Correction to: Quantum Systems Simulatability Through Classical Networks

We have shown that any two quantum systems on finite-dimensional Hilbert spaces are equivalent under local transformations. These transformations give rise to a gauge group that connects the hamiltonian operators associated with each quantum system. Different quantum systems are connected in such a way that studying one of them allows understanding the other. This result can be applied to the field of simulation of quantum systems, in order to mimic more complicated quantum systems from another simulatable quantum system. Given that there is a bridge that allows to simulate a particular quantum system on these kind of Hilbert spaces using classical circuits we will provide a general scenario to extend this bridge to simulate the time evolution, via Schrödinger equation, of any of these quantum systems using classical circuits. This classical systems can be implemented and controlled more easily in the laboratory than the quantum systems.