3 papers
quant-ph2026
Quantum Data Loading for Carleman Linearized Systems: Application to the Lattice-Boltzmann Equation
Reuben Demirdjian, Thomas Hogancamp, Abeynaya Gnanasekaran +2
Nonlinear ordinary and partial differential equations are ubiquitous in science and engineering, yet finding their solutions is often computationally intractable for classical hard…
quant-ph2026
An Efficient Decomposition of the Carleman Linearized Burgers' Equation
Reuben Demirdjian, Thomas Hogancamp, Daniel Gunlycke
Herein, we present a polylogarithmic decomposition method to load the matrix from the linearized 1-dimensional Burgers' equation onto a quantum computer. First, we use the Carleman…
quant-ph2026
A Linear Combination of Unitaries Decomposition for the Laplace Operator
Thomas Hogancamp, Reuben Demirdjian, Daniel Gunlycke
We provide novel linear combination of unitaries decompositions for a class of discrete elliptic differential operators. Specifically, Poisson problems augmented with periodic, Dir…