7 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…
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…
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…
Quantum Algorithm for Estimating Ollivier-Ricci Curvature
Nhat A. Nghiem, Linh Nguyen, Tuan K. Do +2
We introduce a quantum algorithm for computing the Ollivier Ricci curvature, a discrete analogue of the Ricci curvature defined via optimal transport on graphs and general metric s…
Quantum Algorithm for Estimating Intrinsic Geometry
Nhat A. Nghiem, Tuan K. Do, Tzu-Chieh Wei +1
High-dimensional datasets typically cluster around lower-dimensional manifolds but are also often marred by severe noise, obscuring the intrinsic geometry essential for downstream…
Improved Quantum Algorithms for Eigenvalues Finding and Gradient Descent
Nhat A. Nghiem, Tzu-Chieh Wei
Block encoding is a key ingredient in the recently developed quantum singular value transformation (QSVT) framework, which provides a unifying description for many quantum algorith…