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

# Equal superposition state
An important part of most quantum circuits is the equal superposition state. It gives us the power to represent an **exponential** number of states with respect to the number of qubits we have at our disposal.

How can we create a superposition state representing our whole qubit system? You might recall that the **Hadamard** gate $H$ is used to put one qubit in an equal superposition state. This is the key concept here. If we have **five** qubits at our disposal, applying the **Hadamard** gate $H$ on each qubit will enable us to generate a superposition of $2^5$ states. Let's take a look at a simple example using only two qubits:

$$H^{\otimes2}|00\rangle = H|0\rangle \otimes H|0\rangle$$ 

$$H^{\otimes2}|00\rangle = (\frac{1}{\sqrt{2}}|0\rangle + 
 \frac{1}{\sqrt{2}}|1\rangle) \otimes (\frac{1}{\sqrt{2}}|0\rangle + 
 \frac{1}{\sqrt{2}}|1\rangle)$$ 

$$H^{\otimes2}|00\rangle = \frac{1}2(|00\rangle + |01\rangle + |10\rangle + |11\rangle)$$ 

As you can see, the state of our system has an equal chance of 25% to yield either of the states in the superposition upon measurement.
Let's have a look at the circuit diagram.





Let's see how to build proper quantum circuits using the gates we've learned so far.

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

Building Quantum Circuits