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

That was quite a journey with **Number Theory**, **Algebra**, and **Modular Arithmetic**. To ensure that the essential material sticks, let's summarize some concepts that lie at the heart of **Shor's Algorithm**.



The first thing to realize is that **Shor's Algorithm** translates the difficult task of factorization to a task centered around the greatest common divisors. Therefore, this technique of formulating a problem differently can be a potential approach to algorithmic thinking in both classical and quantum computation. So we ask ourselves the question: is there a different way of approaching the same problem? If the answer is yes, in some cases, this can lead to efficient solutions. We saw one instance of this throughout this chapter.

The second technique is more specific to quantum computers. Recall that **Shor's Algorithm** is based on using $QFT$ and $QFT^\dagger$. Essentially, these procedures allow us to _copy_ the phase of a state into some qubits that we then measure to retrieve the hidden phase information. It is a powerful technique, and you'll see it being used in algorithms besides Shor's as well. One example of one such algorithm is $QPE$ itself, which we saw just before starting our discussion on Shor's.

We've also studied $QFT$ in isolation. It was the first preliminary concept we learned to understand **Shor's Algorithm**. The Fourier Transform itself is an incredibly useful technique. Signals, images, sounds can all be processed using it, so $QFT$ qualifies as a crucial ancillary subroutine that forms a part of a more extensive algorithm.


Let’s summarize our findings from Shor's Algorithm.

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

Key Takeaway - Shor's Algorithm