4 papers
An efficient explicit implementation of a near-optimal quantum algorithm for simulating linear dissipative differential equations
Ivan Novikau, Ilon Joseph
We propose an efficient block-encoding technique for the implementation of the Linear Combination of Hamiltonian Simulations (LCHS) for simulating dissipative initial-value problem…
Globalizing the Carleman linear embedding method for nonlinear dynamics
Ivan Novikau, Ilon Joseph
The Carleman embedding method is a widely used technique for linearizing a system of nonlinear differential equations, but fails to converge in regions where there are multiple fix…
Estimating QSVT angles for matrix inversion with large condition numbers
I. Novikau, I. Joseph
Quantum Singular Value Transformation (QSVT) is a state-of-the-art, near-optimal quantum algorithm that can be used for matrix inversion. The QSVT circuit is parameterized by a seq…
Quantum algorithm for the advection-diffusion equation and the Koopman-von Neumann approach to nonlinear dynamical systems
Ivan Novikau, Ilon Joseph
We propose an explicit algorithm based on the Linear Combination of Hamiltonian Simulations technique to simulate both the advection-diffusion equation and a nonunitary discretized…