4 papers
Provable Quantum Speedups for Reaction-Rate Estimation in High-Dimensional Fokker-Planck Dynamics
Tyler Kharazi, Ahmad M. Alkadri, Kranthi K. Mandadapu +1
The Fokker-Planck equation models rare events across sciences, but blue{direct solution of the PDE is intractable for classical computers due to } its high-dimensional nature. Clas…
A Quantum Algorithm for the Finite Element Method
Ahmad M. Alkadri, Tyler D. Kharazi, K. Birgitta Whaley +1
The finite element method (FEM) is a cornerstone numerical technique for solving partial differential equations (PDEs). Here, we present , a fault-tolerant era qua…
Arbitrary Boundary Conditions and Constraints in Quantum Algorithms for Differential Equations via Penalty Projections
Philipp Schleich, Tyler Kharazi, Xiangyu Li +3
Complicated boundary conditions are essential to accurately describe phenomena arising in nature and engineering. Recently, the investigation of a potential speedup through quantum…
Explicit block encodings of boundary value problems for many-body elliptic operators
Tyler Kharazi, Ahmad M. Alkadri, Jin-Peng Liu +2
Simulation of physical systems is one of the most promising use cases of future digital quantum computers. In this work we systematically analyze the quantum circuit complexities o…