Scaling of the energy and entropy errors in quantum circuits

Abstract

Quantum algorithms based on simulating states of a quantum system cannot simulate these states without an error. This work studies the relations between the error of an approximated quantum circuit that simulates the ground state of a Hamiltonian and the error of the energy and Von Neumann entropy of this state. In addition, we relate the errors with the gate cost of the approximated quantum circuit using the Solovay-Kitaev theorem