust features from large-scale data. A key task in TDA is the…
New aspects of quantum topological data analysis: Betti number estimation, and testing and tracking of homology and cohomology classes
Nhat A. Nghiem
We introduce several new quantum algorithms for estimating homological invariants, specifically Betti numbers and persistent Betti numbers, of a simplicial complex given via a stru…
Hybrid Quantum-Classical Algorithm for Hamiltonian Simulation
Nhat A. Nghiem, Tzu-Chieh Wei
We introduce a hybrid classical-quantum algorithm for simulating a Hamiltonian of the form $H= \sum_{i=1}^K H_i = \sum_{i=1}^K H_{i_1} \otimes H_{i_2} \otimes \cdots \otimes H_{i_M…
Toward speedup without quantum coherent access
Nhat A. Nghiem
Along with the development of quantum technology, finding useful applications of quantum computers has been a central pursuit. Despite various quantum algorithms have been develope…
Quantum Kaczmarz Algorithm for Solving Linear Algebraic Equations
Nhat A. Nghiem, Tuan K. Do, Trung V. Phan
We introduce a quantum linear system solving algorithm based on the Kaczmarz method, a widely used workhorse for large linear systems and least-squares problems that updates the so…
Quantum Algorithm for Estimating Betti Numbers Using Cohomology Approach
Nhat A. Nghiem, Xianfeng David Gu, Tzu-Chieh Wei
Topological data analysis has emerged as a powerful tool for analyzing large-scale data. An abstract simplicial complex, in principle, can be built from data points, and by using t…