Project

Knowing the underpinnings of randomized benchmarking addressed in the last part, we first begin with the standard protocol. Standard RB is used to assess the error rate over gates of Clifford group with an assumption that these gates have the same error rate. After that, another improvement of the technique will be introduced, namely Interleaved Randomized Benchmarking. The upgraded version was proposed not to investigate the Clifford group as a whole, but restricted to one single kind of Clifford gate of our choice. ...

In the last part of the previous series, Deutsch algorithm, I introduced a manual way to construct the oracle. That oracle must be built from matrix because the oracle function is undeterminate except for the outcome. In Bernsterin-Vazirani problem, the function is, on the other hand, clearly stated: $f(\mathbf{x}) = \mathbf{s}\cdot\mathbf{x}$. So, it’s unnecessary to repeat the previous procedure; instead, we’ll build the oracle without using matrices by understanding what the function really do. ...

Because the Deutsch algorithm is just a simple instance of the Deutsch-Jozsa algorithm where $n=2$, we’ll only discuss how to implement the general one. Let’s go. Difficulty of reconstructing gates from matrices This is the first time we encounter a so-called black-box function in an algorithm. It’s called a black box since we don’t how it calculate the output from the input, but we do know the output it returns. ...

Let’s implement and verify the teleporation protocol following the procedure we discussed throughout previous parts. First we need to create an arbitrary quantum state. Trong has been curious about the combined effect of rotation gates about the x, y, and z axes. So, he decides to apply three distinct rotation gates, each as a rotation of 60 degrees around one coordinate axis acting on a qubit currently in the Hadamard state $|-\rangle$. ...

Quantum entanglement Have you ever thought of a situation when the happening of an event in an isolated environment dictates the result of another event also in an isolated environment with no communication allowed? That sounds infeasible in our view of reality, except that these two separated events share a somewhat telepathic power. Yes, this telepathy really happens in the realm of quantum entanglement. The phenomenon can be simplified that the result of the first measurement reveals information about the result of the second measurement despite an absolute separation and no communication setting. ...