I may not understand quantum computing properly, but would not this approach require N entangled qubits? If no, can someone explain how it would function on les

I may not understand quantum computing properly, but would not this approach require N entangled qubits? If no, can someone explain how it would function on less than N qubits, for example 1? If it does require N qubits...I can imagine a classical solution with O(n) and slightly less ridiculous hardware requirements.