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

Classical mechanics was based on the idea that the world is deterministic. That is, if given enough information, you would be able to know the past and predict the future of a system and its constituents. As we shall see in just a moment, this is not always true. 

Physics in the $20^{th}$ century stood at a crossroads. Experimental evidence from technologically advanced apparatus started contradicting the established rules of classical mechanics. Experiments involving particles on the scale of electrons and photons started highlighting the chinks in the armor of classical mechanics. To avoid this becoming an expose on physics, we shall briefly describe the key takeaways from **quantum mechanics**.

Quantum mechanics, as the name suggests, is the study of infinitesimal _particles_ (or quanta) that permeate everything around us. Photons, electrons, quarks, gluons, and the like. You may have noticed the italicization of the word ‘particles’ in the previous sentence. This follows Einstein’s discovery of the **Photoelectric Effect** and Thomas Young’s **Double-Slit Experiment**. Einstein’s discovery showed that light is made up of **particles** and earned him the Nobel Prize in Physics. Thomas Young, on the other hand, showed that light also exhibited wave-like behavior. De Broglie later built upon this and proved that every particle has a wavelength associated with it.
 
These shockingly contradictory results laid the foundations of what is known today as the wave-particle duality. In some situations, quanta behave like particles, while in other situations quanta behave like waves. The two formulations of quanta are inseparable from each other and making peace with the duopoly aligned the wave and particle-like nature of quanta. 


Subsequent work by Schrödinger and others also highlighted the non-deterministic nature of quanta. The world of photons, electrons, etc., is founded upon probabilities and uncertainty. This new way of understanding the world, called quantum mechanics, definitively struck the final nail in the coffin of classical mechanics and took its place as the correct explanation of the infinitesimal world. 

In the past lessons, we have discussed **superposition** as one of the peculiarities of quantum mechanics. In the subsequent lessons, we shall now focus on **entanglement** and **interference**. But before we can do that, a discussion of the three postulates of quantum mechanics is necessary.

Without losing our focus on quantum computing, we look at the details of superposition, entanglement, and interference in this chapter.

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

A Short History of Quantum Mechanics