74 citations · 127 across the 20 of their papers we have counts for
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Quantum Topological Data Analysis Beyond Betti Numbers: Complexity Hardness An Algorithm for Torsion Witness
Nhat A. Nghiem, Dominic W. Berry, Trung V. Phan
Recent advances have revealed an interplay between quantum computing and topological data analysis (TDA). Most quantum TDA has focused on Betti numbers, which characterize the conn…
Quantum Advantage in Topological Data Analysis via Mayer Homology
Nhat A. Nghiem, Ryan Babbush, Adam Zalcman +4
Prior work has explored quantum algorithms for topological data analysis (TDA), revealing the possibility of exponential quantum speedups in estimating the ratios of Betti numbers…
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 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…
Fractatomic Physics: An Invitation with Atomic Stability and Rydberg States in Fractal Spaces
Nhat A. Nghiem, Trung V. Phan
We explore the physical quantum properties of atoms in fractal spaces, both as a theoretical generalization of normal integer-dimensional Euclidean spaces and as an experimentally…
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…
Size and Shape of Fuzzy Spheres from Matrix/Membrane Correspondence
Hai H. Vo, Olivia M. Markowich, Angeline Hu +2
We study the size and shape statistics of ground state fuzzy spheres when projected onto the transverse plane, utilizing the regularized SU(N=2) matrix model in D=(1+3)-dimensional…
Equal Radiation Frequencies from Different Transitions in the Non-Relativistic Quantum Mechanical Hydrogen Atom
Kim Tuan Do, Trung Phan
Is it possible that two different transitions in the non-relativistic quantum mechanical model of the hydrogen atom give the same frequency? That is, can different energy level tra…