Quantum entanglement is both a most precious resource for quantum information processing and a headache in computational quantum physics. The study of entanglement in quantum many-body systems has recently led to a breakthrough in computational physics. A numerical algorithm originally designed to study the role of entanglement in quantum computation led to efficient ways of simulating time evolution in one-dimensional quantum many-body systems. Recently, extensions to systems in two spatial dimensions have been proposed. The present pace of progress rises a troubling question: do we really need a quantum computer to simulate quantum physics?