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Optimal Quantum Eigenvalue Transformation via Linear Combinations of Hermitian Matrices
Yanqiao Wang, Yixuan Liang, Hongjia Chen +1
We discover two complementary linear-combination-of-Hermitian-matrices (LCHM) formulations to achieve a general non-normal matrix eigenvalue transformation . Firstly, for $A=…
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…
Quantum Speedups for Derivative Pricing Beyond Black-Scholes
Dylan Herman, Yue Sun, Jin-Peng Liu +5
This paper explores advancements in quantum algorithms for derivative pricing of exotics, a computational pipeline of fundamental importance in quantitative finance. For such cases…