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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…
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…
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…