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Suppose I have three different operators $U_1, U_2,U_3$. Now, these three operators will be applied if my current state of the system is $|\psi_0\rangle,|\psi_1\rangle $ and $|\psi_2\rangle$ respectiv …

Is the following unitary transformation possible? If so, what will be the value of $U$? $$U|i,j_1\rangle = 1/\sqrt{k}(|i,j_1\rangle+|i,j_2\rangle+|i,j_3\rangle...+|i,j_k\rangle)$$ Here, $i$ is a node …

I am reading the following paper: Discrete-time quantum walk on complex networks for community detection by Kanae Mukai We define the Coin operator $C$ by: $C=C_1\otimes C_2....C_n$ , We define coin …

We define the quantum state on a complex network in the form, $$\mid\psi(t)\rangle=\sum_{i=1}^{N}\sum_{j=1}^{k_i}\psi_{i,j}(t)\lvert i\to j\rangle, $$ where $N$ is the total number of nodes, the stat …

I want to perform the following operation: $$U|0\rangle =1/\sqrt{n}\sum_{i=0}^{n}(|i\rangle).$$ I know that Hadmard gate can give me the superposition of states $|0\rangle$ and $|1\rangle$. But it can …

Let us take the initial state with the particle located at the origin $|n=0\rangle$ and the coin state with spin up $|0\rangle$. So, $$ |\psi(0)\rangle = |0\rangle|n=0\rangle, $$ where $|\psi(0)\rangl …

Please, help me understand this statement. The outer product notation for matrices also gives an intuitive input-output relation for them. For instance, the matrix |0⟩ ⟨1| + |1⟩ ⟨0| can be read as "ou …