Many of the phenomena we observe on Earth can be traced back to a few fundamental physical laws, as described by the Maxwell and Schrödinger equations. The vast diversity of our world stems from the complexity that arises when numerous particles interact. As we move from atoms to molecules and then to liquids or solids, predicting their behavior becomes increasingly challenging. In the past four decades, scientists have discovered a growing variety of materials, such as high-temperature superconductors, with unconventional properties that defy traditional explanations. These exotic phenomena are often attributed to strong electron-electron interactions, necessitating novel approaches to their study. For this reason, researchers have developed and applied various numerical methods, including quantum Monte Carlo and tensor networks, to approximate solutions to these complex problems. Each method has its advantages and limitations, making it difficult to determine the optimal approach for a given problem.

A large collaboration of scientists, led by Giuseppe Carleo (Ecole Polytechnique Federale di Lausanne) and also involving Federico Becca (University of Trieste), has introduced a new benchmark called the "V-score". This metric provides a consistent way to compare the performance of different quantum methods on the same problem. Additionally, the V-score can identify the most challenging quantum systems, where current computational methods struggle and where future methods (e.g., quantum computing) might offer a potential advantage. The V-score is a valuable tool for measuring progress in solving quantum problems and can help guide future research efforts by highlighting the most difficult challenges.

The collaboration involved 33 scientists from 29 institutions, including Sandro Sorella, who sadly passed away before the publication of this work. Six of the researchers involved have grown under his influence, during their Ph.D. studies at the International School for Advanced Studies, Trieste.

D. Wu et. al, Science 386, 296 (2024)

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