Quantum Algorithms

I have said something like quantum computing can overpower classical computing several times before. In this series, I’m going to showing you a problem with a quantum algorithm that is exponentially faster in terms of complexity than any classical solution. In this text, we’re going to explore an essential technique and apply it to solve the simplest version of Deutsch problem. Phase kick-back One concept you may encouter numerous times in a Linear Algebra class is eigenvalues and eigenvectors. ...

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 $|-\rangle$. ...

Problem Statement Suppose Trong has just created a wonderful qubit in his lab. He knows his qubit look like $|\psi\rangle = \alpha |0\rangle + \beta |1\rangle$ but doesn’t know $\alpha$ and $\beta$. Now he wants to transport this qubit to his crush, but they don’t have a quantum channel that can help transport quantum information. Of course it’s a very bad idea for Trong to try to figure out $\alpha$ and $\beta$ through measurement because if he does so, he’ll destroy his qubit but only learn extremely little information about it. ...

Here we start exploring a core of Quantum Computing: Quantum Algorithms. Before we dive into the dark and deep pool of such algorithms, it’s helpful to get familiar with a fundamental constraint to Quantum Computing. In contrast, I’ll also introduce you how powerful qubits get in solving problems through a basic protocol: Quantum Teleportation, the “Hello, world!” of Quantum Programming. No-cloning theorem In terms of computer architechture, it’s convenient to copy the state of a bit in order to create a new qubit exactly the same. ...