Which factors influence how quickly a quantum computer can perform calculations? To answer this question, physicists from the University of Bonn and the Technion — Israel Institute of Technology devised an elegant experiment. The study’s findings have been published in the journal Science Advances.
Quantum computers are extremely sophisticated machines that process information using quantum mechanics principles. This should enable them to handle certain problems in the future that are completely intractable for conventional computers. However, even quantum computers have fundamental limits in terms of the amount of data they can process in a given amount of time.
Quantum gates require a minimum time
The information stored in conventional computers can be viewed as a long series of zeros and ones, or bits. It is not the same in quantum mechanics: The data is stored in quantum bits (qubits), which are more like waves than a series of discrete values. When attempting to precisely represent the information contained in qubits, physicists use the term wave functions.
Information in a traditional computer is linked together by so-called gates. Combining several gates enables basic operations such as the addition of two bits. In quantum computers, information is processed in a very similar manner, with quantum gates changing the wave function according to certain rules.
We used fast light pulses to create a so-called quantum superposition of two states of the atom. In a metaphorical sense, the atom behaves as if it were two different colors at the same time. Each atom twin takes a different position in the light bowl depending on the color: one is high up on the edge and “rolls” down from there.
Dr. Andrea Alberti
In another way, quantum gates are similar to their traditional counterparts: “Even in the quantum world, gates do not work infinitely fast,” explains Dr. Andrea Alberti of the University of Bonn’s Institute of Applied Physics. “They need as little time as possible to transform the wave function and the information it contains.”
This minimum time for transforming the wave function was theoretically determined more than 70 years ago by Soviet physicists Leonid Mandelstam and Igor Tamm. Physicists from the University of Bonn and the Technion have now investigated the Mandelstam-Tamm limit for the first time using a complex quantum system in an experiment. They accomplished this by using cesium atoms that moved in a highly controlled manner. “In the experiment, we let individual atoms roll down like marbles in a light bowl and observed their motion,” Alberti, the experiment’s lead author, explains.
Atoms can be described as matter waves in quantum mechanics. Their quantum information changes as they travel to the bottom of the light bowl. The researchers wanted to know how soon this “deformation” could be identified. This time would then serve as experimental evidence for the Mandelstam-Tamm limit. However, in the quantum world, every measurement of the atom’s position inevitably changes the matter wave in an unpredictable way. So, no matter how quickly the measurement is taken, it always appears that the marble has deformed. “As a result, we devised a different method to detect deviation from the initial state,” Alberti explains.
To that end, the researchers began by creating a clone of the matter wave, or an almost exact twin. “We used fast light pulses to create a so-called quantum superposition of two states of the atom,” explains Gal Ness, the study’s first author and a doctoral student at the Technion. “In a metaphorical sense, the atom behaves as if it were two different colors at the same time.” Each atom twin takes a different position in the light bowl depending on the color: one is high up on the edge and “rolls” down from there. The other, on the other hand, is already at the bottom of the bowl. This twin does not move — after all, it cannot roll up the walls and so does not change its wave function.
At regular intervals, the physicists compared the two clones. They accomplished this through the use of a technique known as quantum interference, which allows differences in waves to be detected very precisely. This allowed them to determine when the first significant deformation of the matter wave occurred.
Two factors determine the speed limit
The physicists were also able to control the average energy of the atom by varying the height above the bottom of the bowl at the start of the experiment. Average because, in theory, the amount cannot be determined precisely. As a result, the atom’s “position energy” is always uncertain. “We were able to demonstrate that the minimum time for the matter wave to change depends on this energy uncertainty,” explains Professor Yoav Sagi, who led the Technion partner team: “The greater the uncertainty, the shorter the Mandelstam-Tamm time.”
This is precisely what the two Soviet physicists predicted. However, there was a second effect: if the energy uncertainty was increased until it exceeded the atom’s average energy, the minimum time did not decrease further, contrary to what the Mandelstam-Tamm limit would actually suggest. Thus, the physicists demonstrated a second speed limit that had been theoretically discovered about 20 years ago. In the quantum world, the ultimate speed limit is thus determined not only by energy uncertainty, but also by mean energy.
“It is the first time that both quantum speed boundaries for a complex quantum system have been measured, and even in a single experiment,” Alberti exclaims. Future quantum computers may be able to solve problems quickly, but they, too, will be limited by these fundamental constraints.
