When quan­tum par­ti­cles fly like bees: Quantum simulator provides insights into the dynamics of complex quantum systems

At first glance, a system consisting of 51 ions may seem manageable. But even if these charged atoms only change back and forth between two states, the result is more than two quadrillion (1015) various orders that the system can take on.

The behavior of such a system is almost impossible to calculate with conventional computers, especially since an excitation introduced into the system can propagate irregularly. The excitation follows a statistical pattern called a Lévy Flight.

A characteristic of such movements is that in addition to the smaller jumps that are to be expected, there are also significantly larger jumps. This phenomenon can also be observed in bees’ flights and in unusually hard movements in the stock market.

Simulation of quantum dynamics: Traditionally a difficult task

While simulating the dynamics of a complex quantum system is a very big task for even traditional supercomputers, the task is a child’s play for quantum simulators. But how can the results of a quantum simulator be verified without the ability to perform the same calculations as it can?

Observation of quantum systems indicated that it might be possible to represent at least the long-term behavior of such systems with equations such as those developed by the Bernoulli brothers in the 18th century to describe the behavior of liquids.

To test this hypothesis, the authors used a quantum system that simulates the dynamics of quantum magnets. They could use it to prove that the system, after an initial phase dominated by quantum mechanical effects, could actually be described with equations of the type known from fluid dynamics.

Furthermore, they showed that the same Lévy Flight statistics that describe the search strategies used by bees also apply to fluid dynamic processes in quantum systems.

Captured ions as a platform for controlled quantum simulations

The quantum simulator was built at the Institute for Quantum Optics and Quantum Information (IQOQI) at the Austrian Academy of Sciences at the University of Innsbruck Campus. “Our system effectively simulates a quantum magnet by representing the north and south poles of a molecular magnet using two energy levels of the ions,” said IQOQI Innsbruck researcher Manoj Joshi.

“Our biggest technological advancement was the fact that we were able to individually address each of the 51 ions individually,” states Manoj Joshi. “As a result, we were able to examine the dynamics of any number of initial states, which was necessary to illustrate the origin of the fluid dynamics.”

“While the number of qubits and the stability of quantum states are currently very limited, there are issues for which we can already use the enormous computing power of quantum simulators today,” said Michael Knap, professor of collective quantum dynamics at the Technical University of Munich.

“In the near future, quantum simulators and quantum computers will be ideal platforms for researching the dynamics of complex quantum systems,” explains Michael Knap. “Now we know that after a certain time, these systems follow the laws of classical fluid dynamics. Any strong deviations from it are an indication that the simulator is not working properly.”

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Material provided by University of Innsbruck. Note! The content can be edited for style and length.

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