From the 1 of 9 linked papers with an AI index.
9 papers
Structure-Preserving Quantum Simulation of Wave Equations on a Trapped-Ion Processor
Abhishek Shringi, Hsuan-Cheng Wu, Ahmed Shokry +2
The authors design and benchmark Fourier-based quantum circuits that preserve structure for simulating one- and two-dimensional acoustic wave and Dirac equations on a trapped‑ion p…
Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables
Xiantao Li
Can a quantum PDE algorithm avoid the polynomial cost of resolving a fine spatial mesh? For standard fixed-order discretizations, direct classical methods require work polynomial i…
A Quantum Path to Partial Differential Equations
Xiantao Li
Partial differential equations are a promising application area for fault-tolerant quantum algorithms, but the subject lies between two communities with different languages: numeri…
Dynamically Optimal Unraveling Schemes for Simulating Lindblad Equations
Yu Cao, Mingfeng He, Xiantao Li
Stochastic unraveling schemes are powerful computational tools for simulating Lindblad equations, offering significant reductions in memory requirements. However, this advantage is…
Toward Efficient End-to-End Quantum Elliptic PDE Solvers: a Multilevel Correction Algorithm for Direct Observable Estimation
Xiantao Li
A central test case for quantum linear system algorithms (QLSA) is elliptic PDEs after a finite element discretization. Most existing analyses focus on preparing a normalized solut…
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…