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Structure-Preserving Quantum Simulation of Wave Equations on a Trapped-Ion Processor
Abhishek Shringi, Hsuan-Cheng Wu, Ahmed Shokry +2
Wave equations provide a natural testbed for near-term quantum simulation of partial differential equations, but hardware demonstrations have remained limited in spatial dimension,…
From Nonlinear Stochastic Differential Equations to Quantum Channels: The Kolmogorov--Lindblad Mapping
Hsuan-Cheng Wu, Xiantao Li
Nonlinear stochastic differential equations (SDEs) underlie molecular modeling and drug discovery, quantitative finance, stochastic learning, and uncertainty quantification. Their…
Quantum Simulation of Differential-Algebraic Equations with Applications to Unsteady Stokes Flow
Hsuan-Cheng Wu, Xiantao Li
Differential-algebraic equations (DAEs) arise naturally in constrained dynamical systems, but their algebraic constraints and hidden compatibility conditions make them more subtle…
Universal Dilation of Linear Itô SDEs: Quantum Trajectories and Lindblad Simulation of Second Moments
Hsuan-Cheng Wu, Xiantao Li
We present a universal framework for simulating -dimensional linear Itô stochastic differential equations (SDEs) on quantum computers with additive or multiplicative noises. Bui…
Structure-preserving quantum algorithms for linear and nonlinear Hamiltonian systems
Hsuan-Cheng Wu, Xiantao Li
Hamiltonian systems of ordinary and partial differential equations are fundamental mathematical models spanning virtually all physical scales. A critical property for the robustnes…
Quantum Algorithms for Nonlinear Dynamics: Revisiting Carleman Linearization with No Dissipative Conditions
Hsuan-Cheng Wu, Jingyao Wang, Xiantao Li
In this paper, we explore the embedding of nonlinear dynamical systems into linear ordinary differential equations (ODEs) via the Carleman linearization method. Under dissipative c…