A speed limit also applies in the quantum world

February 19, 2021

Even in the world of the smallest particles with their own special rules, things cannot proceed infinitely fast. Physicists at the University of Bonn have now shown what the speed limit is for complex quantum operations. The study also involved scientists from MIT, the universities of Hamburg, Cologne and Padua, and the Jülich Research Center. The results are important for the realization of quantum computers, among other things. They are published in the prestigious journal Physical Review X, and covered by the Physics Magazine of the American Physical Society.

Suppose you observe a waiter (the lockdown is already history) who on New Year's Eve has to serve an entire tray of champagne glasses just a few minutes before midnight. He rushes from guest to guest at top speed. Thanks to his technique, perfected over many years of work, he nevertheless manages not to spill even a single drop of the precious liquid.

A little trick helps him to do this: While the waiter accelerates his steps, he tilts the tray a bit so that the champagne does not spill out of the glasses. Halfway to the table, he tilts it in the opposite direction and slows down. Only when he has come to a complete stop does he hold it upright again.

Atoms are in some ways similar to champagne. They can be described as waves of matter, which behave not like a billiard ball but more like a liquid. Anyone who wants to transport atoms from one place to another as quickly as possible must therefore be as skillful as the waiter on New Year's Eve. "And even then, there is a speed limit that this transport cannot exceed," explains Dr. Andrea Alberti, who led this study at the Institute of Applied Physics of the University of Bonn.

Cesium atom as a champagne substitute

In their study, the researchers experimentally investigated exactly where this limit lies. They used a cesium atom as a champagne substitute and two laser beams perfectly superimposed but directed against each other as a tray. This superposition, called interference by physicists, creates a standing wave of light: a sequence of mountains and valleys that initially do not move. "We loaded the atom into one of these valleys, and then set the standing wave in motion - this displaced the position of the valley itself," says Alberti. "Our goal was to get the atom to the target location in the shortest possible time without it spilling out of the valley, so to speak."

The fact that there is a speed limit in the microcosm was already theoretically demonstrated by two Soviet physicists, Leonid Mandelstam and Igor Tamm more than 60 years ago. They showed that the maximum speed of a quantum process depends on the energy uncertainty, i.e., how "free" the manipulated particle is with respect to its possible energy states: the more energetic freedom it has, the faster it is. In the case of the transport of an atom, for example, the deeper the valley into which the cesium atom is trapped, the more spread the energies of the quantum states in the valley are, and ultimately the faster the atom can be transported. Something similar can be seen in the example of the waiter: If he only fills the glasses half full (to the chagrin of the guests), he runs less risk that the champagne spills over as he accelerates and decelerates. However, the energetic freedom of a particle cannot be increased arbitrarily. "We can't make our valley infinitely deep - it would cost us too much energy," stresses Alberti.

Beam me up, Scotty!

The speed limit of Mandelstam and Tamm is a fundamental limit. However, one can only reach it under certain circumstances, namely in systems with only two quantum states. "In our case, for example, this happens when the point of origin and destination are very close to each other," the physicist explains. "Then the matter waves of the atom at both locations overlap, and the atom could be transported directly to its destination in one go, that is, without any stops in between - almost like the teleportation in the Starship Enterprise of Star Trek."

However, the situation is different when the distance grows to several dozens of matter wave widths as in the Bonn experiment. For these distances, direct teleportation is impossible. Instead, the particle must go through several intermediate states to reach its final destination: The two-level system becomes a multi-level system. The study shows that a lower speed limit applies to such processes than that predicted by the two Soviet physicists: It is determined not only by the energy uncertainty, but also by the number of intermediate states. In this way, the work improves the theoretical understanding of complex quantum processes and their constraints.

The physicists' findings are important not least for quantum computing. The computations that are possible with quantum computers are mostly based on the manipulation of multi-level systems. Quantum states are very fragile, though. They last only a short lapse of time, which physicists call coherence time. It is therefore important to pack as many computational operations as possible into this time. "Our study reveals the maximum number of operations we can perform in the coherence time," Alberti explains. "This makes it possible to make optimal use of it."

The study was funded by the German Research Foundation (DFG) as part of the Collaborative Research Center SFB/TR 185 OSCAR. Funding was also provided by the Reinhard Frank Foundation in collaboration with the German Technion Society, and by the German Academic Exchange Service.

Publication: Manolo R. Lam, Natalie Peter, Thorsten Groh, Wolfgang Alt, Carsten Robens, Dieter Meschede, Antonio Negretti, Simone Montangero, Tommaso Calarco und Andrea Alberti: Demonstration of Quantum Brachistochrones between Distant States of an Atom; Physical Review X;


Dr. Andrea Alberti
Institut für Angewandte Physik der Universität Bonn
Tel. +49 228 73-3471
E-mail: alberti@iap.uni-bonn.de

University of Bonn

Related Quantum Computers Articles from Brightsurf:

Optical wiring for large quantum computers
Researchers at ETH have demonstrated a new technique for carrying out sensitive quantum operations on atoms.

New algorithm could unleash the power of quantum computers
A new algorithm that fast forwards simulations could bring greater use ability to current and near-term quantum computers, opening the way for applications to run past strict time limits that hamper many quantum calculations.

A new technique prevents errors in quantum computers
A paper recently published in Nature presents a protocol allowing for the error detection and the protection of quantum processors in case of qubit loss.

New method prevents quantum computers from crashing
Quantum information is fragile, which is why quantum computers must be able to correct errors.

Natural radiation can interfere with quantum computers
Radiation from natural sources in the environment can limit the performance of superconducting quantum bits, known as qubits.

New model helps to describe defects and errors in quantum computers
A summer internship in Bilbao, Spain, has led to a paper in the journal Physical Review Letters for Jack Mayo, a Master's student at the University of Groningen, the Netherlands.

The first intuitive programming language for quantum computers
Several technical advances have been achieved recently in the pursuit of powerful quantum computers.

Hot qubits break one of the biggest constraints to practical quantum computers
A proof-of-concept published today in Nature promises warmer, cheaper and more robust quantum computing.

Future quantum computers may pose threat to today's most-secure communications
Quantum computers that are exponentially faster than any of our current classical computers and are capable of code-breaking applications could be available in 12 to 15 years, posing major risks to the security of current communications systems, according to a new RAND Corporation report.

Novel error-correction scheme developed for quantum computers
Experimental quantum computers are plagued with errors. Here Dr Arne Grimsmo from the University of Sydney and colleagues from RMIT and the University of Queensland offer a novel method to reduce errors in a scheme applicable across different types of quantum hardware.

Read More: Quantum Computers News and Quantum Computers Current Events
Brightsurf.com is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to Amazon.com.