Introduction to this blog, the why

It has been quite a while since I started this site. The forces in the world of technology have shifted. There is now simply no denying what AI is and what impact it is having, and will have, on everything. Almost a year ago now I [hard] pivoted to AI from Quantum Computing. I've been in IT almost 40 years and I have never seen the winds of change blow this hard. So most of this introduction post is about quantum computing. But going froward, this is going to be pretty much an AI blog. I wonder if I can get my myaij.com? *Update - yes - I did get that domain :)

Below this point in this post it is mostly about Quantum Computing.

I wanted a place to document my journey into quantum computing. So, here I am.

This blog is just a place for me to document some of the things I have learned. But mostly a place to catalogue the resource I have so painstakingly curated from the Internet, books, and AI. This field is so new (new in terms of science but has roots back to the 1970's and 80's), and so vast, and draws from so many different fields of study, that it is very difficult to know what resources to use. And just as important, what order to put those resources in. What are the foundational concepts you need to know in order to go on to more complex topics.

Along those same line, when you start to write quantum programs (the goal is to eventually make these things useful), what is the best environment to do that in? There are many frameworks. Here are some of the more popular - more on them in subsequent posts:

• IBM Quantum

• Google Cirq

• AWS Braket

• Azure Quantum

• Xanadu PennyLane

I am not really here for the views. Matter of fact, I'm so happy with this journey, it gives me so much joy, that I'm scared to try to put anything out there for anyone to read because, for me, the why is just because I love it. I don't really want anyone to put a damper on that. I'm not trying to be known to anyone else or show what I know about quantum computing or physics. Lord knows I am no expert. But I suppose if someone does see it and it is helpful to them in some way, I would be happy about that. Certainly if you are already employed in this field, or have a graduate degree in it, the information here won't really be helpful to you. But, who knows, you might see a resource that you like about a particular topic - that would be a good thing.

You might say, "I don't get it, why do this if you don't really care if anyone sees it?" For me, doing these types of write-ups helps me clear fuzzy areas when I have to write about them and sort-of explain them in a post. Indeed this is a well documented study technique - to act like your are teaching a concept to you help master it - commit it to long term memory. When I have to go lock down those last few details before I can write something about it - something that someone else might see - it forces me to put a little extra polish on that concept.

As of April 6 2024, I am 11 months into this journey. I know the day it started. I was at a conference in Dallas, Texas and I heard a session given by Denis Mandich, CTO for a company called Qrypt (qrypt.com - go there - very cool company doing cool stuff). I was hooked after that and I still am. I had always liked physics and have worked in IT for MANY years and this seemed like a good marriage of those two parts of my life.

But I had, and still have to some extent, an uphill battle as I had to spend a bunch of time on just laying a foundation for learning quantum computing. Meaning there was a whole bunch of physics and linear algebra between me and understanding a lot of the resources out there regarding quantum computing. It is possible to not go crazy deep in to physics and the math of quantum computing and still be able to write some programs that do some things. But to really understand what is going on, you can't really skip the physics or the math in my humble opinion. And even if you could, that wouldn't be any fun.

So, over the next months ... years(?) I hope to document my journey here. For now, I find it oddly motivating this blogging. Hopefully that doesn't fade. Partly because I like to talk and on this blog I can just talk and talk and there is no one here to tell me "its enough already".

Side bar: In this blog, when I say I watched a video, I mean I watched it slowly and took copious notes in OneNote. Some times it could take many hours to get through a 10-15 minute video as the videos often required me to go down a bunch of "side roads" to learn what was being said in the video I was trying to initially learn. A 15 minute video could, and often did, result in up to 40 "pages" of notes in OneNote.

After about six months, I made a list of all the concepts I could think of that I still needed to gain mastery of in order to get where I wanted to go. I have probably worked my way through about 75% of this list in the last several months. Brace yourself, here is that list. Please do not try to make sense of this numbering system, its a fools errand. [Update 4/12/24 - I removed the inane numbering.] I did leave my initial priority numbering system but my view on the priorities of some of these has changed since I first started this list. Apologies - copying this list to this post I saw there is some overlap of some concepts (for one I see entanglement is on there twice - oops). I have massive sections in OneNote for about 60-70% of these concepts by now. That is the information I am hoping to document here and, by doing so, help solidify the information for me while hopefully providing some information that is useful to you.

I'm going to try to make posts that are the most impactful first. Things I had trouble with that are vital to quantum computation and information.

10 Basis vectors

10 Quantum State Vectors

10 Unit vectors - especially differentiation from Basis vectors

10 Standard Basis - Standard Basis State - Standard Basis vector

• Are all unit vectors basis vectors?  NO

• Are all basis vectors unit vectors?  NO

• Are unit vectors a subset of basis vectors?  NO

• Are basis vectors a subset of unit vectors? NO

10 Standard Basis Measurement

10 Tensors, Tensor products of vectors & of matrices & quantum state vectors

• Tensor Networks

10 Linearity

10 Linear Combination

10 Linearly dependent

10 Linearly independent

10 Quantum System 

10 Blochspere - also Operator, Observable, Measurable Value

9 inner product 

9 Dot product

9 cross products

9 Unitary Matrix

9 Hermitian matrix

9 Conjugate transpose

9 Entanglement 

9 Dirac Notation

9 Stochastic Matrix, Markov matrix

9 Commutative, noncommutative

9 Complex Numbers - are algebraically closed. They can be commutative and associative however.

9 Complex Plane - Complex Space - Goes with Hilbert Space.

9 Euclidean Norm

9 Complex Matrix

9 Orthogonal vector

9 Orthogonality

9 Orthonormal

9 Orthonormality

9 Inverse of a matrix

9 Unitary operations

9 Unitary / Unitary matrix

9 Circuit Gates, Pauli Gates, Pauli Operations, Pauli Matrices

• Pauli Z Basis

9 Hadamard gate/operation

9 Phase gates/operations

9 Quantum Sates

9 Bell States

9 Bell Basis

9 Subspace in Linear Algebra

9 Projections

9 Projective measurements

9 Irrelevance of Global Phases

9 No Cloning Theorem

9 Eigenvalue, Eigenvector, Eigenstate

9 Decoherence

9 P vs NP vs NP Hard vs NP Complete vs EXP (Complexity Theory)

9 Superposition

9 Entanglement

9 Non-locality

9 Quantum teleportation

9 Span (in Linear Algebra)

9 Calculus / Functions

9 Dimension - Understanding Dimension

9 Vector Space

9 Determinant (Linear Algebra)

9 State Vector

9 Complex Valued Function

9 Quantum Wave Function and Probability Density, Density Operator, Density Matrix

9 Quantum Teleportation

9 Contravariant components of a  vector

9 Hilbert space

9 Dual Vectors

9 Linear Functional

9 Dual Space & Dual Vectors

9 Convector/Dual/1-form

9 Covariance (contra and covariance vectors)

9 Born's rule

9 Primitives on Qiskit

9 Computational Basis / Computational Basis State

9 Modulus vs Absolute Value

9 Pauli Exclusion Principle

9 Adjacency Matrix (to represent finite graph)

9 Quantum Approximate Optimization Algorithm (QAOA) Especially around portfolio optimization

9 QUBO - Quadratic Unconstrained Binary Optimization

9 Trotterization and Hamiltonian

9 Quantum Fourier Transform

9 Singular Value Decomposition

9 VQE - Variable Quantum Eigensolver

9 Global Phase

9 Relative Phase

9 Cauchy-schwarz Inequality

9 DMRG - Density Matrix Renormalization Group

8 The Unit Circle

8  Potential Energy Well / Potential Well

8 Scalar

8 Quantum Circuit Model

8 Sin

8 Cosine

8 Tangent

8 SOH CAH TOA

8 Quantum Tunneling

8 Linear Map

8 Dimensions in Linear Algebra

8 Electron Orbitals - Quantum numbers associated to Electron Orbitals (n, l, m_l, m_s) the fourth number for spin - not often included)

8 Probability vector

7 Probabilistic operations

7 The Greek Alphabet

7 Number theory - Real numbers are a subset of complex numbers, Imaginary numbers are a subset of complex numbers, integers, whole numbers, counting numbers

7 Tuple, n-tuple

6 outer product

6 Boolean Algebra

6 Deterministic operations

6 Markov Chains

6 Quaternions are associative but not commutative.

6 Cellular automata - Wolfram

6 Entropy 

6 Monte Carlo on quantum

Who knew that learning quantum computing meant learning

• quantum physics

• linear algebra

• some geometry/trigonometry

• some calculus

• some electrical engineering

• some computer science

• Data Science

• python

• jupyter notebooks / VSCode

• some statistics

• some AI/ML

I'm sure it is clear that I used YouTube quite often. But, a tool that I consider even more important than YouTube at this point in the journey is ChatGPT version 4.0. Not version 3.5. Those two versions are as different as the the iPhone 15 and the iPhone 1. And of course, arxiv.org is imperative as many other resources point to papers on arxiv. I've also bought about 20 books on the subject. I'd say about 8 of those are worth having. That sounds like good fodder for a post eh?