1 citations · 1 across the 9 of their papers we have counts for
9 papers
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,…
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…
Toward Efficient End-to-End Quantum Elliptic PDE Solvers: a Multilevel Correction Algorithm for Direct Observable Estimation
Xiantao Li
Spatial derivatives pose a basic challenge for quantum algorithms for partial differential equations: their standard discretizations have operator norms that grow as the mesh is re…
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…
A Residual-Based Quantum Linear System Algorithm with Dynamic Stopping and Applications to Elliptic PDEs
Xiantao Li
Quantum linear-system algorithms (QLSAs) have rigorous worst-case complexity guarantees, but their runtimes are often chosen from spectral information assumed in advance. What is l…
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…
Reducing Circuit Depth in Lindblad Simulation via Step-Size Extrapolation
Pegah Mohammadipour, Xiantao Li
We study algorithmic error mitigation via Richardson-style extrapolation for quantum simulations of open quantum systems modelled by the Lindblad equation. Focusing on two specific…
Direct Analysis of Zero-Noise Extrapolation: Polynomial Methods, Error Bounds, and Simultaneous Physical-Algorithmic Error Mitigation
Pegah Mohammadipour, Xiantao Li
Zero-noise extrapolation (ZNE) is a widely used quantum error mitigation technique that artificially amplifies circuit noise and then extrapolates the results to the noise-free cir…