Compiling basic linear algebra subroutines for quantum computers

Efficiently processing basic linear algebra subroutines is of great importance for a wide range computational problems. In this paper, we consider techniques to implement matrix functions on quantum computer. We embed given matrices into 3 times larger Hermitian and assume as input set unitary operators generated by the embedding matrices. With formula, give Trotter-based elementary operations include addition, multiplication, Kronecker sum, tensor product, Hadamard arbitrary real eigenvalue single-matrix functions. then discuss composed in terms estimation scalar quantities such inner products, traces, determinants, Schatten p-norms with bounded errors. thus provide framework compiling instructions algebraic computations gate sequences actual computers. The calculating more efficient than best classical counterpart