Entropy Scaling and Simulability by Matrix Product States

We investigate the relation between the scaling of block entropies and the efficient simulability by matrix product states (MPSs) and clarify the connection both for von Neumann and Rényi entropies. Most notably, even states obeying a strict area law for the von Neumann entropy are not necessarily approximable by MPSs. We apply these results to illustrate that quantum computers might outperform classical computers in simulating the time evolution of quantum systems, even for completely translational invariant systems subject to a time-independent Hamiltonian.

Figure 1

Relation between scaling of block Rényi entropies and approximability by MPSs. In the “undetermined” region, nothing can be said about approximability just from looking at the scaling.