Poet, scientists and warriors all in one? Conquerors of the useless.
A wise teacher from University of São Paulo once told the class Ciro Santilli attended an anecdote about his life:It turned out that, about 10 years later, Ciro ended up following this advice, unwittingly.
I used to want to learn Mathematics.But it was very hard.So in the end, I became an engineer, and found an engineering solution to the problem, and married a Mathematician instead.
Mathematics and Computer science course of the University of Oxford Updated 2025-07-11 +Created 1970-01-01
Public landing page: www.ox.ac.uk/admissions/undergraduate/courses/course-listing/mathematics-and-computer-science
A mixed cross department course with the Mathematical Institute of the University of Oxford.. Its corresponding masters is known as Oxford MMathCompSci. The handbook is together with the computer science one: Section "Computer science course of the University of Oxford".
Mathematics and Statistics course of the University of Oxford Updated 2025-07-11 +Created 1970-01-01
Tends to be Ciro's pick if gnuplot can't handle the use case, or if the project is really really serious.
Couldn't handle exploration of large datasets though: Survey of open source interactive plotting software with a 10 million point scatter plot benchmark by Ciro Santilli
Examples:
- matplotlib/hello.py
- matplotlib/educational2d.py
- matplotlib/axis.py
- matplotlib/label.py
- Line style
- Subplots
- matplotlib/two_lines.py
- Data from files
- Specialized
Published by Werner Heisenberg in 1925-07-25 as quantum mechanical re-interpretation of kinematic and mechanical relations by Heisenberg (1925), it offered the first general formulation of quantum mechanics.
It is apparently more closely related to the ladder operator method, which is a more algebraic than the more analytical Schrödinger equation.
It appears that this formulation makes the importance of the Poisson bracket clear, and explains why physicists are so obsessed with talking about position and momentum space. This point of view also apparently makes it clearer that quantum mechanics can be seen as a generalization of classical mechanics through the Hamiltonian.
QED and the men who made it: Dyson, Feynman, Schwinger, and Tomonaga by Silvan Schweber (1994) mentions however that relativistic quantum mechanics broke that analogy, because some 2x2 matrix had a different form, TODO find that again.
Inward Bound by Abraham Pais (1988) chapter 12 "Quantum mechanics, an essay" part (c) "A chronology" has some ultra brief, but worthwhile mentions of matrix mechanics and the commutator.
As usual, it is useful to think about how a bilinear form looks like in terms of vectors and matrices.
Unlike a linear form, which was a vector, because it has two inputs, the bilinear form is represented by a matrix which encodes the value for each possible pair of basis vectors.
The matrix ring of degree n is the set of all n-by-n square matrices together with the usual vector space and matrix multiplication operations.
Given a function :we want to find the points of the domain of where the value of is smaller (for minima, or larger for maxima) than all other points in some neighbourhood of .
- from some space. For beginners the real numbers but more generally topological spaces should work in general
- to the real numbers
In the case of Functionals, this problem is treated under the theory of the calculus of variations.
Just like a classic programmer does not need to understand the intricacies of how transistors are implemented and CMOS semiconductors, the quantum programmer does not understand physical intricacies of the underlying physical implementation.
The main difference to keep in mind is that quantum computers cannot save and observe intermediate quantum state, so programming a quantum computer is basically like programming a combinatorial-like circuit with gates that operate on (qu)bits:
For this reason programming a quantum computer is much like programming a classical combinatorial circuit as you would do with SPICE, verilog-or-vhdl, in which you are basically describing a graph of gates that goes from the input to the output
For this reason, we can use the words "program" and "circuit" interchangeably to refer to a quantum program
Also remember that and there is no no clocks in combinatorial circuits because there are no registers to drive; and so there is no analogue of clock in the quantum system either,
Quantum Computation and Quantum Information by Nielsen and Chuang Updated 2025-07-11 +Created 1970-01-01
Lists of the most promising implementations:
As of 2020, the hottest by far are:
Super quick overview of the main types of quantum computer physical implementations, so doesn't any much to a quick Google.
He says he's going to make a series about it, so then something useful might actually come out. The first one was: Video "How to Turn Superconductors Into A Quantum Computer by Lukas's Lab (2023)", but it is still too basic.
The author's full name is Lukas Baker, www.linkedin.com/in/lukasbaker1331/, found with Google reverse image search, even though the LinkedIn image is very slightly different from the YouTube one.
Quantum computers are not expected to solve NP-complete problems Updated 2025-07-11 +Created 1970-01-01
Only NP-intermediate, which includes notably integer factorization:
- quantumcomputing.stackexchange.com/questions/16506/can-quantum-computer-solve-np-complete-problems
- www.cs.virginia.edu/~robins/The_Limits_of_Quantum_Computers.pdf by Scott Aaronson
- cs.stackexchange.com/questions/130470/can-quantum-computing-help-solve-np-complete-problems
- www.quora.com/How-can-quantum-computing-help-to-solve-NP-hard-problems
TODO WTF is this? How is it built? What is special about it?
Mentioned a lot in the context of superconducting quantum computers, e.g. youtu.be/t5nxusm_Umk?t=268 from Video "Quantum Computing with Superconducting Qubits by Alexandre Blais (2012)",
Lecture notes found by Googling "quantum field theory pdf":
- www.ppd.stfc.ac.uk/Pages/Dasgupta_08_Intro_to_QFT.pdf "An Introduction to Quantum Field Theory" by Mrinal Dasgupta from the University of Manchester (2008). 48 pages.
- www.thphys.uni-heidelberg.de/~weigand/QFT2-14/SkriptQFT2.pdf "Quantum Field Theory I + II" by Timo Weigand from the Heidelberg University. Unknown year, references up to 2008.
- edu.itp.phys.ethz.ch/hs12/qft1/ Quantum Field Theory 1 by Niklas Beisert
Man-in-the-middle attack
quantumcomputing.stackexchange.com/questions/142/advantage-of-quantum-key-distribution-over-post-quantum-cryptography/25727#25727 Advantage of quantum key distribution over post-quantum cryptography has Ciro Santilli's comparison to classical encryption.
Long story short:
- QKD allows you to generate shared keys without public-key cryptography. You can then use thses shared keys
- QKD requires authentication on a classical channel, exactly like a classical public-key cryptography forward secrecy would. The simplest way to do this is a with a pre-shared key, just like in classical public key cryptography. If that key is compromised at any point, your future messages can get man-in-the-middle'd, exactly like in classical cryptography.
QKD uses quantum mechanics stuff to allow sharing unsnoopable keys: you can detect any snooping and abort communication. Unsnoopability is guaranteed by the known laws of physics, up only to engineering imperfections.
Furthermore, it allows this key distribution without having to physically take a box by car somewhere: once the channel is established, e.g. optical fiber, you can just keep generating perfect keys from it. Otherwise it would be pointless, as you could just drive your one-time pad key every time.
However, the keys likely have a limited rate of generation, so you can't just one-time pad the entire message, except for small text messages. What you would then do is to use the shared key with symmetric encryption.
Therefore, this setup usually ultimately relies on the idea that we believe that symmetric encryption is safer than , even though there aren't mathematical safety proofs of either as of 2020.
At Section "Quantum computing is just matrix multiplication" we saw that making a quantum circuit actually comes down to designing one big unitary matrix.
Instead, they use quantum logic gates.
Quantum matter physics course of the University of Oxford Updated 2025-07-11 +Created 1970-01-01
2011- professor: Steven H. Simon. His start date is given e.g. at: www-thphys.physics.ox.ac.uk/people/SteveSimon/condmat2012/LectureNotes2012.pdf which is presumably an older version of: www-thphys.physics.ox.ac.uk/people/SteveSimon/QCM2022/QuantumMatter.pdf
Notes/book: www-thphys.physics.ox.ac.uk/people/SteveSimon/QCM2022/QuantumMatter.pdf Marked as being for Oxford MMathPhys, so it appears that this is a 4th year course normally. TODO but where is it listed under the course list of MMapthPhys? mmathphys.physics.ox.ac.uk/course-schedule
Course page index: www-thphys.physics.ox.ac.uk/people/SteveSimon/
www-thphys.physics.ox.ac.uk/people/SteveSimon/QCM2023/quantummatter.html mentions it is given in Hilary term
2023 syllabus as per www-thphys.physics.ox.ac.uk/people/SteveSimon/QCM2023/quantummatter.html#Syllabus:
- Fermi Liquids
- Weakly Interacting Fermions
- Response Functions and Screening
- Thomas Fermi
- RPA
- Plasmons
- Landau Fermi Liquid Theory
- Superfluidity
- Two Fluid Model and Quantized Circulation
- Landau Criterion for Superfluidity
- Two Fluid Model for Superconductors
- London Theory
- Flux Vortices
- Type I and Type II superconductors
- Microscopic Superfluidity
- Coherent States
- Bose Condensation
- Gross Pitaevskii Equation
- Off Diagonal Long Range Order
- Feynman Theory of Superfluidity (in book, but will skip in lectures. Not examinable)
- Ginzburg Landau Theory of Superfluids
- BCS Theory of Superconductors
There are unlisted articles, also show them or only show them.