Aaron Lauda has explored an area of mathematics for which most physicists have seen little use, wondering if he could have practical applications. In a twist even to what he did not expect, it turns out that this type of mathematics could be the key to overcoming a long -standing obstacle in quantum computer – and perhaps even to understand the quantum world in a whole new way.
Quantum computers, which exploit the peculiarities of quantum physics for speed of speed and computer capacity on conventional machines, can one day revolutionize technology. For the moment, however, this dream is out of reach. One of the reasons is that the qubits, the constituent elements of quantum computers, are unstable and can easily be disturbed by environmental noise. In theory, a more solid option exists: topological qubits distribute information on a wider area than ordinary qubits. However, in practice, they were difficult to achieve. Until now, the machines that manage to use them are not universal, which means that they cannot do everything that large -scale quantum computers can do. “It’s like trying to type a message on a keyboard with only half of the keys,” explains Lauda. “Our work fills the missing keys.” He and his group from the University of Southern California published their conclusions in a new article in the journal Nature communications.
Lauda and her colleagues solve some of the problems with topological qubits using a class of theoretical particles that they call negligence, named how they have been derived from neglected theoretical mathematics. These particles could open a new path to the experimental realization of universal topological quantum computers.
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Unlike ordinary qubits, which store information in the state of a single particle, topological qubits store it in the arrangement of several particles – which is a world property, not a local property, which makes them much more robust.
Take, for example, braided hair. The type and number of braids of a person are global properties that remain the same, whatever the way it shakes its head. On the other hand, the position of a bit of individual hair is a local property which can move with the slightest movement.
Aaron Lauda’s mathematical notation for his research study “Universal quantum calculation using Anyons of a non -semess topological field theory also” on a table.
Topological qubits work on a similar principle known as Anyon braiding. Everyone are quasiparticles – not real particles like protons, for example, but rather emerging phenomena of the collective behavior of many particles, such as undulations in a pond. They appear in two -dimensional quantum systems.
In our three -dimensional world, exchanging two particles is like weaving a chain on or under the other. You can always restore them to their original structure. However, when you exchange particles in two dimensions, you cannot pass or under; You must pass the strings by each other, which permanently modifies the structure of the strings.
Due to this property, the exchange of two Anyons can completely transform the state of a system. These Swaps can be repeated between several Anyons – a process called Anyon backing. The final state depends on the order in which exchanges, or braids, form, a bit like the way in which the model of a braid depends on the sequence of its strands.
Because the braiding of everything changes the quantum state of the qubit, the procedure can be used as a quantum door. Just like a logical door in a regular computer changes bits from 0 to 1 to allow calculation, quantum doors handle qubits. This logic based on braids is the basis of the way in which topological quantum computers calculate.
Theoretically, many types of everyone exist. A variety, called Ising Anyons, “are our best chances of quantum computer science in real systems,” explains Lauda. “However, in themselves, they are not universal for quantum calculation.”
Imagine a qubit in number on a calculator display and the quantum doors in the form of buttons of the calculator. A non -university computer is like a calculator that has only buttons to double or suppress in half. You can reach many figures, but not all, which limits your computing power. A universal quantum computer could reach all figures.
Most experimenters make computers Ising Universals using a special state of everything. But this state, as a single wick of non -bizarre hair, is not protected by global topological properties, making it vulnerable to errors and therefore knowing the main advantage of the use of everything.
Lauda’s team has found a different way of making a universal ising computer by introducing a new type of Unon, The Neglecton. It emerges from a broader mathematical framework called the theory of unimpined topological quantum fields, which modifies the way in which certain “negligible” components are counted. For years, these components have been thrown because they could cause absurd behavior, causing probabilities that reach more than one or drop below zero, or other results that have no physical sense. By finding a way to give them a meaning to the place of throwing them away, the Lauda team has released an unexplored area of quantum theory.
It is a change that evokes the first days of imaginary numbers, which are numbers built on negative square roots. They were originally only a mathematical tip without physical significance – to Erwin Schrödinger used them in the equation of waves which has become a cornerstone of quantum mechanics. “It’s similar,” explains Eric Rowell, Mathematician of Texas A & M University, who was not involved in work. “It is as if there was another door that we had not continued because we could not see him as physical. Maybe he had to be opened now.”
“In the world of topology, this idea turned out to be very powerful,” explains Lauda. It was like looking in quantum theory with a magnifying glass. In the design of Lauda, negligence remains stationary while the other is braid around him. This configuration has a new door that makes the quantum computer universal. In the image of the calculator of the Quiet states, this door acts as adding or subtraction 1; Over time, the process can happen to all figures, unlike the non -universal version of the calculator.
The capture is that the addition of risk of negligence pushing everything in a non -physical territory, in which the probabilities cease to add the way they should. “There is this much larger theory,” says Lauda, ”and sitting inside, there is a place where everything has physically meaning.” It’s like when you get away from the card in a video game – the game starts in Glitching, you can browse the walls and all the rules. The trick is to build an algorithm that keeps the player safe inside the card. This work fell on the graduate student of Lauda, Filippo Iulianelli, who reworked an algorithm he had met in a recent class.
The next obstacle is to find a real version of this system; Negligence remains entirely hypothetical for the moment. Lauda is optimistic. In the 1930s, physicists used mathematical symmetries to predict the existence of a strange subatomic particle – the meson – there was before the experiences confirmed it. “We do not pretend that we are in the same situation,” he says, “but our work gives experimenters a target to seek in the same systems that realize everything.”
Shawn Cui, mathematician at Purdue University who assessed the new article, calls for the search for “very exciting theoretical progress” and hopes to see studies exploring physical systems where such Anyons could emerge. Rowell agrees and he suggests that negligence could result from a certain interaction between an Ising system and its environment. “Maybe there is just a little additional engineering necessary to build this negligence,” he said.
For Lauda, implementation is only part of the excitement. “My goal is to make a case as convincing as possible to other researchers as the non-fixed framework is not only valid, but an exciting approach to better understand quantum theory,” he says. Negligence is unlikely to be overlooked longer.
