Fig. 4: Given a set of bit strings over which to prepare the superposition state, this walk-based family of methods applies a heuristic for choosing an ordering of the basis states and then applies a sequence of merging (or equivalently splitting) operations to reduce (expand) an initial state to a desired endpoint.
Each merge (split) operation can be interpreted as a sequence of quantum walks. Ref. 19 uses the controlled G Gate as the primary merging operation, but this gate is equivalent to the action of a controlled P, controlled Rx, and controlled P gate, which are the CTQWs in this work.
