Predicting the topological properties of quantum spin liquids using Rydberg atom lattices

Topological quantum systems are physical systems exhibiting properties that depend on the overall connectivity of their underlying lattice, as opposed to local interactions and their microscopic structure. Predicting the evolution of these systems over time and their long-range quantum correlations is often challenging, as their behavior is not defined by magnetization or other parameters linked to local interactions.

Researchers at École Polytechnique Fédérale de Lausanne (EPFL) recently simulated a type of topological matter known as quantum spin liquid employing a new numerical approach. This approach, outlined in a paper published in Nature Physics, was demonstrated using a widely used experimental protocol that relies on Rydberg atoms (i.e., atoms in which one or more electrons are excited to produce high-energy states).

“Everything started with the study published by Semeghini et al in which they experimentally studied a topological spin liquid,” Linda Mauron, first author of the paper, told Phys.org. “This paper was quite important as it was one of the first to observe such a state outside of theory.

“However, we realized that all the numerical benchmarks, as for many other experiments occurring in Rydberg atom platforms, failed to capture some of the central particularities of the experimental setup and were thus potentially wrongly compared.”

Building on earlier research studies, Mauron and her colleagues set out to simulate a topological spin liquid using a Rydberg atom-based simulator. The approach they employed, like several other numerical simulation techniques employed in the past, relies on the parameterization of the quantum state that one is studying.

“To keep it simple, instead of learning the probabilities of every single state that could possibly exist (which, for a system of N spins, equals 2^N states to learn), we encode the quantum state with a few parameters which instead learn the features of the state,” explained Mauron.

“In our specific case, the key ingredient was to directly encode the correlations within the wave function. This is an advantage compared to many standard methods used for such simulations, which typically struggle once entanglement (quantum correlations) increases.”

Finally, the researchers used a widely used numerical scheme to simulate the evolution of the quantum state they were studying over time. Notably, the scheme they used, known as the time-dependent variational Monte Carlo (t-VMC) scheme, does not require the approximation of a system’s size, the shape of its lattice or its time evolution.

“We demonstrated the capacity of our approach to faithfully simulate an experimental protocol on a Rydberg atom simulator, without making any approximation, while still being able to scale up this scheme to meaningful system sizes,” said Mauron. “As a direct consequence, our study allows us to draw conclusions about the capabilities of the simulated protocol.”

Using their numerical simulation strategy, the researchers were able to predict values that cannot be derived in real-world experiments, such as a quantum system’s topological entanglement entropy. This is an important quantity that can help to discern between a truly topological quantum state and a disordered quantum state that is not topologically ordered.

In the future, their proposed approach could be adapted and used by other research teams to simulate quantum spin liquid states and shed more light on their underlying dynamics.

“We are now focusing on the ability to simulate additional quantum devices and protocols using similar techniques,” added Mauron. “We are also further investigating the characteristics of the state prepared through the herein-described protocol.”

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