Abstract: I will discuss recent advances in improving and costing quantum algorithms for linear differential equations. I will introduce a stability-based analysis of Berry et al.’s 2017 algorithm that greatly extends its scope and leads to complexities sublinear in time in a broad range of settings – Hamiltonian simulation being a boundary case that prevents this kind of broad fast-forwarding. I illustrate these gains via toy examples such as the linearized Vlasov-Possion equation, networks of coupled, damped, forced harmonic oscillators and quadratic nonlinear systems of ODEs. I will also present the first detailed cost analysis for a general quantum differential equation solver, taking the form of a plug-and-play analytical formula that takes in dynamical parameters and outputs query counts. Ref: https://arxiv.org/abs/2309.07881. Joint work with David Jennings (PsiQuantum), Robert B. Lowrie (LANL), Sam Pallister (PsiQuantum), Andrew T. Sornborger (LANL)
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