The pattern of crossing the knot -making threads can be detected mathematically.Credit: Ili Lupsku/500 PX via Getty
Are quantum computers worth billions that are being invested in them? The answer is probably many years away. However, machines can prove to be particularly favorable to solve problems in mathematics – especially in topology, a branch of mathematics that studies size.
Posted on Arxiv in March in a preprint1Quantinum researchers, a company headquartered at Cambridge, UK, reported using their quantum machine H2-2, saying that the difference between different types of knots based on topological properties, and shows that this method can be faster than those who run on ordinary, or ‘classical’, computers. Quantinum Chief Excise Officer Ilas Khan says a quantum computer, which is expected to be released on the end of this year, can reach very close to the beating of Helios, classical super computers, analyzing complex complex knots.
Although other groups have already made the same claims as ‘Quantum Advantage’, usually for ad hoc calculations that have no practical use, classical algorithms finally do to catch. But theoretical results2,3 Suggest that for some topology problems, the quantum algorithm can be faster than any possible classical counterpart. This is due to mysterious relationships between topology and quantum physics. “These things are related, the mind-borne, I think,” a quantinum researcher Constentinose Mechtzidis, who led the work behind the preprint.
Knot problems
In that work, Meichanetzidis and his colleagues used a quantum computer to calculate the knot ‘Invenants’ – which describe a special type of knot. The invaders he saw were prepared by New Zealand -born mathematician von Jones.
Not invoices are generally calculated by a pattern of crossing – how the knot is crossed into the cross when the knot is flattened on one surface – but only depends on the topological type of the knot. In other words, the same knot can be flattened in two different ways, which have very different crossing patterns, but the knot will still be unchanged. If two crossing patterns have separate knot attacks, it means they come from lumps that are topologically different. (However, Convats is not always true: In rare cases, two topologically different lumps can give the same irreversible.)
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Meichanetzidis team implemented a quantum algorithm, proposed to calculate notes of notes.4 By Jones and Computer Scientists Dorit Ahronov and Zaf Landau. The algorithm is a series of quantum operations suit the crossing of a flat knot. Researchers used it to calculate the Jones Inverterates for knots with 104 crossings on Quantinum’s H2-2 quantum computer. It is still under classical computing, but the company’s machines must eventually be able to handle 3,000 crossings either, the point at which the fastest classical supercomputers will move out of the steam, say mathetzidis.
Mathematically, the theoretical equivalence between knot crossing and quantum algorithms has been known for decades, but now only the team can completely practice it, Ahronov says, Ahronov says, which is in Hebrewl University in Jerusalem. “I hoped the transition between languages would be very efficient,” she says.
