Compiling basic linear algebra subroutines for quantum computers

Abstract

Efficiently processing basic linear algebra subroutines is of great importance for a wide range of computational problems. In this paper, we consider techniques to implement matrix functions on a quantum computer, which are composed of basic matrix operations on a set of matrices. These matrix operations include addition, multiplication, Kronecker sum, tensor product, Hadamard product, and single-matrix functions. We discuss the composed matrix functions in terms of the estimation of scalar quantities such as inner products, trace, determinant and Schatten p-norms. We thus provide a framework for compiling instructions for linear algebraic computations into gate sequences on actual quantum computers.