Bernstein-Vazirani Algorithm

Here is some personal notes on Bernstein-Vazirani algorithm. Assume that we have a black box that does nothing but compute , where is an input binary vector and is another binary vector that we don’t know its value. Note that all operation is bit-wise and so the output is binary also. The question is how…

Hadamard gates on multiple qubits

The effect of applying Hadamard gates to multiple qubits is rather subtle and is used in many quantum algorithms. Consider input qubits, . What will be the output if we apply the Hadamard gate to each of the qubit? Note that a Hadamard gate maps to and to . So ignoring the scaling factor, the…

Quantum Teleportation

Let say Alice wants to pass her qubit to Bob. By no cloning theorem, we know that Alice cannot duplicate her qubit to Bob. However, she can “teleport” her qubit to Bob if they share a Bell state . First, Alice will apply CNOT gate from to her qubit in the shared Bell state. This…

Proof of no cloning theorem

I’m still studying the online course on quantum computing where Prof. Vazirani went through the no cloning theorem. It is very interesting to see that something that can lead to some very subtle consequence can also have a very simple proof. Below is a summary. Basically, the theorem states that no quantum state can be…

Bell’s Experiment

I am studying the online class on quantum computing (coursera). I did a quantum mechanic course more than a decade ago but I didn’t go into the detail of the Bell’s experiment then. The explanation from Prof. Vazirani is great and I feel that I finally understand the setup after all these years! Here, I…