CAREER: Pseudorandomness and Quantum Many-Body Physics

This CAREER award supports research and education activities aiming to advance the frontier of quantum information science and quantum physics through the concept of pseudorandomness, which is the ability of simple, deterministic systems to display behavior that appears complex and random. Originally developed in the field of cryptography to securely hide and protect information, pseudorandomness has become increasingly important in physics as well. It provides a new lens on long-standing fundamental questions, such as how complexity and thermodynamic irreversibility arise from simple, reversible interactions between quantum particles; at the same time, it addresses practical issues at the forefront of quantum technology applications, including how to learn from quantum experiments most efficiently. By advancing our understanding of quantum pseudorandomness in different physical settings, the research component of this project seeks to develop new theoretical tools and practical protocols for learning complex features of quantum dynamics on present and future quantum computers and simulators. The education component of the project focuses on developing freely available resources on quantum physics and quantum computation, including a series of video lectures and interactive computational tutorials, aimed at a broad non-expert audience. Through an accessible, hands-on approach, these materials will support the training of the next generation of quantum scientists and engineers. This project will advance the study of pseudorandomness in quantum many-body physics along three interrelated directions. First, it will develop new diagnostics of equilibration and chaos in Hamiltonian or driven dynamics based on projected ensembles of logical unitary operations in quantum error-correcting codes. These diagnostics will be applied as possible probes of localization transitions and of "completely ergodic" dynamics that densely explores the Hilbert space. Second, the project will characterize the computational hardness of learning measurement-induced phenomena, such as entanglement phase transitions, under distinct and physically motivated experimental access models. This thrust will use a combination of constructive approaches based on randomized measurement protocols and no-go theorems based on pseudorandom unitaries, aiming to sharpen the definition of learnability in these systems. Third, the project will seek to extend the cryptographic notion of pseudorandomness to many-body eigenstates and tie it to the Eigenstate Thermalization Hypothesis, a foundational statement of quantum statistical mechanics. Together, these efforts aim to deepen our understanding of complex behavior in quantum systems and to establish the limits of what is efficiently learnable from experiments on programmable quantum matter. 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. NSF Award ID: 2542880 | Program: 01003031DB NSF RESEARCH & RELATED ACTIVIT,01002627DB NSF RESEARCH & RELATED ACTIVIT,01002930DB NSF RESEARCH & RELATED ACTIVIT | Principal Investigator: Matteo Ippoliti | Institution: University of Texas at Austin, AUSTIN, TX | Award Amount: $310,466 View on NSF Award Search: https://www.nsf.gov/awardsearch/show-award/?AWD_ID=2542880 View on Research.gov: https://www.research.gov/awardapi-service/v1/awards/2542880.html