Consider a Heisenberg spin chain Hamiltonian, \(H=-J \sum_{i} \vec{\sigma}_{i} \cdot \vec{\sigma}_{i+1}\), where \(\vec{\sigma}_{i}\) are the Pauli matrices at site \(i\) on a spin chain or, equivalently, on the data for a quantum computation, and the operator \(W=\sigma_{k}^{1}\), where \(k\) is a fixed site. Show that, indeed, \(W(t)\) spreads along the spin chain away from \(k\) as time evolves.