Can one use a quantum circuit as a part of a path finding algorithm?

I posted a more detailed description of the problem here: https://quantumcomputing.stackexchange.com/questions/13731/can-one-use-a-quantum-circuit-as-a-pathfinding-algorithm But the gist of it is: if quantum computing can be viewed as a binary search tree, then can the circuit be viewed as the directions to take in order to quickly get to the solution? It seems that if we start with a linear tree in the |0> state, and space out the Hadamard gates so that comparison/conditional branches can be closed as soon as possible, then the size of the BST we obtain is limited by the height, which is the number of bits in the system, times the width, which is the number of qubits in superposition that are interacting with a conditional bit at any given time, which seems that, with proper circuit design, can be limited to two qubits being compared at any one time. Thus, the complexity of solving the circuit on a classical computer should be about 4 * height. It seems plausible that this could improve classical simulations of quantum systems. Or do quantum circuits become too complex to be modeled in such a way?

Edit: I believe the complexity of solving the circuit should actually be the # of solutions * 4 * the height of the tree.

Asked on September 14, 2020 in Optimization.
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