B6 Complexity in Many-Body Quantum Systems
While correlations, entanglement and entropy measures have become well established and widely studied tools in many-body quantum physics, the role of complexity is considerably less explored. The goal of the proposed project is to develop and study suitable complexity measures for quantum evolutions, quantum states and families thereof.
The project will focus on circuit complexity and its relation to other complexity notions including computational, descriptive, sampling and learning complexity. Our goal is to provide a conceptual foundation, a systematic investigation and novel mathematical tools for quantifying the intrinsic complexity of quantum states and evolutions. Notable consequences concern bounds on the descriptive power of ansatz states for variational physics, complexity-theoretic bounds on classical as well as quantum simulability of quantum processes, and estimates on the accuracy of tomographic methods and learning protocols.