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Ciro Santilli  40 Updated 2025-07-16

Ciro Santilli  40 Updated 2026-09-20

Output:

sin(t)
fft
real 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
imag 0 -10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
rfft
real 0 0 0 0 0 0 0 0 0 0 0
imag 0 -10 0 0 0 0 0 0 0 0 0

sin(t) + sin(4t)
fft
real 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
imag 0 -10 0 0 -10 0 0 0 0 0 0 0 0 0 0 0 10 0 0 10
rfft
real 0 0 0 0 0 0 0 0 0 0 0
imag 0 -10 0 0 -10 0 0 0 0 0 0

With our understanding of the discrete Fourier transform we see clearly that:

the signal is being decomposed into sinusoidal components
because we are doing the Discrete Fourier transform of a real signal, for the fft, $X_{k} = \overset{ˉ}{X_{N - k}}$ so there is redundancy in the. We also understand that rfft simply cuts off and only keeps half of the coefficients

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Department of Computer Science of the University of Oxford by

Ciro Santilli  40 Updated 2025-07-16

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www.cs.ox.ac.uk

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Year 4 of the computer science course of the University of Oxford by

Ciro Santilli  40 Updated 2025-07-16

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Quantum Information course of the University of Oxford by

Ciro Santilli  40 Updated 2025-07-16

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www.cs.ox.ac.uk/teaching/courses/qi/

2023: Jonathan Barrett

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Year 2 or 3 course of the computer science course of the University of Oxford by

Ciro Santilli  40 Updated 2025-07-16

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Busy Beaver Challenge by

Ciro Santilli  40 Updated 2025-07-16

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bbchallenge.org/story

Project trying to compute BB(5) once and for all. Notably it has better presentation and organization than any other previous effort, and appears to have grouped everyone who cares about the topic as of the early 2020s.

Very cool initiative!

By 2023, they had basically decided every machine: discuss.bbchallenge.org/t/the-30-to-34-ctl-holdouts-from-bb-5/141

In June 2024 they felt that they had verified the result after a full Coq proof was published:

So now onto BB(6) I guess.

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Computer science course of the University of Oxford by

Ciro Santilli  40 Updated 2025-07-16

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Public landing page: www.ox.ac.uk/admissions/undergraduate/courses/course-listing/computer-science

Course lists: www.cs.ox.ac.uk/teaching/courses/ True to form, courses appear to have identifiers, e.g. qi for the Quantum Information course of the University of Oxford rather than more arbitrary A1/A2/A3, B1/B2/B3, naming convention used by the Mathematics course of the University of Oxford and the Physics course of the University of Oxford, and URLs can either have years or not:

www.cs.ox.ac.uk/teaching/courses/qi/: no year: goes to latest
www.cs.ox.ac.uk/teaching/courses/2023-2024/qi/: has year, fixed year. Disgraceful repetition of redundant 2023-2024, but OK.

The "course materials" section of each course leads to courses.cs.ox.ac.uk/ which is paywalled by IP (accessible via Eduroam): TODO which system does it use? Some courses place their materials directly on "www.cs.ox.ac.uk", and when that is the case they are publicly accessible. So it is very much hit and miss. E.g. www.cs.ox.ac.uk/teaching/courses/2022-2023/quantum/index.html from Quantum Processes and Computation course of the University of Oxford has the assignments such as www.cs.ox.ac.uk/people/aleks.kissinger/courses/qpc2022/assignment1.pdf publicly visible, but e.g. www.cs.ox.ac.uk/teaching/courses/2022-2023/modelsofcomputation/ has nothing.

Handbook:

2022:
- general www.cs.ox.ac.uk/files/13731/CS%20Handbook%20final.pdf
- Year 1 (Prelims): www.cs.ox.ac.uk/files/13794/Handbook%202022%20Part%20C%20-%20V1.3.pdf
- Year 2/3 (Parts A/B): www.cs.ox.ac.uk/files/13793/Handbook%202022%20Parts%20A%20&%20B%20V1.3.pdf There is some mixture on which courses can be taken on year 2 or 3. This also implies that they cannot have the usual A2/B2 naming scheme. They just don't have names instead mostly. It is also the most beautiful illustration of why you shouldn't do Compute Science at university: there's no depth to the subject. You can just take random courses and you learn it all quickly. Section "The only reason for universities to exist should be the laboratories".
  - Year 2 has four mandatory core courses:
    Models of Computation
    Algorithms and Data Structures
    Compilers (mandatory for compsi, but not mathematics and computer science)
    Concurrent programming
    A only:
    Probability
  - Hilary term
    Concurrent Programming (mandatory for compsi, but not mathematics and computer science)
    Quantum information
- Year 4 (Part C): www.cs.ox.ac.uk/files/13794/Handbook%202022%20Part%20C%20-%20V1.3.pdf
  - Michaelmas term
    Bayesian Statistical Probabilistic Programming
    Concurrent Algorithms and Data Structures
    Quantum Processes and Computation
    Computational Learning Theory
    Computational Biology
    Advanced Complexity Theory
    Graph Representation Learning
  - Hilary term
    Advanced Security
    Database Systems Implementation
    Ethical Computing in Practice
    Law and Computer Science
    Quantum Software course of the University of Oxford
    Geometric Deep Learning
    Foundations of Self-Programming Agents
    Deep Learning in Healthcare

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qiskit/hello.py by

Ciro Santilli  40 Updated 2025-07-16

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Our example uses a Bell state circuit to illustrate all the fundamental Qiskit basics.

Sample program output, counts are randomized each time.

First we take the quantum state vector immediately after the

∣ 00 ⟩

input.

input:
state:
Statevector([1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],
            dims=(2, 2))
probs:
[1. 0. 0. 0.]

We understand that the first element of Statevector is

∣ 00 ⟩

, and has probability of 1.0.

Next we take the state after a Hadamard gate on the first qubit:

h:
state:
Statevector([0.70710678+0.j, 0.70710678+0.j, 0.        +0.j,
             0.        +0.j],
            dims=(2, 2))
probs:
[0.5 0.5 0.  0. ]

We now understand that the second element of the Statevector is

∣ 01 ⟩

, and now we have a 50/50 propabability split for the first bit.

Then we apply the CNOT gate:

cx:
state:
Statevector([0.70710678+0.j, 0.        +0.j, 0.        +0.j,
             0.70710678+0.j],
            dims=(2, 2))
probs:
[0.5 0.  0.  0.5]

which leaves us with the final

\frac{∣ 00 ⟩ + ∣ 11 ⟩}{2}

Then we print the circuit a bit:

qc without measure:
     ┌───┐
q_0: ┤ H ├──■──
     └───┘┌─┴─┐
q_1: ─────┤ X ├
          └───┘
c: 2/══════════

qc with measure:
     ┌───┐     ┌─┐
q_0: ┤ H ├──■──┤M├───
     └───┘┌─┴─┐└╥┘┌─┐
q_1: ─────┤ X ├─╫─┤M├
          └───┘ ║ └╥┘
c: 2/═══════════╩══╩═
                0  1
qasm:
OPENQASM 2.0;
include "qelib1.inc";
qreg q[2];
creg c[2];
h q[0];
cx q[0],q[1];
measure q[0] -> c[0];
measure q[1] -> c[1];

And finally we compile the circuit and do some sample measurements:

qct:
     ┌───┐     ┌─┐
q_0: ┤ H ├──■──┤M├───
     └───┘┌─┴─┐└╥┘┌─┐
q_1: ─────┤ X ├─╫─┤M├
          └───┘ ║ └╥┘
c: 2/═══════════╩══╩═
                0  1
counts={'11': 484, '00': 516}
counts={'11': 493, '00': 507}

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Qiskit Aer by

Ciro Santilli  40 Updated 2025-07-16

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github.com/Qiskit/qiskit-aer

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Qiskit hello world by

Ciro Santilli  40 Updated 2025-07-16

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The official hello world is documented at: qiskit.org/documentation/intro_tutorial1.html and contains a Bell state circuit.

Our version at qiskit/hello.py.

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SageMath by

Ciro Santilli  40 Updated 2025-07-16

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A Python wrapper over a bunch of numeric and computer algebra system packages to try and fully replace MATLAB et. al.

For example, their

Quickstart tutorial at: www.sagemath.org/tour-quickstart.html From this we see that they are very opinionated, you don't need to import anything, everything has a pre-defined global name, which is convenient, e.g.:

Q Q^{3}

(1)

is the 3D vector space over the rationals. This also suggests that they are quite focused on computer algebra as opposed to numerical.

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Binet Gaussienne by

Ciro Santilli  40 Updated 2025-07-16

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This is likely a joke binet, but the idea is epic: its members would in principle take the hardest courses and purposefully get bad grades on them to improve the grades of others, as grades are always normalized to a normal distribution.

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Turing machine regex tape notation by

Ciro Santilli  40 Updated 2025-07-16

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Turing machine regex tape notation is Ciro Santilli's made up name for the notation used e.g. at:

Most of it is just regular regular expression notation, with a few differences:

$0^{i n f}$ denotes the right or left edge of the (zero initialized) tape. It is often omitted as we always just assume it is always present on both sides of every regex
A, B, C, D and E denotes the current machine state. This is especially common notation in the context of the BB(5) problem
< and > next to the state indicate if the head is on top of the left or right element. E.g.:
```
11 (01)^n <A 00 (0011)^{n+2}
```
indicates that the head A is on top of the last 1 of the last sequence of n 01s to the left of the head.

This notation is very useful, as it helps compress long repeated sequences of Turing machine tape and extract higher level patterns from them, which is how you go about understanding a Turing machine in order to apply Turing machine acceleration.

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Bell circuit by

Ciro Santilli  40 Updated 2025-07-16

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A quantum circuit which when fed with input

∣ 00 ⟩

produces the Bell state.

In Qiskit at: qiskit/hello.py.

Figure 1.
Quantum circuit that generates the Bell state
. Source.
The fundamental intuition for this circuit is as follows.
First the Hadamard gate makes the first qubit be in a 50/50 state.
Then, the CNOT gate gets controlled by that 50/50 value, and the controlled qubit also gets 50/50 chance as a result.
However, both qubits are now entangled: the result of the second qubit depends on the result of the first one. Because:
if the first qubit is 0, cnot is not active, and so the second qubit remains 0 as its input
if the first qubit is 1, cnot is active, and so the second qubit is flipped to 1

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PyZX by

Ciro Santilli  40 Updated 2025-07-16

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github.com/Quantomatic/pyzx

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Regular expression by

Ciro Santilli  40 Updated 2025-07-16

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OpenQASM by

Ciro Santilli  40 Updated 2025-07-16

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On Qiskit qiskit==0.44.1:

qc.qasm()

E.g. with our qiskit/hello.py, we obtain the Bell state circuit:

OPENQASM 2.0;
include "qelib1.inc";
qreg q[2];
creg c[2];
h q[0];
cx q[0],q[1];
measure q[0] -> c[0];
measure q[1] -> c[1];

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Quantum circuit description language by

Ciro Santilli  40 Updated 2025-07-16

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These are a bit like the Verilog of quantum computing.

One would hope that they are not Turing complete, this way they may serve as a way to pass on data in such a way that the receiver knows they will only be doing so much computation in advance to unpack the circuit. So it would be like JSON is for JavaScript.

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Quantum compiler benchmark by

Ciro Santilli  40 Updated 2025-07-16

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These appear to be benchmarks that don't involve running anything concretely, just compiling and likely then counting gates:

github.com/ArlineQ/arline_benchmarks

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 Pinned article: Introduction to the OurBigBook Project

Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.

Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!

Video 1.

Intro to OurBigBook

. Source.

We have two killer features:

topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculus
Articles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1.
Screenshot of the "Derivative" topic page
. View it live at: ourbigbook.com/go/topic/derivative
Video 2.
OurBigBook Web topics demo
. Source.
local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
Figure 2.
You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website
.
Figure 3.
Visual Studio Code extension installation
.
Figure 4.
Visual Studio Code extension tree navigation
.
Figure 5.
Web editor
. You can also edit articles on the Web editor without installing anything locally.
Video 3.
Edit locally and publish demo
. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.
Video 4.
OurBigBook Visual Studio Code extension editing and navigation demo
. Source.
Internal cross file references done right:
Infinitely deep tables of contents:
Figure 6.
Dynamic article tree with infinitely deep table of contents
.
Live URL: ourbigbook.com/cirosantilli/chordate
Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade