From the 1 of 12 linked papers with an AI index.
12 papers
Optimal Quantum Eigenvalue Transformation via Linear Combinations of Hermitian Matrices
Yanqiao Wang, Yixuan Liang, Hongjia Chen +1
The paper presents two complementary linear-combination-of-Hermitian-matrices (LCHM) frameworks for implementing general eigenvalue transformations of non‑normal matrices on quantu…
From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms
Yanqiao Wang, Jin-Peng Liu, Peng Li +1
AI-assisted mathematics is often evaluated on solving predefined problems. In practice, however, many important advances begin earlier, when a vague research intuition is transform…
Structure-Preserving Quantum Method of Lines for Evolutionary PDEs with Mixed Boundary Conditions
Yixuan Liang, Jin-Peng Liu
We give detailed analysis and circuit design of structure-preserving quantum algorithms for second-order linear evolutionary PDEs, including parabolic equations and hyperbolic equa…
Sign Embedding Quantum Algorithms for Matrix Equations and Matrix Functions
Yanqiao Wang, Jin-Peng Liu
We develop a systematic sign-embedding framework of operator-output quantum algorithms for matrix equations and matrix functions. Differing from the contour-integral treatment, we…
Quantum Algorithms for Gibbs Expectation of Non-log-concave and Heavy-tailed Distributions
Xinmiao Li, Jin-Peng Liu
We establish a systematic framework of unbiased quantum sampling and estimation protocols for the classical Gibbs expectation. This framework generalizes existing approaches to the…
Efficient Quantum Simulation for Nonlinear Stochastic Differential Equations
Xiangyu Li, Ahmet Burak Catli, Ho Kiat Lim +4
Nonlinear stochastic differential equations (NSDEs) are a pillar of mathematical modeling for scientific and engineering applications. Accurate and efficient simulation of large-sc…