Quantum Computing #1: Dirac's Bra-Ket Notation and Tensor Product

This is the first lecture of the quantum computing course. In this lecture, I explain the fundamentals of Dirac's Bra-Ket notation, which are essential to understanding quantum computing. I demonstrate how to compute tensor products and their relationship with ket-ket and bra-bra, providing examples for better comprehension. We learn to convert ket-notation to bra-notation and vice versa via the conjugate-transpose operation. Additionally, I demonstrate how to express matrices using ket-bra and compute inner products using bra-ket notation.

Link to the course's playlist:

**** References Used: ****
[1] Nielsen, Michael A., and Isaac L. Chuang. Quantum computation and quantum information. Cambridge university press, 2010.
[2] John Watrous, "CPSC 519/619: Quantum Computation". Jan 10, 2006
[3] Childs, Andrew M. "Lecture notes on quantum algorithms." Lecture notes at University of Maryland (2017).

Chapters:
00:00 Introduction
01:37 Ket-Notation
05:24 Express Vectors in Standard Basis
08:32 Bra-Notation
09:53 Computing Conjugate-Transpose
14:00 Tensor Product with Example
16:40 Learning Ket-Ket with Examples
21:57 Learning Bra-Bra with Examples
24:09 Write Matrices with Ket-Bra
38:02 Inner Product with Bra-Ket
39:45 Unit Vectors
41:34 Orthogonal Vectors
43:03 Example of Inner Product
47:52 Concluding Remarks

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[jullyanolino]

Great lecture.

Thank you for sharing this basic information about quantum information science in a didactic way.

[csestudents]

sir your way of explaining things is very clear and precise. Thank you for uploading this amazing lecture series.

[MichaelNortonFGSW]

Excellent presentation and primer on BraKet and Dirac.

[JanLearningSkills]

The video is much more informative and i have learned much form it.

[leulfanuel]

great video! was confused at one point but got it.

[ashtondoane]

Excellent work. This is fantastic stuff, keep it up.

[soumyachakraborty]

Sir watching your video was never tiresome, Wonderful Insights I have gained thanks a lot .

[AmazingMrFox-srwh]

This was shockingly easy to understand and follow

[madhaviajudiya]

A very good way to teach quantum computing basic

[ralphwalters]

You are an Excellent Instructor. Thank You.

[adrianb]

C++ counts from zero. Sometimes when discusing elements of an array I've used "zeroth, oneth, twoth, ..." This avoids using "zeroth, first", etc.

[TheAnnaRam]

Thank you very much for the very easily understandable lectures on a cutting edge science - Sir, is there any text book with problems which will enable me to practice the calculations? I am a retired senior citizen and a hobby learner.

[MAJIDK-zsbq]

You are best sir😊 thank you for your time

[PankajKumar-ytqp]

is this complete playlist for college exams ?

[messapatingy]

Tensor Product preserves the norm. Nice to know. ||ψ⟩ ⊗ |φ⟩|| = ||ψ⟩|| * ||φ⟩||, Thanks.

[firstyfirst]

31:54 How does iota come here there was no iota in question