IQIM Postdoctoral and Graduate Student Seminar

Abstract: In this talk, I will present quantum algorithms to estimate and transform eigenvalues of high dimensional matrices. Such an eigenvalue processing problem arises from applications such as simulating non-Hermitian physics, transcorrelated quantum chemistry and solving differential equations, but is out of the reach of existing quantum singular value algorithms, because eigenvalues are different from singular values for non-normal operators. I will show a natural reduction to the quantum linear system problem, whose solution produces a quantum superposition of Faber polynomials---a nearly-best polynomial basis for function approximation over the complex plane. I will introduce an extremely simple quantum linear system solver with optimal query complexity based on block preconditioning. I will also describe a circuit to generate $n$ Fourier coefficients in superposition with $O(polylog(n))$ gates improving over the standard approach with gate complexity $\Theta(n)$. Based on arXiv:2401.06240 and arXiv:2410.18178.

Following the talk, lunch will be provided on the lawn outside East Bridge.