Fig. 1: Cartoon illustration of the scrambling process.

a, The conventional CUT process, which uses a single unitary transform U to diagonalize a Hamiltonian H, smoothly transforming it from the initial basis (l = 0) to the diagonal basis (l → ∞). b, The scrambling transform S first induces ‘effective disorder’, even in completely clean systems, which allows established CUT techniques to then take over and efficiently diagonalize the scrambled Hamiltonian S†HS with a second unitary transform U.