Seminario Q-Math
Rational functions in quantum computing
Ponente: Niel Van Buggenhout (UC3M)Fecha: martes 12 de noviembre de 2024 - 13:00Lugar: Room 2.2.D08, Universidad Carlos III de Madrid
Online: https://eu.bbcollab.com/guest/d3ed81bffda3423692c5df53a2d584f4 (active on request)
Resumen:
In classical computing, rational functions form an essential tool for developing effective algorithms for solving interior eigenvalue problems and approximating matrix functions.
In quantum computing, the use of rational functions is underexplored. In this talk we introduce new methods for computing with rational functions on a quantum computer based on real-time evolution. We focus on computing matrix resolvents, since any rational function of a matrix can be written as a sum of resolvents.
The matrix resolvent can be represented as an integral in terms of a complex matrix exponential. We propose two techniques for the approximation of this integral. The first technique discretizes the integral into the sum of time samples of the matrix exponential. We give a detailed quantification of the computational cost of this technique. The second technique expands the weight function of the integral as a sum of Gaussians, splitting the integral into the sum of easy-to-compute integrals.
