Context-aware quantum simulation of a matrix stored in quantum memory

Abstract

In this paper, a storage method and a context-aware circuit simulation idea are presented for the sum of block diagonal matrices. Using the design technique for a generalized circuit for the Hamiltonian dynamics through the truncated series, we generalize the idea to (0-1) matrices and discuss the generalization for the real matrices. The presented circuit requires O(n) number of quantum gates and yields the correct output with the success probability depending on the number of elements: For matrices with poly(n), the success probability is 1 / poly(n). Since the operations on the circuit are controlled by the data itself, the circuit can be considered as a context-aware computing gadget. In addition, it can be used in variational quantum eigensolver and in the simulation of molecular Hamiltonians.