Figure 2

Proposed comparator. Scheme of the proposed comparator, for the \(N=4\) digit case. Two numbers a and b are compared. \(a_{i}\) represent the digits of a, whereas the digits of b are encoded in the circuit using quantum gates. Boxes labelled with numbers \(0\ldots N-1\) represent such digits, so that boxes marked as 0 will be Pauli-I or Pauli-X gates depending on whether \(b_{0}\) is 0 or 1, respectively; boxes marked as 1 will be Pauli-I or Pauli-X gates depending on whether \(b_{1}\) is 0 or 1, respectively, and so on for each digit of b. Qubits labelled with an A are prepared in the \(\frac{1}{\sqrt{2}}(| 0 \rangle + e^{\frac{i\pi}{4}} | 1 \rangle )\) state for be used with temporary logical-AND gates