Is a decision problem of determining if something belongs to a non-recursive language.
Or in other words: there is no Turing machine that always halts for every input with the yes/no output.
Every undecidable problem must obviously have an infinite number of "possibilities of stuff you can try": if there is only a finite number, then you can brute-force it.
Some undecidable problems are of recursively enumerable language, e.g. the halting problem.
Lists of undecidable problems.
Coolest ones besides the obvious boring halting problem:
- mortal matrix problem
- Diophantine equation existence of solutions: undecidable Diophantine equation problems
Quantum circuits vs classical circuits by 
Ciro Santilli 35 Updated 2024-12-23 +Created 1970-01-01
Ciro Santilli 35 Updated 2024-12-23 +Created 1970-01-01Just 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,
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.
Does not require entangled particles, unlike E91 which does.
en.wikipedia.org/w/index.php?title=Quantum_key_distribution&oldid=1079513227#BB84_protocol:_Charles_H._Bennett_and_Gilles_Brassard_(1984) explains it well. Basically:
- Alice and Bob randomly select a measurement basis of either 90 degrees and 45 degrees for each photon
- Alice measures each photon. There are two possible results to either measurement basis: parallel or perpendicular, representing values 0 or 1. TODO understand better: weren't the possible results supposed to be pass or non-pass? She writes down the results, and sends the (now collapsed) photons forward to Bob.
- Bob measures the photons and writes down the results
- Alice and Bob communicate to one another their randomly chosen measurement bases over the unencrypted classic channel.This channel must be authenticated to prevent man-in-the-middle. The only way to do this authentication that makes sense is to use a pre-shared key to create message authentication codes. Using public-key cryptography for a digital signature would be pointless, since the only advantage of QKD is to avoid using public-key cryptography in the first place.
- they drop all photons for which they picked different basis. The measurements of those which were in the same basis are the key. Because they are in the same basis, their results must always be the same in an ideal system.
- if there is an eavesdropper on the line, the results of measurements on the same basis can differ.Unfortunately, this can also happen due to imperfections in the system.Alice and Bob must decide what level of error is above the system's imperfections and implies that an attacker is listening.
Formulated as a quantum field theory.
Quarks, Gluon flux tubes, Strong Nuclear Force, & Quantum Chromodynamics by Physics Videos by Eugene Khutoryansky (2018)
Source. Some decent visualizations of how the field lines don't expand out like they do in electromagnetism, suggesting color confinement.PHYS 485 Lecture 6: Feynman Diagrams by Roger Moore (2016)
Source. Despite the title, this is mostly about QCD. Organization developing quantum software by Ciro Santilli 35 Updated 2024-12-23 +Created 1970-01-01
Ciro Santilli 35 Updated 2024-12-23 +Created 1970-01-01The 1890 US Census and the history of punchcard computing by Stand-up Maths (2020)
Source. It was basically a counting machine! Shows a reconstruction at the Computer History Museum. There are unlisted articles, also show them or only show them.