Fast quantum subroutines for the simplex method

Abstract

We propose quantum subroutines for the simplex method that avoid classical computation of the basis inverse. For sparse problems the quantum subroutines scale better in m and n (but worse in the condition number of the basis and a precision tolerance), and may therefore have a worst-case asymptotic advantage. An important feature of our paper is that this asymptotic speedup does not depend on the data being available in some ``quantum form'': the input of our quantum subroutines is the natural classical description of the problem, and the output is the index of the variables that should leave or enter the basis.