Gain insights into quantum computing, starting with qubits and quantum mechanics. Discover quantum gates, circuits, and algorithms like Grover’s search and Shor’s factoring. Explore potential applications.

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Quantum Computing

Jupyter Notebook

Firms like IBM, Honeywell, Zapata, Rigetti, Amazon, Google, IonQ, and others are all adopting and investing heavily in quantum computing. This is a great opportunity to get involved.

In this course, you will learn the fundamentals of quantum computing, starting with quantum bits or qubits. These are the centerpiece and most basic computational unit. 

You will then move on to quantum mechanics and the role of quantum gates, circuits, and simulating computers. From there, you will get acquainted with the many different quantum algorithms that are asymptotically faster than their classical counterparts. These include: Deutsch Jozsa, Grover’s search, and Shor’s factoring.

By the end of this course, you will have the foundations in place to start exploring more applications of quantum computing. This is just the beginning!

The Fundamentals of Quantum Computing

We've introduced you to the basic single qubit and multi-qubit gates that are widely used while working on quantum algorithms. However, those gates always perform a fixed operation or a fixed rotation around one of the axes of the **Bloch** Sphere. What if we wanted to change the state of a qubit to any state of our choice or, perform a rotation on the **Bloch** Sphere using some arbitrary value? This is where **parametric** gates come in. Such gates come in handy while working on **variational quantum algorithms.**

# The $\space R_\phi \space$ gate

The $R_z$ gate is parameterized by $\phi$, which tells it exactly what operation to perform, or in other words, it defines a rotation of $\phi$ radians across the $Z$-axis of the **Bloch** Sphere. The parameter $\phi$ can be any real number. Let's take a look at how it is defined as a matrix:

$$R_z(\phi)=\begin{bmatrix}1&0\\0&e^{i\phi}\end{bmatrix}$$

One thing you'll notice is that at $\phi=\pi$, this gate becomes identical to the $Z$-gate. We can think of this as a more general gate that we can use to generate all possible gates that perform rotations across the $Z$-axis of the **Bloch** Sphere.

If we substitute $\phi=\pi/2$, the resultant gate is known as the **S-gate**. It's basically the same as the $Z$-gate but performs a half rotation. Two $S$-gates in succession would be equivalent to one $Z$-gate.

We'll look at some general gates that are useful for advanced quantum algorithms.

Baby Steps

The Essence of Quantum Mechanics

Quantum Gates and Circuits

Simulating Quantum Computers

Getting Started with Quantum Algorithms

The Deutsch-Jozsa Algorithm

Grover's Search Algorithm

Shor's Factoring Algorithm

The Future

Parametric Gates

The $\space R_\phi \space$ gate

Parametric Gates

The Rϕ \space R_\phi \space Rϕ​ gate

The $\space R_\phi \space$ gate