Nhat A. Nghiem

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…

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 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 Algorithms for Computing Maximal Quantum $f$ -divergence and Kubo-Ando means

Trung Hoa Dinh, Nhat A. Nghiem

The development of quantum computation has resulted in many quantum algorithms for a wide array of tasks. Recently, there is a growing interest in using quantum computing technique…

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 topological data analysis algorithm for dynamical systems

Nhat A. Nghiem

Dynamical systems appear in nearly every aspect of the physical world. As such, understanding the properties of dynamical systems is of great importance. Typically, a dynamical sys…

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…

Towards quantum topological data analysis: torsion detection

Nhat A. Nghiem

Topological data analysis (TDA) has become an attractive area for the application of quantum computing. Recent advances have uncovered many interesting connections between the two…

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…

Refined Quantum Algorithms for Principal Component Analysis and Solving Linear System

Nhat A. Nghiem

We outline refined versions of two major quantum algorithms for performing principal component analysis and solving linear equations. Our methods are exponentially faster than thei…

Quantum Advantage in Testing (Local) Convexity and Monotonicity of Function

Nhat A. Nghiem

It is shown that a quantum computer can test the convexity and monotonicity of a given function exponentially more efficiently than a classical computer. This establishes another p…

Quantum Speedup in Dissecting Roots and Solving Nonlinear Algebraic Equations

Nhat A. Nghiem

It is shown that quantum computer can detect the existence of root of a function almost exponentially more efficient than the classical counterpart. It is also shown that a quantum…

Quantum Algorithms Without Coherent Quantum Access

Nhat A. Nghiem

Demonstrating quantum advantage has been a pressing challenge in the field. Most claimed quantum speedups rely on a subroutine in which classical information can be accessed in a c…

New Quantum Algorithm For Solving Linear System of Equations

Nhat A. Nghiem

Linear equations play a pivotal role in many areas of science and engineering, making efficient solutions to linear systems highly desirable. The development of quantum algorithms…

Estimation of Nonlinear Physical Quantities By Measuring Ancillas

Nhat A. Nghiem, Tzu-Chieh Wei

In this article, we present quantum algorithms for estimating von Neumann entropy and Renyi entropy, which are crucial physical and information-theoretical properties of a given qu…

quant-ph2025★ 1 cited

New Quantum Algorithm for Principal Component Analysis

Nhat A. Nghiem

Quantum principal component analysis (QPCA) ignited a new development toward quantum machine learning algorithms. Initially showcasing as an active way for analyzing a quantum syst…

A Framework For Estimating Amplitudes of Quantum State With Single-Qubit Measurement

Nhat A. Nghiem

We propose and analyze a simple framework for estimating the amplitudes of a given $n$ -qubit quantum state $∣ ψ ⟩ = \sum_{i = 0}^{2^{n} - 1} a_{i} ∣ i ⟩$ in computational basis, utilizin…

Simple Quantum Gradient Descent Without Coherent Oracle Access

Nhat A. Nghiem

The gradient descent method aims at finding local minima of a given multivariate function by moving along the direction of its gradient, and hence, the algorithm typically involves…

Improved Time-independent Hamiltonian Simulation

Nhat A. Nghiem

We describe a simple method for simulating time-independent Hamiltonian $H$ that could be decomposed as $H = \sum_{i = 1}^{m} H_{i}$ where each $H_{i}$ can be efficiently simulated. Approa…