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Researchers at ICFO have significantly reduced computational costs for Navascués-Pironio-Acín (NPA) hierarchy optimization by reframing moment selection as a combinatorial problem solvable via Restricted Boltzmann Machines. This approach achieves nearly two orders of magnitude improvement over brute force methods, demonstrating that machine learning can effectively navigate complex synergistic interactions in quantum noncommutative polynomial problems. The work establishes a scalable framework for bounding solutions to ubiquitous quantum physics challenges with substantially lower overhead.
Certifying RBMs Cut NPA Hierarchy Optimization Costs by 100×

The Navascués–Pironio–Acín (NPA) hierarchy provides a convergent sequence of semidefinite programming (SDP) relaxations for bounding the solution to noncommutative polynomial optimisation problems, ubiquitous in quantum physics. A relevant problem is understanding how to select moments to get tighter bounds for a fixed computational effort, given the computational overhead when increasing the hierarchy level.
Researchers at ICFO, The Barcelona Institute of Science and Technology and collaborating institutions have outperformed a key technique used in quantum physics by reframing a complex problem as one of efficient selection. The team tackled the Navascués-Pironio-Acín (NPA) hierarchy, a method for bounding solutions to problems in quantum physics, which suffers from computational overhead as its complexity increases. By reframing the problem of choosing moments within the NPA hierarchy as one of combinatorial subset selection, they developed optimization methods, including one leveraging a…
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