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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

Which quantum phenomena give quantum computing its power? (You can choose more than one answer)

Which quantum phenomena give quantum computing its power? (You can choose more than one answer)

It can exist in two locations in space-time at once.

It can be a classical bit and a quantum bit at the same time.

It can be both a `0` and `1` at the same time.

It's a new third state of a bit in addition to `0` and `1`.

What does it mean for a qubit to be in a `superposition`? (You can choose more than one answer)

What does it mean for a qubit to be in a <code>superposition</code>? (You can choose more than one answer)

All quantum gates must be reversible, but this is not necessary for classical gates.

Quantum gates only have one input and one output, unlike classical gates like `AND`.

Quantum gates cannot perform logical operations like `AND` or `XOR`

Quantum gates run faster than classical gates.

What's the key difference between classical and quantum gates?


What’s the key difference between classical and quantum gates?

A set of quantum states that are in superposition.

A set of matrices that are inverse of each other.

A set of vectors that can span an entire vector space.

A set of numbers that cannot be represented as a fraction.

What is a quantum state, mathematically?

These are the states in which the qubit is doing some computation.

When computing a solution to a specific problem, these are the states we obtain when we measure a qubit.

These states form a set of vectors that can span the complex vector space.

The states have a value of 0 or 1 and can be used to perform binary calculations.

Why are $|0\rangle$ and $|1\rangle$ called the `computational` basis states?

Why are <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∣</mi><mn>0</mn><mo stretchy="false">⟩</mo></mrow><annotation encoding="application/x-tex">|0\rangle</annotation></semantics></math>∣0⟩ and <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∣</mi><mn>1</mn><mo stretchy="false">⟩</mo></mrow><annotation encoding="application/x-tex">|1\rangle</annotation></semantics></math>∣1⟩ called the <code>computational</code> basis states?

What are the properties of a quantum state? (You can choose more than one answer)

What are the properties of a quantum state? (You can choose more than one answer)

Let take an example of a quantum state:
$$|\psi\rangle =\frac{1}{\sqrt{2}}|0\rangle+\frac{1}{\sqrt{2}}|1\rangle$$

If we measure it once, what are the chances that we would get $|0\rangle$?

Let take an example of a quantum state:
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi mathvariant="normal">∣</mi><mi>ψ</mi><mo stretchy="false">⟩</mo><mo>=</mo><mfrac><mn>1</mn><msqrt><mn>2</mn></msqrt></mfrac><mi mathvariant="normal">∣</mi><mn>0</mn><mo stretchy="false">⟩</mo><mo>+</mo><mfrac><mn>1</mn><msqrt><mn>2</mn></msqrt></mfrac><mi mathvariant="normal">∣</mi><mn>1</mn><mo stretchy="false">⟩</mo></mrow><annotation encoding="application/x-tex">|\psi\rangle =\frac{1}{\sqrt{2}}|0\rangle+\frac{1}{\sqrt{2}}|1\rangle
</annotation></semantics></math>∣ψ⟩=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
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If we measure it once, what are the chances that we would get <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∣</mi><mn>0</mn><mo stretchy="false">⟩</mo></mrow><annotation encoding="application/x-tex">|0\rangle</annotation></semantics></math>∣0⟩?

Let's continue with the example of a quantum state:
$$|\psi\rangle =\frac{1}{\sqrt{2}}|0\rangle+\frac{1}{\sqrt{2}}|1\rangle$$

After measuring it once we got $|0\rangle$. What are the chances that we would get $|1\rangle$ if we measure it a second time?

Let’s continue with the example of a quantum state:
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi mathvariant="normal">∣</mi><mi>ψ</mi><mo stretchy="false">⟩</mo><mo>=</mo><mfrac><mn>1</mn><msqrt><mn>2</mn></msqrt></mfrac><mi mathvariant="normal">∣</mi><mn>0</mn><mo stretchy="false">⟩</mo><mo>+</mo><mfrac><mn>1</mn><msqrt><mn>2</mn></msqrt></mfrac><mi mathvariant="normal">∣</mi><mn>1</mn><mo stretchy="false">⟩</mo></mrow><annotation encoding="application/x-tex">|\psi\rangle =\frac{1}{\sqrt{2}}|0\rangle+\frac{1}{\sqrt{2}}|1\rangle
</annotation></semantics></math>∣ψ⟩=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
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After measuring it once we got <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∣</mi><mn>0</mn><mo stretchy="false">⟩</mo></mrow><annotation encoding="application/x-tex">|0\rangle</annotation></semantics></math>∣0⟩. What are the chances that we would get <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∣</mi><mn>1</mn><mo stretchy="false">⟩</mo></mrow><annotation encoding="application/x-tex">|1\rangle</annotation></semantics></math>∣1⟩ if we measure it a second time?

They're different tools for the same job but proposed by two different scientists.

Q-Sphere is a more generalized visualization than a Bloch-Sphere and can represent multiple qubits.

A collection of Bloch-Spheres representing one qubit each is called a Q-Sphere.

The Q-Sphere is actually a high-dimensional sphere whereas the Bloch-Sphere is 3-D.

What's the difference between a Bloch Sphere and a Q-Sphere?

What’s the difference between a Bloch Sphere and a Q-Sphere?

Fundamentals of Quantum Computing

Fundamentals of Quantum Computing

Let's review the fundamentals of quantum computing covered thus 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

Quiz: Baby Steps