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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

Particles can gain energy to transform into waves.

Waves can gain energy to transform into particles.

Particles can behave like waves and waves can behave like particles. 

It means there are only two possibilities, something can either be a particle or just a wave.

What is wave-particle <code>duality</code>?

Discrete, quantum properties (energy, momentum, etc.) of particles are `quantized`.

Continuous, we can have an infinite number of quantum states.

Discrete, because there are finite types of physical properties of particles that we can measure.

Continuous, quantum states are complex-valued vectors and complex numbers are continuous.

Is the world defined by the laws of quantum mechanics, `discrete` or `continuous`? and why?

Is the world defined by the laws of quantum mechanics, <code>discrete</code> or <code>continuous</code>? and why?

Let's take a look at an example state:
$$|\phi\rangle=\frac{1}{\sqrt{2}}|00\rangle+\frac{1}{\sqrt{2}}|11\rangle$$

What properties do you notice for the state $|\phi\rangle$? (You can select multiple answer)

Let’s take a look at an example state:
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi mathvariant="normal">∣</mi><mi>ϕ</mi><mo stretchy="false">⟩</mo><mo>=</mo><mfrac><mn>1</mn><msqrt><mn>2</mn></msqrt></mfrac><mi mathvariant="normal">∣</mi><mn>00</mn><mo stretchy="false">⟩</mo><mo>+</mo><mfrac><mn>1</mn><msqrt><mn>2</mn></msqrt></mfrac><mi mathvariant="normal">∣</mi><mn>11</mn><mo stretchy="false">⟩</mo></mrow><annotation encoding="application/x-tex">|\phi\rangle=\frac{1}{\sqrt{2}}|00\rangle+\frac{1}{\sqrt{2}}|11\rangle
</annotation></semantics></math>∣ϕ⟩=2<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z'/></svg>​1​∣00⟩+2<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z'/></svg>​1​∣11⟩
What properties do you notice for the state <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∣</mi><mi>ϕ</mi><mo stretchy="false">⟩</mo></mrow><annotation encoding="application/x-tex">|\phi\rangle</annotation></semantics></math>∣ϕ⟩? (You can select multiple answer)

Yes, since the qubits are entangled, Ather's qubit will most definitely measure a 12.

Not instantly, The time delay to figure it out is limited by the speed of light. 

Yes, when Wasiq measures their own qubits, Ather's qubits will instantly collapse to a 12 as well.

It's not possible to know, Ather's qubits could have any value from $0$ to $2^5-1$

Let's say Wasiq and Ather have 5 pairs of `entangled qubits` at their lab, Wasiq keeps one of each pair and goes back home to measure their qubits, turns out they get the number 12 in binary as a result. 

Can Ather somehow `instantly` know what their qubits will give them without measuring?

Let’s say Wasiq and Ather have 5 pairs of <code>entangled qubits</code> at their lab, Wasiq keeps one of each pair and goes back home to measure their qubits, turns out they get the number 12 in binary as a result.
Can Ather somehow <code>instantly</code> know what their qubits will give them without measuring?

Yes, it looks like the theory of quantum mechanics has some holes in it.

No, walking through walls isn't possible because a human has a large momentum.

No, walking through walls isn't possible because a human has billions and billions of particles.

Yes, it should be theoretically possible but hasn't been proven mathematically.


Humans are made up of particles. You can interact with other matters. Following the logic `wave-particle duality`, shouldn't you be able to walk through walls like a wave?! 


Humans are made up of particles. You can interact with other matters. Following the logic <code>wave-particle duality</code>, shouldn’t you be able to walk through walls like a wave?!

Fundamentals of Quantum Mechanics

Fundamentals of Quantum Mechanics

Let's review some key concepts of quantum mechanics that empower the world of computing.

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

Quiz: Quantum Mechanics