Ciro Santilli @cirosantilli 35

This section is about companies that were primarily started as computer makers.

For companies that make integrated circuits, see also: Section "Semiconductor company".

Something where DC voltage comes in, and a periodic voltage comes out.

A computer is a highly layered system, and so you have to decide which layers you are the most interested in studying.

Although the layer are somewhat independent, they also sometimes interact, and when that happens it usually hurts your brain. E.g., if compilers were perfect, no one optimizing software would have to know anything about microarchitecture. But if you want to go hardcore enough, you might have to learn some lower layer.

It must also be said that like in any industry, certain layers are hidden in commercial secrecy mysteries making it harder to actually learn them. In computing, the lower level you go, the more closed source things tend to become.

But as you climb down into the abyss of low level hardcoreness, don't forget that making usefulness is more important than being hardcore: Figure 1. "xkcd 378: Real Programmers".

First, the most important thing you should know about this subject: cirosantilli.com/linux-kernel-module-cheat/should-you-waste-your-life-with-systems-programming

Here's a summary from low-level to high-level:

It is quite amazing to read through books such as The Supermen: The Story of Seymour Cray by Charles J. Murray (1997), as it makes you notice that earlier CPUs (all before the 70's) were not made with integrated circuits, but rather smaller pieces glued up on PCBs! E.g. the arithmetic logic unit was actually a discrete component at one point.

The reason for this can also be understood quite clearly by reading books such as Robert Noyce: The Man Behind the Microchip by Leslie Berlin (2006). The first integrated circuits were just too small for this. It was initially unimaginable that a CPU would fit in a single chip! Even just having a very small number of components on a chip was already revolutionary and enough to kick-start the industry. Just imagine how much money any level of integration saved in those early days for production, e.g. as opposed to manually soldering point-to-point constructions. Also the reliability, size an weight gains were amazing. In particular for military and spacial applications originally.

Given a bunch of interlinked standard cell library elements from the logic synthesis step, actually decide where exactly they are going to go on 2D (stacked 2D) integrated circuit surface.

Sample output format of place and route would be GDSII.

This is a quick tutorial on how a quantum computer programmer thinks about how a quantum computer works. If you know:a concrete and precise hello world operation can be understood in 30 minutes.

Although there are several types of quantum computer under development, there exists a single high level model that represents what most of those computers can do, and we are going to explain that model here. This model is the is the digital quantum computer model, which uses a quantum circuit, that is made up of many quantum gates.

Beyond that basic model, programmers only may have to consider the imperfections of their hardware, but the starting point will almost always be this basic model, and tooling that automates mapping the high level model to real hardware considering those imperfections (i.e. quantum compilers) is already getting better and better.

The way quantum programmers think about a quantum computer in order to program can be described as follows:

To operate a quantum computer, you follow the step of operation of a quantum computer:

Each time you do this, you are literally conducting a physical experiment of the specific physical implementation of the computer:and each run as the above can is simply called "an experiment" or "a measurement".

The output comes out "instantly" in the sense that it is physically impossible to observe any intermediate state of the system, i.e. there are no clocks like in classical computers, further discussion at: quantum circuits vs classical circuits. Setting up, running the experiment and taking the does take some time however, and this is important because you have to run the same experiment multiple times because results are probabilistic as mentioned below.

Unlike in a classical computer, the output of a quantum computer is not deterministic however.

But the each output is not equally likely either, otherwise the computer would be useless except as random number generator!

This is because the probabilities of each output for a given input depends on the program (unitary matrix) it went through.

Therefore, what we have to do is to design the quantum circuit in a way that the right or better answers will come out more likely than the bad answers.

We then calculate the error bound for our circuit based on its design, and then determine how many times we have to run the experiment to reach the desired accuracy.

The probability of each output of a quantum computer is derived from the input and the circuit as follows.

First we take the classic input vector of dimension N of 0's and 1's and convert it to a "quantum state vector" $\overrightarrow{q_{in}}$ of dimension $2^n$:

We are after all going to multiply it by the program matrix, as you would expect, and that has dimension $2^n\times 2^n$!

Note that this initial transformation also transforms the discrete zeroes and ones into complex numbers.

For example, in a 3 qubit computer, the quantum state vector has dimension $2^3=8$ and the following shows all 8 possible conversions from the classic input to the quantum state vector:

This can be intuitively interpreted as:

Now that we finally have our quantum state vector, we just multiply it by the unitary matrix $Q$ of the quantum circuit, and obtain the $2^n$ dimensional output quantum state vector $\overrightarrow{q_{out}}$:

And at long last, the probability of each classical outcome of the measurement is proportional to the square of the length of each entry in the quantum vector, analogously to what is done in the Schrödinger equation.

For example, suppose that the 3 qubit output were:

Then, the probability of each possible outcomes would be the length of each component squared:i.e. 75% for the first, and 25% for the third outcomes, where just like for the input:

All other outcomes have probability 0 and cannot occur, e.g.: 001 is impossible.

Keep in mind that the quantum state vector can also contain complex numbers because we are doing quantum mechanics, but we just take their magnitude in that case, e.g. the following quantum state would lead to the same probabilities as the previous one:

This interpretation of the quantum state vector clarifies a few things:

As we could see, this model is was simple to understand, being only marginally more complex than that of a classical computer, see also: quantumcomputing.stackexchange.com/questions/6639/is-my-background-sufficient-to-start-quantum-computing/14317#14317 The situation of quantum computers today in the 2020's is somewhat analogous to that of the early days of classical circuits and computers in the 1950's and 1960's, before CPU came along and software ate the world. Even though the exact physics of a classical computer might be hard to understand and vary across different types of integrated circuits, those early hardware pioneers (and to this day modern CPU designers), can usefully view circuits from a higher level point of view, thinking only about concepts such as:as modelled at the register transfer level, and only in a separate compilation step translated into actual chips. This high level understanding of how a classical computer works is what we can call "the programmer's model of a classical computer". So we are now going to describe the quantum analogue of it.

Bibliography:

Communicating at a distance, from Greek "tele" for distance!

A very cool thing about telecommunication is, besides how incredibly fast it advanced (in this sense it is no cooler than integrated circuit development), how much physics and information theory is involved in it. Applications of telecommunication implementation spill over to other fields, e.g. some proposed quantum computing approaches are remarkably related to telecommunication technology, e.g. microwaves and silicon photonics.

This understanding made Ciro Santilli wish he had opted for telecommunication engineering when he was back in school in Brazil. For some incomprehensible reason, telecommunications was the least competitive specialization in the electric engineering department at the time, behind even power electronics. This goes to show both how completely unrelated to reality university is, and how completely outdated Brazil is/was. Sad stuff.

This is a general principle of software/hardware design that Ciro feels holds wide applicability.

The most extreme case of this is of course the integrated circuit itself, in which it is essentially impossible (?) to observe the specific value of some indidual wire at some point.

Somewhat on the other extreme, we have high level programming languages running on top of an operating system: at this point, you can just GDB step debug your program, print the value of any variable/memory location, and fully understand anything that you want. Provided that you manage to easily reach that point of interest.

And for anything in between we have various intermediate levels of complication. The most notable perhaps being developing the operating system itself. At this level, you can't so easily step debug (although techniques do exist). For early boot or bootloaders for example, you might want to use JTAG for example on real hardware.

In parallel to this, there is also another very important pair of closely linked tradeoffs:

Emulation also has another potential downside: unless you are very careful at implementing things correctly, your model might not be representative of the real thing. Also, there may be important tradeoffs between how much the model looks like the real thing, and how fast it runs. For example, QEMU's use of binary translation allows it to run orders of magnitude faster than gem5. However, you are unable to make any predictions about system performance with QEMU, since you are not modelling key elements like the cache or CPU pipeline.

Instrumentation is another technique that has can be considered to achieve greater observability.

Borrow from the Internet Archive for free: archive.org/details/supermenstory00murr

Initial chapters put good clarity on the formation of the military-industrial complex. Being backed by the military, especially just after World War II, was in itself enough credibility to start and foster a company.

It is funny to see how the first computers were very artisanal, made on a one-off basis.

Amazing how Control Data Corporation raised capital IPO style as a startup without a product. The dude was selling shares at dinner parties in his home.

Very interesting mention on page 70 of how Israel bought CDC's UNIVAC 1103 which Cray contributed greatly to design, and everyone knew that it was to make thermonuclear weapons, since that was what the big American labs like this mention should be added to: en.wikipedia.org/wiki/Nuclear_weapons_and_Israel but that's Extended Protected... the horrors of Wikipedia.

Another interesting insight is how "unintegrated" computers were back then. They were literally building computers out of individual vacuum tubes, then individual semiconducting transistors, a gate at a time. Then things got more and more integrated as time went. That is why the now outdated word "microprocessor" existed. When processors start to fit into a single integrated circuit, they were truly micro compared to the monstrosities that existed previously.

Also, because integration was so weak initially, it was important to more manually consider the length of wire signals had to travel, and try to put components closer together to reduce the critical path to be able to increase clock speeds. These constraints are also of course present in modern computer design, but they were just so much more visible in those days.

The book does unfortunately not give much detail in Crays personal life as mentioned on this book review: www.goodreads.com/review/show/1277733185?book_show_action=true. His childhood section is brief, and his wedding is described in one paragraph, and divorce in one sentence. Part of this is because he was very private about his family most likely note how Wikipedia had missed his first wedding, and likely misattribute children to the second wedding; en.wikipedia.org/wiki/Talk:Seymour_Cray section "Weddings and Children".

Crays work philosophy is is highlighted many times in the book, and it is something worthy to have in mind:

Cray's final downfall was when he opted to try to use a promising but hard to work with material gallium arsenide instead of silicon as his way to try and speed up computers, see also: gallium arsenide vs silicon. Also, he went against the extremely current of the late 80's early 90's pointing rather towards using massively parallel systems based on silicon off-the-shelf Intel processors, a current that had DARPA support, and which by far the path that won very dramatically as of 2020, see: Intel supercomputer market share.