Speed ​​limits also apply to the quantum world


The study "Demonstration of Quantum Brachistochrones between Distant States of an Atom", conducted by the University of Bonn in collaboration with the University of Padua and published in the journal "Physical Review X", has shown speed limits for complex quantum operations, such results are especially important for quantum computing. They discovered that a ‘speed limit’ serves to reach the maximum number of operations that quantum computers can perform.

Even in the world of the smallest particles, with their special rules, things cannot go infinitely fast. Physicists at the University of Bonn have shown the speed limits for complex quantum operations. Scientists from MIT (Massachusetts Institute of Technology), the universities of Hamburg, Cologne, Padua and the Jülich Research Center also participated in the study, which was featured in the American Physical Society's Physics Magazine.

Imagine it’s New Year's Eve, a few minutes from midnight (a time before lockdowns), and you’re watching a waiter hurry around, getting ready to serve an entire tray full of champagne glasses. The waiter runs from guest to guest at full speed. Thanks to his skills, perfected over many years of work, the waiter manages to avoid spilling a single drop of the precious liquid. However, this skilful waiter has a trick: while accelerating his steps, the waiter tilts the tray just slightly to prevent the champagne from spilling out of the glasses. Halfway to the table, the waiter tilts the tray in the opposite direction and slows it down. Only when the waiting makes a complete stop does the tray return to its full upright position.

In some respects atoms, in their microscopic world, are similar to champagne. In fact, it is better to think of atoms as waves of matter that behave like liquids and not like billiard balls. If you want to transport atoms from one place to another as soon as possible, you need the same skills as our New Year's Eve waiter. “Still, there is a speed limit that this transport cannot exceed,” explains Dr. Andrea Alberti, who led the study at the Institute of Applied Physics at the University of Bonn.

"Fifteen years ago, when we began to develop control techniques to manipulate quantum many-body systems and studying their theoretical limits, we didn't think we would see their experimental demonstration in the laboratory so quickly” explains Simone Montangero, Professor in the Department of Physics and Astronomy of the University of Padua and Deputy Director of the University Interdepartmental Center for Quantum Technologies

Andrea Alberti and the team of researchers used cesium atoms as a substitute for the champagne, completely overlapping two laser beams, but pointing them at each other as a substitute for the tray. This overlap, which physicists call interference, creates a standing wave of light, like a succession of mountains and valleys that do not move, at first.

We loaded the atom into one of these valleys and then we set the light wave in motion by moving the valley to which the atom is confined,” says Alberti. “Our goal was to get the atom to its destination as quickly as possible without ‘spilling out’ of the valley.”

"To do this we used an algorithm for quantum optimal control systems that were previously introduced and for which has been in development for almost ten years, but for which is becoming a standard for the development of quantum technologies” adds Prof. Montangero.

Two Soviet physicists, Leonid Mandelstam and Igor Tamm, already theoretically substantiated the fact that there is a speed limit in the microcosm during the middle of the last century. They proved that the maximum speed of a quantum process depends on the uncertainty of energy, that is, how much the manipulated particle is ‘free’ with respect to its possible energy states. The higher the degree of freedom of energy, the faster the speed. In atomic transport, for example, the deeper the valley in which the wave of the matter is confined, the wider the range of energy that the quantum states within the valley can handle, and the faster the atom can be transported. Returning to the waiter who runs from table to table, if the glasses were only half filled (at the chagrin of guests), reduces the risk of the champagne spilling out during the acceleration and deceleration phase.

"However, the energy freedom of a particle cannot be increased at will, says Andrea Alberti, ‘that is, we cannot make the valley where the atom is trapped infinitely deep because it would take up too much energy."

Mandelstam and Tamm speed limits are fundamental limits that can only be reached in certain situations, that is, under the limitations of a system in which there are only two quantum states.

In our case, for example, this happens when the origin and destination are very close to each other,” explains Alberti. “Then, the atom de Broglie waves overlap in both places, allowing the atoms to be transported directly to their destination at once, which means they don’t stop in between, as in Star Trek’s Starship Enterprise teleportation.”

However, when the distance increases and becomes many times greater than the size of the matter wave, as in the experiment carried out in Bonn, the situation is different. For such distances, direct ‘teleportation’ is impossible and therefore the minimum time needed for the transfer becomes longer. The study shows that a lower speed limit than that predicted by Soviet physicists applies to such processes. This limit is determined, not only by the energy uncertainty as in the previous case but also by the number of intermediate states it crossed. This finding improves the theoretical understanding of complex quantum processes and the constraints to which they are subject. The discoveries of physicists are particularly important for quantum computing, as the calculations made possible with quantum computers are based on the manipulation of systems between many levels.

Quantum states, however, are very sensitive and only last a very short time which physicists call coherence time. It is therefore important to enclose as many calculation operations as possible in this time frame. Our study - concludes Andrea Alberti - shows how to practically reach the maximum number of operations that can be performed in the quantum coherence time ».

The study was funded under the SFB / TR 185 of the German Research Foundation (DFG). Funding was also provided by the Reinhard Frank Foundation and the German Academic Exchange Service.