The power of constant-depth quantum circuits of unbounded size
The research investigates implementing arbitrary quantum operations in constant depth using circuits built from single-qubit and generalized Toffoli gates, even without size or ancillary qubit restrictions. It finds exact constant-depth constructions for basis state permutations and pure state preparation. For general unitaries, it shows a method via port-based teleportation achieving O(√d) depth for fixed input dimension.