Weizmann Institute of Science scientists have found new evidence for the existence of a system of particles that "remembers" which quantum states it was in before, taking another step toward a fault-tolerant quantum computer.
In the future, quantum computers should solve problems that were considered unsolvable, predict how chemicals will react with each other, and even provide reliable weather forecasts, but for now they are very sensitive to environmental interference and loss of information. New research from Dr.'s lab Yuval Ronen At the Weizmann Institute of Science, published today in the scientific journal Nature, reveals new evidence for the existence of exotic particles "non-Abelian anions" – promising candidates for building a fault-tolerant quantum computer – within the material bilayer graphene.
In quantum mechanics, particles also behave like waves, and their properties are described by a wave function. The wave function can describe the state of a single particle or a system of particles. Physicists classify particles in nature into groups according to how the wave function of two particles changes when they swap places. Until the 80s, physicists recognized only two types of particles – particles whose wave function does not change when they swap places (bosons), such as light particles, and particles whose function is reversed (fermions), such as electrons. However, in 1982, a new state of matter was discovered in which another type of particle, which does not exist naturally, can exist. When these particles swap places, the wave function can rotate by any angle between 0 and 180 degrees – hence the name “anyons”, which comes from the word “any”.
Anions appear only at temperatures close to absolute zero, under a strong magnetic field, when there are strong bonds between the particles, and only in two-dimensional systems, that is, in thin pieces of material in which vertical movement is not possible. In these situations, it turned out that electrons in a material stop behaving as whole particles and start behaving as electron fragments – the anions. According to the theory that has developed since then, there are actually two types of anions: "Abelian anions", for which a change of place rotates the wave function only, and "non-Abelian anions", for which a change of place rotates the wave function and changes its shape. Electron fragments with an odd denominator – such as a third electron – are Abelian anions, and it is assumed that electron fragments with an even denominator – such as a quarter electron – are non-Abelian.
"Quantum computers are currently limited to narrow research fields and for them to be more useful they must be reliable. The new research takes us another step forward on the road there."
"The replacement of non-Abelian anions leaves an imprint on the shape of the wave function," explains Dr. Ronen. "If we take three non-Abelian anions and replace the first with the second and then the second with the third, we get a wave function with a different shape than we would get if we replaced them in a different order. This is a way to encode and store information, which are part of the conditions for developing a computer."
"In some existing models, the basic information units of the quantum computer (qubits) are single particles, which are sensitive to environmental disturbances," adds Dr. Ronen. "In non-Abelian anions, the information about the order of exchanges is preserved not locally, but in the wave function of the entire system. Systems whose important properties are preserved at the level of the entire system are resistant to a single fault and are called topological systems. These systems are among the most promising solutions to the problem of reliability of quantum computers." Although scientists have recently succeeded in measuring Abelian anions, so far non-Abelian anions have not been directly measured.
From classical optics to a quantum computer
The new study, led by Dr. Jeyhun Kim and Himanshu Dov from Dr. Ronen's lab in the Institute's Department of Condensed Matter Physics, used a material developed in recent years called bilayer graphene. It is a kind of "sandwich" made of two thin layers of carbon atoms, each arranged in a honeycomb pattern. In this material, the state in which non-Abelian anions are supposed to appear is stable, and scientists can closely control the anions' trajectories.
The experiment conducted by the institute's scientists is based on a famous experiment in optics from the 19th century. In the classic experiment, a beam of light is trapped between two mirrors. Each time the beam hits one of the mirrors and is reflected, its wave function rotates by a certain angle (phase). As long as the reflected beam of light is not synchronized with the original beam, they cancel each other out, and weak light is obtained. After several reflections, the wave function completes a full rotation and returns to the original phase, so that the beams are synchronized and strong light is obtained. The experiment produces a pattern of light and dark stripes called an interference pattern, and from the precise pattern, physicists deduce the properties of the original wave trapped between the mirrors.
In the parallel quantum experiment, the scientists first brought the electrons in the material to a state where non-Abelian anions should be found. They created a loop path in which a wave of one anion circles an island containing other anions and a magnetic field, and then meets the original wave again. In the first part of the experiment, the scientists only examined how a magnetic field changes the phase of the anion that circles the island. With each rotation, the phase of the returning wave changed under the influence of the magnetic field, and when they met the original wave, they either cancelled out or combined. Like the optical experiment, this experiment also produces an interference pattern, but not of light and dark bands but of high and low electrical resistance bands, from which we can learn the properties of the rotating anion.
"We were able to measure an electron fraction with an even denominator in the experiment," describes Dr. Ronen. "But contrary to the accepted assumption that non-Abelian anions are a quarter of an electron, we were surprised to see in the measurements that a wave of half an electron was circulating around the island. Following additional experiments we conducted, we estimate that the reason for this is that two non-Abelian anions are circling the island together, and we have not yet been able to separate them. Nevertheless, this is an important step on the way to directly measuring and identifying non-Abelian anions, and these days we are trying to separate them."
In another experiment, the scientists wanted to learn about the properties of the particles of matter inside the island. These particles interact with the rotating particle, so the scientists hypothesized that they could use it to learn about them. They changed the density of the particles in the island and examined to what extent this changed the wave function of the rotating particle and, as a result, the interference pattern. A change in the slope of the fringes in the interference pattern indicates the charge of the particles in the island, and the scientists learned from this that they have a quarter-electron charge, as expected from non-Abelian anions, and as previously measured in the laboratory of Prof. Motti Heiblom, also at the Weizmann Institute, in tunneling experiments.
"We have shown that in bilayer graphene there are particles that are most likely non-Abelian anions," says Dr. Ronen. "The next step will be to be able to directly observe the 'memory' of a system of non-Abelian anions, that is, to be able to measure how each order of particle exchanges produces a unique signature in the wave function. Quantum computers are currently limited to narrow research fields and in order for them to be more useful they must be reliable. The new research takes us another step forward on the path to developing a fault-tolerant quantum computer."
Also participating in the study were Amit Shair, Dr. Ravi Kumar, Dr. Alexei Ilin, Dr. Andre Haug, Shelly Iskus, Prof. David Meros and Prof. Adi Stern from the Institute's Condensed Matter Physics Department; Prof. Kenji Watanabe and Prof. Takashi Taniguchi from the National Institute for Materials Science, Tsukuba, Japan.
Science books
To describe the quantum state of just 300 qubits, that is, to store all the information stored in them, a classical computer would need to remember more than 34 quintillion complex numbers.
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