Quantum Bayesian Networks

May 16, 2020

My Million Dollar LinkedIn & Twitter Publicity Campaign

Filed under: Uncategorized — rrtucci @ 3:25 pm

I’ve been posting on LinkedIn (https://www.linkedin.com/in/robert-r-tucci-6604b4a1/) & Twitter (@artistexyz) in order to publicize my pa & ma company http://www.ar-tiste.xyz These are the original posts before I transferred them to LinkedIn & Twitter.

  1. Reinforcement Learning & Bayesian Networks
  2. Quantopian & Bayesian Networks
  3. Capturing the Golden State Killer & Bayesian Networks
  4. Baby’s first Bayesian Network onesie
  5. Bill Gates, The Richest Man in the World, loves Bayesian Networks
  6. Black Swans & Bayesian Networks
  7. Mark Twain & Bayesian Network Statistics
  8. Nate Silver, Sports Prediction & Bayesian Networks
  9. Marketing & Bayesian Networks
  10. Medical Diagnosis & Bayesian Networks
  11. Daphne Koller, cofounder of Coursera and Insitro, loves Bayesian Networks
  12. Farming (Hydroponics) & Bayesian Networks
  13. Sports Betting (soccer/football in UK) & Bayesian Networks
  14. Factor Technology Inc., computer steered oil well drilling & Bayesian Networks
  15. Making your Smart Grid **smarter** & Bayesian Networks
  16. Risk Assessment, Fenton/Neil book & Bayesian networks
  17. Recommendation Systems & Bayesian Networks

April 11, 2020

My new website and business model

Filed under: Uncategorized — rrtucci @ 7:31 am

For the past year, I’ve been mulling over my future, especially as it pertains to quantum computing. Finally, in the last few days, I believe that I have finally converged to a local minimum. Yes, I know, I am a very slowly converging series. But I do converge eventually. Lo and behold, today I find that I have converged close to where I started my journey 20 years ago. So, I must have been travelling in circles all that time! 20 years ago, I started Artiste as a small, optimistic, but not overly ambitious, software company with the website http://www.ar-tiste.com . Today, I am restarting Artiste, again as a small, optimistic, but not overly ambitious (or VC dominated like most qc startups), software company. To mark the occasion, I’ve started a new website. Please check it out if you like my previous work and you think you’d like to hire us/me to write classical or quantum bayesian network software for you:





May 29, 2020

Crunchbase List of AI startups

Filed under: Uncategorized — rrtucci @ 7:09 pm

Crunchbase List of AI Startups (4,700+ companies)


Filed under: Uncategorized — rrtucci @ 6:58 pm

Umbrella that follows you

Filed under: Uncategorized — rrtucci @ 6:56 pm

May 27, 2020

You remember it differently

Filed under: Uncategorized — rrtucci @ 1:43 pm

Insitro, Bayesian Networks Powerhouse, Annouces $143M Raised in Series B Financing

Filed under: Uncategorized — rrtucci @ 1:06 am

Today, Insitro (website, crunchbase) announced that it has raised an extra $143M in series B financing. According to Crunchbase, their previous disclosed financing totaled $100M . This certainly makes Insitro a heavy weight in the Machine Learning world.

But not just any kind of ML heavy weight. As I explained in a previous blog post of mine entitled ‘ Daphne Koller: “Use the Bayesian-Network-Force, Luke. Let Go!” ‘, Daphne Koller, the sole founder of Insitro, has been a fervent Bayesian Networks lover for most of her career. The Bayesian probability that B Nets play a significant role in the software of Insitro is 100%.

Unfortunately, that software is mostly secret and proprietary, as evinced by Insitro’s shamefully meager Github presence. Also shameful is the fact that Insitro has a strong partnership with Gilead of Big Pharma. Greedy Big Pharma has been a major contributor to the decline and fall of the American empire.

May 21, 2020

State of The Quantum Computing Union

Filed under: Uncategorized — rrtucci @ 4:53 pm

Current Quantum Computer situation

IBM quantum computer now offers a clear quantum advantage to all its partners! IBM’s golden chandelier penis. It is often said of some men that they think with their penis. This robot literally does.
Microsoft anyonic quantum computer has been coming next year for 20 years.
Without Martinis, Google’s quantum computer is closing soon.

May 20, 2020

Quantum Bayesian Network view of hybrid quantum-classical computation

Filed under: Uncategorized — rrtucci @ 4:33 am


Hybrid Quantum-Classical Computing (HQCC) (a.k.a. Variational Quantum Eigensolver (VQE)) is often touted as one of the main algorithms of Quantum AI. In fact, Rigetti, a Silicon Valley company which for several years has provided cloud access to their superconductive quantum computer, has designed its services around the HQCC paradigm.

In this brief blog post, I will explain how HQCC can be understood in terms of quantum Bayesian networks. In the process, I will review some basic facts about classical and quantum Bayesian networks (bnets).

HQCC is often symbolized by a feedback loop between a quantum computer and a classical computer.

Created with GIMP

Classical Bayesian Networks

First, let’s review some basic facts about classical bnets.

Consider the chain rule for conditional probabilities. For the case of a probability distribution P() that depends on 5 random variables x0, x1, …, x4, one has


This last equation can be represented graphically by the following bnet, a “fully connected” DAG (Directed Acyclic Graph) in which an arrow points into xj from all its predecessors xj-1, xj-2,…, x1, x0 for j=1, 2, …,4:

For definiteness, we have chosen the number of nodes nn=5. How to generalize this so that nn equals any integer greater than 1 is obvious.

Henceforth, we will represent a random variable by an underlined letter and the values it assumes by a letter that is not underlined. For instance, x= x.

Mathematicians often represent a random variable by an upper case letter and the values it assumes by a lower case letter. For instance, X= x. For a physicist like me, that convention is not very convenient because physicists use upper case letters to mean all sorts of things that aren’t random variables. Likewise, they often want to use a lower case letter for a random variable. For this reason, I personally find the upper case letter convention for denoting random variables too burdensome. That is why I use the underlined letter convention instead.

Mathematicians have a rigorous definition for a random variable, but for the purposes of this blog post, a random variable is just the name given to a node of a bnet. This will be true for both classical and quantum bnets.

The arrows in a bnet denote dependencies. The fully connected bnet given above contains all possible dependencies. When each node depends only on its immediate predecessor, we get what is called a Markov chain. The Markov chain with nn=5 is:



bnets are technically acyclic graphs, so feedback loops are forbidden. However, as long as you understand that the following diagram should be “unrolled” into a Markov chain in which there are 2 types of nodes (the ones with an even subscript and the ones with an odd subscript), one can represent this special type of Markov chain with two types of nodes by the following diagram, where j=0, 1, …, nn-1:


This last diagram is a special case of what is called in the business, a dynamical Bayesian network (DBN). An early type of DBN that you might already be familiar with is the famous Kalman filter.

Note that in this brief intro to classical bnets, we have only used discrete nodes with a discrete random variable xj for j=0, 1, 2, …, nn-1. However, any one of those nodes can be easily replaced by a continuous node with a continuous random variable xj. A continuous node xj has a probability density instead of a probability distribution as its transition matrix P(xj| parents of xj), and one integrates rather than sums over its states xj.

The definition of classical bnets is very simple. In the final analysis, bnets are just a graphical way to display the chain rule for conditional probabilities. It’s a simple but extremely productive definition. Classical bnets remind me of another simple but extremely productive definition, that of a Group in Mathematics. To paraphrase the bard Christopher Marlowe, the definition of a Group (and that of a bnet) is the definition that launched a thousand profound theorems.

Quantum Bayesian Networks

Next, we will review some basic facts about quantum bnets.

A brief history of quantum bnets: The first paper about quantum bnets was this one by me. In that paper, quantum bnets are used to represent pure states only. In subsequent papers, for instance, this one, I explained how to use quantum bnets to represent mixed states too. Quantum bnets led me to the invention of the definition of squashed entanglement.

Born’s Rule says that in Quantum Mechanics, one gets a probability P by taking the absolute value squared of a complex-valued “probability amplitude” A. In other words, P=|A|2.

To define a quantum bnet, we write a chain rule for conditional probability amplitudes (A’s instead of P’s). For example, for nn=5, one has


This chain rule can be represented by the same diagram that we used above to represent the fully connected nn=5 classical bnet. However, note that now
node xj has a complex-valued transition matrix A(xj|parents of xj) instead of a real-valued one P(xj|parents of xj). For that reason, henceforth, we will represent quantum nodes by a fluffy blue ball instead of the small brown balls that we have been using to represent classical nodes.

Just like we defined Markov chains for classical bnets, one can define them for quantum bnets. In both cases, every node depends only on its immediate predecessor. For a quantum Markov chain with nn=5, one has


which can be represented by the following quantum bnet:


It’s important to stress that quantum bnets have always, from the very beginning, been intended merely as a graphical way to represent the state vectors of quantum mechanics. They do not add any new constraints to the standard axioms of quantum mechanics. Furthermore, they are not intended to be a new interpretation of quantum mechanics.

Coherent and Incoherent sums

In this section, we will consider coherent and incoherent sums of quantum bnets. For simplicity, we will restrict the discussion of this section to quantum Markov chains, but everything we say in this section can be easily generalized to an arbitrary quantum bnet, including the fully connected one.

Suppose we have a classical Markov chain with nodes x0, x1, …, x4 and we want to calculate the probability distribution P(x4) of its last node. One does so by summing over all nodes except the last one:


This last equation can be rewritten in terms of amplitudes in the equivalent form:


In the classical case above, we sum over all the variables outside the magnitude squared. A sum over a variable that is placed outside the absolute value squared will be called an incoherent sum. But the axioms of quantum mechanics also allow and give a meaning to, sums of variables that are placed inside the magnitude squared. A sum over a variable that is placed inside the absolute value squared will be called a coherent sum. For example, in the last equation, if we replace all the incoherent sums by coherent ones, we get:


But that’s not the whole story. One does not have to sum over all variables in an incoherent way or over all variables in a coherent way. One can sum over some variables coherently and over others incoherently. For example, one might be interested in the following sums:


(Footnote: The quantities called P(x4) and P(x3) in the equations of this section might require normalization before they are true probability distributions.)

Quantum Bayesian Network point of view

The last 2 equations can be represented using dynamical quantum bnets, as follows:


(Footnote: One can also consider 2 diagrams like the last 2 diagrams, but with

  • coherent sums of the xj with j even (instead of odd) and
  • incoherent sums of the xj with j odd (instead of even).

Also, nn itself is usually very large to allow convergence to an equilibrium distribution of P(xnn-1) and P(xnn-2), and nn can be either odd or even.)

The graphical part of the last two diagrams can be represented by the following feedback loop:


This last feedback loop is equivalent to the feedback loop with the Fantasia cartoon of Mickey Mouse that we started this blog post with and that we described as a symbolic representation of HQCC.

May 7, 2020

IBM’s new quantum computer finally achieves quantum advantage. Dario Gil presenting the IBM quantum computer during Think 2020

Filed under: Uncategorized — rrtucci @ 4:58 am

The online conference, IBM Think 2020, was held in May 5-6 2020. During that conference, Dario Gil, IBM Research Director, was visibly, almost orgasmically, excited with his new toy, an IBM quantum computer.


The IBM quantum computer already gives a clear quantum advantage to all IBM partners, as long as they rent the version that is mounted on a Mecha. What is a Mecha?, we asked. To explain, Dario shared with us this picture of his recent visit to the latest quantum startup and IBM quantum network partner, MegaBots Inc., in Hayward, California.

robot-penis-dario IBM’s golden penis chandelier

May 6, 2020

2020 Cube Interview of Jamie Thomas, IBM

Filed under: Uncategorized — rrtucci @ 1:58 am

Oh my God! Sarah Huckabee Sanders dyed her hair platinum blond, and now works as the IBM Quantum Press Secretary! She delivers her alternative facts with a charming Southern twang. You’all, quantum computing is already advantageous to our partners and our startups are profitable. Error correction necessary first? Naw, only on Tuesdays.

It’s not a question of if IBM stock will take a dive once the investors find out that IBM was lying and quantum computing won’t be profitable for another 10 years, it’s only a question of when.

May 5, 2020

Famous Quotes about Statistics by Mark Twain

Filed under: Uncategorized — rrtucci @ 10:23 pm

“There are three kinds of lies: lies, damned lies, and statistics.” [Mark Twain, 1907]

“There are 3 kinds of truths: data, data analyzed by a frequentist, and Bayesian Network statistics.” [Mark Twain, 2020]

“If I had used Bayesian Network Statistics, I would have never gone bankrupt at the age of 59 by making bad investments in the stock market.” [Mark Twain, 2020]

brought to you by http://www.ar-tiste.xyz, Mark Twain’s preferred purveyor of high quality and low cost Bayesian Network Software & Services.

Writer Samuel Clemens (aka Mark Twain) circa 1907

April 30, 2020

A Day in the Life of a Quantum Startup CEO

Filed under: Uncategorized — rrtucci @ 3:45 pm

Check out this funny video

The CEO of this video is an archetype that encompasses all the traits that a typical CEO of a tech-startup aspires to attain. If you specialize this video to quantum startups in particular, you will find that most quantum CEOs are a less imaginative, duller, paler version of this archetype. But deep inside the peanut-sized brain of every quantum CEO, and the even smaller brains of the VCs that fund them, this video is the ideal that they strive to achieve.

A few examples of quantum startup CEOs:


1Qbit CEO, Andrew Fursman, What is the brown stuff on his face? He is a Bald Canadian ass licker, and he is really good at it. He has licked DWave’s, Fujitsu’s and Microsoft’s asses until they were as clean as a whistle.


Q-CNTRL CEO, Mike Biercuk (aka Twitter alpha male and world authority in quantum computing horology)


QCWare CEO, Matt Johnson, Scott Aaronson’s boss


StrangeWorks CEO, Whurley, his book “Quantum Computing for babies” is highly recommended by Eric Trump


Xanadu AI CEO, Elizabeth Holmes (aka Christian Weedbrook with main scientific advisor and pedophile enabler, Seth Lloyd)


Zapata Computing CEO, Christopher Savoie, Judo Expert. Wow, I’m scared, but what does it have to do with qc?

April 27, 2020

How I learned to love Unix

Filed under: Uncategorized — rrtucci @ 9:27 am

Nowadays, most serious programmers in AI/Data Science first target the Unix OS, and later on, they might target the Microsoft (MS) Windows OS, as an afterthought. Gone are the days when all apps were first written for the Windows OS. Unix (especially Linux) and Open Source won the war against MS in the cloud, where it matters most for commerce. Nowadays, Unix OS and Open Source rule the Internet, AI, Data Science, …

For that reason, if you do any kind of serious programming in AI/Data Science, I advise you to do it using a Unix OS instead of Windows OS. That leaves you with 2 main possibilities, Apple Unix (called Darwin) and Linux. If you are poor like me, go with Linux. You can get yourself an excellent second hand laptop running Linux for about $150, as I explain below.

The purpose of this brief blog post is to give you a quick history of how I took my first steps in Linux world, and to advise you on how to do the same, if you haven’t done so already.

In my case, I first got into Linux because I was trying to flee Windows…

Long ago, in order to begin using Windows 10, I went to Ebay and bought myself a second-hand Dell Laptop with Windows 10 installed for around $150 (8GB memory, 250GB ssd).

I found Windows 10 to be incredibly ugly, illogical and annoying compared to the good old days of Windows XP when the Windows OS was almost elegant. So then I tried to make my laptop a dual boot machine that ran both Windows 10 and Ubuntu (the most popular version of Linux). After trying very hard to install that dual boot, I had to give up. Turns out that MS has installed all kinds of “security” measures into Windows 10 to make it well neigh impossible to make a machine running Windows 10 dual bootable. Assholes!

So then I went back to Ebay, and bought myself a second second-hand Dell Laptop with Linux Mint installed for around $130 (Again, with 8GB memory, 250GB ssd). Thereafter, it was a cake walk to replace Linux Mint by the more popular Linux Ubuntu, and I was off to the races.

I find Ubuntu to be much more beautiful and logical than Windows 10. Try it!

If you are new to the Unix command line, I have 2 great references.

First, the

ComputerHope website

is a masterpiece.  I can’t say enough good things about it. Any time that I have any doubts about what a particular Linux command means, or if I want an example of how to use a command, I go there first.

Second, the FREE 482-page pdf book

The Linux Command Line: A Complete Introduction, by William E. Shotts Jr. 

is another masterpiece. So beautifully written!

A final piece of advice. If you prefer using Python scripts instead of Bash scripts, as I often do, there is a neat way of inserting Bash commands inside your Python script, using the Python module called “subprocess“.

(footnote) IMHO, Dell laptops are excellent devices. My hypothesis for why second-hand Dell laptops are so cheap and numerous is that a lot of startups buy one for every employee, and then, most of them go bankrupt and flood the market with second-hand laptops.

April 21, 2020

Martinis Resigns from The Google

Filed under: Uncategorized — rrtucci @ 7:56 am


Quantum Supremacy (the movie)

Quantum Supremacy (the movie)

6 years ago, I wrote the above satirical article about Hartmut Neven, the head of Google’s quantum AI lab . Today, Martinis, the main inventor of that lab, resigned. I don’t see how Google’s quantum computing hardware program can continue without Martinis. Neven may be close to the janitorial fate that my movie predicted, back in the year 2040.

April 18, 2020

Google’s Quantum Stallion

Filed under: Uncategorized — rrtucci @ 3:56 pm

A recent thread in Reddit gave links to 4 talks available on YouTube about Google’s Sycamore quantum computer. My comment in that thread has received a very negative rating. Reddit readership has such poor taste! Here is my comment:

All 4 speakers are girlie men. Bring back Hartmut Neven. At least he’s a handsome stud of a man. What a hunk! Google’s Quantum Stallion.

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