Challenging Quantum Advantage with Quantum Many-Body KAM Theory in Closed and Open Quantum System Paradigms

This project advances quantum information science and technology by quantifying a key mathematical challenge to the promise of quantum computing. Understanding and advancing quantum computing is important because current classical computers are rapidly coming to their limit in energy and efficiency, and quantum computing offers a powerful alternative in certain cases. By understanding this particular challenge, called near-integrability, and so far unsolved in the quantum context, the proposal will develop new workforce talent via student training and result in better design of quantum algorithms and hardware. Quantum computing is important to US national security on many fronts including encryption, optimization, and materials science. The best-known classical algorithms currently challenging quantum computing are tensor network / neural network based. This project will pursue a complementary alternate route to both quantum advantage and classical challenges to quantum computation: near quantum many-body integrability. A key new toolset newly ported from machine learning (ML) into the quantum computing context will be introduced in the process, emergent topological complexity. Both these developments will be highly useful to academic-industry collaborations pursuing scientific and commercial quantum advantage. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.