Quantum marbles in a bowl of light
An international study shows which factors determine the speed limit for quantum computations

Date:
December 22, 2021
Source:
University of Bonn
Summary:
Which factors determine how fast a quantum computer can perform
its calculations? Physicists have devised an elegant experiment
to answer this question.



FULL STORY ========================================================================== Which factors determine how fast a quantum computer can perform its calculations? Physicists at the University of Bonn and the Technion --
Israel Institute of Technology have devised an elegant experiment to
answer this question. The results of the study are published in the
journal Science Advances.


========================================================================== Quantum computers are highly sophisticated machines that rely on the
principles of quantum mechanics to process information. This should
enable them to handle certain problems in the future that are completely unsolvable for conventional computers. But even for quantum computers, fundamental limits apply to the amount of data they can process in a
given time.

Quantum gates require a minimum time The information stored in
conventional computers can be thought of as a long sequence of zeros and
ones, the bits. In quantum mechanics it is different: The information
is stored in quantum bits (qubits), which resemble a wave rather than a
series of discrete values. Physicists also speak of wave functions when
they want to precisely represent the information contained in qubits.

In a traditional computer, information is linked together by so-called
gates.

Combining several gates allows elementary calculations, such as the
addition of two bits. Information is processed in a very similar way in
quantum computers, where quantum gates change the wave function according
to certain rules.

Quantum gates resemble their traditional relatives in another respect:
"Even in the quantum world, gates do not work infinitely fast," explains
Dr. Andrea Alberti of the Institute of Applied Physics at the University
of Bonn. "They require a minimum amount of time to transform the wave
function and the information this contains." More than 70 years ago,
Soviet physicists Leonid Mandelstam and Igor Tamm deduced theoretically
this minimum time for transforming the wave function.

Physicists at the University of Bonn and the Technion have now
investigated this Mandelstam-Tamm limit for the first time with an
experiment on a complex quantum system. To do this, they used 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 observe
their motion," explains Alberti, who led the experimental study.



========================================================================== Atoms can be described quantum mechanically as matter waves. During
the journey to the bottom of the light bowl, their quantum information
changes. The researchers now wanted to know when this "deformation" could
be identified at the earliest. This time would then be the experimental
proof of the Mandelstam- Tamm limit. The problem with this, however,
is: that in the quantum world, every measurement of the atom's position inevitably changes the matter wave in an unpredictable way. So it always
looks like the marble has deformed, no matter how quickly the measurement
is made. "We therefore devised a different method to detect the deviation
from the initial state," Alberti says.

For this purpose, the researchers began by producing a clone of the
matter wave, in other words 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, a doctoral student at the Technion and first
author of the study.

"Figuratively speaking, the atom behaves as if it had two different
colors at the same time." Depending on the color, each atom twin takes
a different position in the light bowl: One is high up on the edge and
"rolls" down from there. The other, conversely, 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.

The physicists compared the two clones at regular intervals. They did this using a technique called quantum interference, which allows differences in waves to be detected very precisely. This enabled them to determine after
what time a significant deformation of the matter wave first occurred.

Two factors determine the speed limit By varying the height above the
bottom of the bowl at the start of the experiment, the physicists were
also able to control the average energy of the atom. Average because,
in principle, the amount cannot be determined exactly.

The "position energy" of the atom is therefore always uncertain. "We
were able to demonstrate that the minimum time for the matter wave to
change depends on this energy uncertainty," says Professor Yoav Sagi,
who led the partner team at Technion: "The greater the uncertainty,
the shorter the Mandelstam-Tamm time." This is exactly what the two
Soviet physicists had predicted. But there was also a second effect:
If the energy uncertainty was increased more and more until it exceeded
the average energy of the atom, then the minimum time did not decrease
further -- contrary to what the Mandelstam-Tamm limit would actually
suggest. The physicists thus proved a second speed limit, which was theoretically discovered about 20 years ago. The ultimate speed limit
in the quantum world is therefore determined not only by the energy uncertainty, but also by the mean energy.



==========================================================================
"It is the first time that both quantum speed boundaries could be
measured for a complex quantum system, and even in a single experiment," Alberti enthuses.

Future quantum computers may be able to solve problems rapidly, but they
too will be constrained by these fundamental limits.

Funding: The study was funded by the Reinhard Frank Foundation (in collaboration with the German Technion Society), the German Research
Foundation (DFG), the Helen Diller Quantum Center at the Technion,
and the German Academic Exchange Service (DAAD).

========================================================================== Story Source: Materials provided by University_of_Bonn. Note: Content
may be edited for style and length.


========================================================================== Journal Reference:
1. Gal Ness, Manolo R. Lam, Wolfgang Alt, Dieter Meschede, Yoav
Sagi, Andrea
Alberti. Observing crossover between quantum speed limits. Science
Advances, 2021; 7 (52) DOI: 10.1126/sciadv.abj9119 ==========================================================================

Link to news story: https://www.sciencedaily.com/releases/2021/12/211222151153.htm

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