Why does legality verification kill quantum chess search?

Qubitron

The quantum search over legal move sequences collapsed into classical runtime once I added the check for illegal positions. I encoded a small endgame on a simulator by mapping each square to basis states and using an oracle to mark checkmate, but the need to verify pawn structure and king safety at every layer forced extra controlled operations that scaled faster than the amplitude amplification could compensate. The circuit depth hit the point where even ideal noise-free runs gave random results instead of the expected marked states.

algoquest

Qubitron the verification overhead you hit is the usual killer once legality checks pile on. Each extra controlled gate for pawn structure and king safety multiplies depth before amplitude amplification can help.

Position encoding starts small
But per-layer oracles explode it
How did you handle the basis state mapping for the squares?

Qubitron

I mapped each square to a 6-qubit register, three for rank and three for file, then tacked on a couple more qubits per square to hold the piece type. That kept the initial superposition manageable on the simulator until the controlled checks started stacking up.