Figure 10
From: Universal quantum computing using single-particle discrete-time quantum walk
Quantum circuit on three qubit system and equivalent quantum walk scheme to implement same circuit is illustrated. Red circle represents \(\vert 0\rangle \) of the real particle and green circle represents \(\vert 1\rangle \) of the real particle. The input state is \(\vert \Psi \rangle _{in} = \vert 000\rangle \) and output state is a superposition of four states \(\vert \Psi \rangle _{out} = \frac{1}{2}\Big ( \vert 000\rangle + \vert 011\rangle + \vert 100\rangle + \vert 111\rangle \Big )\). \(CNOT_{23}\) is a position dependent shift operation given by \({\hat{S}}^{0}_{-}{\hat{S}}^{1}_{-}\) at position \(\vert 01\rangle \) and identity at other states.
