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A new study reveals the solution to Euler's 243-year-old mathematical problem

A new study reveals the solution to Euler's 243-year-old mathematical

A mathematical problem developed 243 years ago can only be solved using quantum entanglement, new research reveals.

The problem of mathematics is a bit like Sudoku on steroids and is called the problem of Euler's officers, according to Leonhard Euler, the mathematician who first proposed it in 1779. Here's the enigma: You are commanding an army of six regiments. Each regiment contains six different officers of six different ranks. Can you arrange them in a 6 by 6 square without repeating an order or regiment in any given row or column?

Euler could not find such an arrangement, and subsequent calculations proved that there was no solution.

Now, however, researchers have found a new solution to Euler's problem. As reported by Daniel Garisto of Quanta Magazine, a new study posted on the arXiv preprint database reveals that you can organize six regiments with six officers of six different ranks in a network without repeating any ranks or regiments of more than one times in each row or column… if officers are in a state of quantum confusion.

The paper, which was submitted for peer review in the journal Physical Review Letters, benefits from the fact that quantum objects can be in as many possible states as possible until measured. (Quantum entrapment was famously demonstrated by Schrodinger's cat's thought experiment, in which a cat is trapped in a box of radioactive poison; the cat is dead and alive until you open the box.)

In Euler's classic problem, every officer has a regiment and static ranks. They could be a first lieutenant in the Red Regiment, for example, or a captain in the Blue Regiment. (Colors are sometimes used in grid visualization to make regiments easier to identify.)

Por një oficer kuantik mund të zërë më shumë se një regjiment ose gradë njëherësh. Një oficer i vetëm mund të jetë ose një toger i parë i Regjimentit të Kuq ose një kapiten i Regjimentit Blu; një major i Regjimentit të Gjelbër ose kolonel i Regjimentit të Purpurt. (Ose, teorikisht, ndonjë kombinim tjetër.)

Çelësi për zgjidhjen e problemit të Euler-it me këtë ndërrues identiteti është se oficerët në rrjet mund të jenë në një gjendje të ngatërresës kuantike. Në ndërthurje, gjendja e një objekti informon gjendjen e një tjetri. Nëse oficeri nr. 1 është, në fakt, një toger i parë i Regjimentit të Kuq, oficeri nr. 2 duhet të jetë major në Regjimentin e Gjelbër, dhe anasjelltas.

Using computer power with brutal force, the authors of the new paper, led by Adam Burchardt, a postdoctoral researcher at Jagiellonian University in Poland, proved that filling the network with quantum officers made the solution possible.

The results could have real impacts on quantum data storage, according to Quanta Magazine. Confused states can be used in quantum computing to ensure that data is safe even in the event of an error - a process called quantum error correction. By confusing 36 quantum officers into a state of interdependent relationships, the researchers found what is called an absolutely maximally confused state. Such states can be important for the elastic storage of data in quantum computing.