Program optimization Updated +Created
Mathematical formulation of quantum field theory Updated +Created
TODO holy crap, even this is hard to understand/find a clear definition of.
The Dirac equation, OK, is a partial differential equation, so we can easily understand its definition with basic calculus. We may not be able to solve it efficiently, but at least we understand it.
The formulation of QFT also appears to be a form of infinite-dimentional calculus.
Quantum electrodynamics by Lifshitz et al. 2nd edition (1982) chapter 1. "The uncertainty principle in the relativistic case" contains an interesting idea:
The foregoing discussion suggests that the theory will not consider the time dependence of particle interaction processes. It will show that in these processes there are no characteristics precisely definable (even within the usual limitations of quantum mechanics); the description of such a process as occurring in the course of time is therefore just as unreal as the classical paths are in non-relativistic quantum mechanics. The only observable quantities are the properties (momenta,
polarizations) of free particles: the initial particles which come into interaction, and the final particles which result from the process.
Projective elliptic geometry Updated +Created
Each elliptic space can be modelled with a real projective space. The best thing is to just start thinking about the real projective plane.
Projective space Updated +Created
A unique projective space can be defined for any vector space.
The projective space associated with a given vector space is denoted .
The definition is to take the vector space, remove the zero element, and identify all elements that lie on the same line, i.e.
The most important initial example to study is the real projective plane.
Endocytosis Updated +Created
Mathematician Updated +Created
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:
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.
It turned out that, about 10 years later, Ciro ended up following this advice, unwittingly.
Figure 1.
xkcd 435: Fields arranged by purity
. Source.
Matrix mechanics Updated +Created
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.
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.
Matrix representation of a bilinear form Updated +Created
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.
In terms of that matrix, the form is then given by:
Matrix ring Updated +Created
Maxima and minima Updated +Created
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 .
In the case of Functionals, this problem is treated under the theory of the calculus of variations.
Publish or perish Updated +Created
2023:
One of the world’s most cited scientists, Rafael Luque, suspended without pay for 13 years
The prolific chemist, who has published a study every 37 hours this year
You can't apparently fire someone in academia!
Rafael Luque, has been suspended without pay for the next 13 years
Quantum circuits vs classical circuits Updated +Created
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.
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,
Another consequence of this is that programming quantum computers does not look like programming the more "common" procedural programming languages such as C or Python, since those fundamentally rely on processor register / memory state all the time.
Quantum programmers can however use classic languages to help describe their quantum programs more easily, for example this is what happens in Qiskit, where you write a Python program that makes Qiskit library calls that describe the quantum program.
Quantum computer physical implementation Updated +Created
Video 1.
How To Build A Quantum Computer by Lukas's Lab (2023)
Source.
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.
As of 2023 he was a PhD student at NYU.
Quantum dot Updated +Created

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