Quantum computers are designed based on quantum mechanics principle, they are most suitable to solve the Schrodinger equation, and linear PDEs (and ODEs) evolved by unitary operators. Nonlinearity and Nonunitarity are the main challenges for quantum simulations of PDEs. For linear PDEs (and ODEs) Schroginerization provides a general method to unitarize them for quantum simulation. For nonlinear problems we first introduce our quantum algorithms for (nonlinear) Hamiton-Jacobi equations, for both multi-valued solutions and viscosity solutions that are needed beyond the formation of caustics. We also introduce quantum algorithms for Young measures associated with nonlinear PDEs, which are effective tools to compute weak solutions to nonlinear PDEs that have singular solutions such as shocks, caustics, physical instabilities or (random) uncertainties.
We also introduce “UnitaryLab”, which is an AI-powered research software package of quantum algorithms for scientific computing.
Streaming of the seminar will be possible upon request by emailing: giacomo.albi@univr.it
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