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pro vyhledávání: '"Nghiem, Nhat A."'
Autor:
Nghiem, Nhat A.
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. Approaches relying on product formula generally work by splitting the evolut
Externí odkaz:
http://arxiv.org/abs/2410.15256
Autor:
Nghiem, Nhat A.
We propose a new method for simulating certain type of time-dependent Hamiltonian $H(t) = \sum_{i=1}^m \gamma_i(t) H_i$ where $\gamma_i(t)$ (and its higher order derivatives) is bounded, computable function of time $t$, and each $H_i$ is time-indepen
Externí odkaz:
http://arxiv.org/abs/2410.14418
Autor:
Nghiem, Nhat A.
We describe a simple quantum algorithm for simulating time-dependent Hamiltonian, extending the methodology of quantum signal processing. Thus, the framework achieves optimal scaling up to some factor scaling with other parameters, and nearly optimal
Externí odkaz:
http://arxiv.org/abs/2410.14366
Autor:
Nghiem, Nhat A., Wei, Tzu-Chieh
Functions are a fundamental object in mathematics, with countless applications to different fields, and are usually classified based on certain properties, given their domains and images. An important property of a real-valued function is its convexi
Externí odkaz:
http://arxiv.org/abs/2409.03312
Quantum singular value transformation (QSVT) is a framework that has been shown to unify many primitives in quantum algorithms. In this work, we leverage the QSVT framework in two directions. We first show that the QSVT framework can accelerate one r
Externí odkaz:
http://arxiv.org/abs/2407.11744
Autor:
Nghiem, Nhat A., Wei, Tzu-Chieh
Nonlinear equations are challenging to solve due to their inherently nonlinear nature. As analytical solutions typically do not exist, numerical methods have been developed to tackle their solutions. In this article, we give a quantum algorithm for s
Externí odkaz:
http://arxiv.org/abs/2404.03810
Autor:
Nghiem, Nhat A.
Topological data analysis (TDA) is a fast-growing field that utilizes advanced tools from topology to analyze large-scale data. A central problem in topological data analysis is estimating the so-called Betti numbers of the underlying simplicial comp
Externí odkaz:
http://arxiv.org/abs/2403.04686
Autor:
Nghiem, Nhat A., Wei, Tzu-Chieh
Block encoding is a key ingredient in the recently developed quantum signal processing that forms a unifying framework for quantum algorithms. Initially showcased for simplifying and optimizing resource utilization in several problems, such as search
Externí odkaz:
http://arxiv.org/abs/2312.14786
Autor:
Nghiem, Nhat A., Wei, Tzu-Chieh
Following the celebrated quantum algorithm for solving linear equations (so-called HHL algorithm), Childs, Kothari and Somma [SIAM Journal on Computing, {\bf 46}: 1920, (2017)] provided an approach to solve a linear system of equations with exponenti
Externí odkaz:
http://arxiv.org/abs/2311.14044
Topological data analysis has emerged as a powerful tool for analyzing large-scale data. High-dimensional data form an abstract simplicial complex, and by using tools from homology, topological features could be identified. Given a simplex, an import
Externí odkaz:
http://arxiv.org/abs/2309.10800