Quantum physics beyond the low-complexity regime

forthcoming

Quantum complexity measures how many elementary operations are required to prepare a given quantum state or to implement a given quantum operation. A key concept for both quantum computing and for physics, it can identify intricate entanglement structures that elude traditional methods based on locality and entanglement. My research will leverage my new tools in quantum complexity to answer two key questions: (i) What are the fundamental limits to engineering quantum complexity on quantum hardware, and how can they be reached? and (ii) How can we describe the physical behavior of many-body systems qualitatively and quantitatively beyond the low-complexity regime? Both questions relate closely to the structure of quantum states beyond the low-complexity regime and draw on my expertise in quantum error correction, quantum thermodynamics, and quantum complexity, in order to enable new approaches to study entangled phases of quantum matter. I will build a unified picture of the fundamental minimal overheads in number of qubits and computation complexity required to process information that is encoded in a quantum error-correcting code; I will identify regimes allowing for schemes with reduced overheads. I will then establish a stronger tie between quantum complexity and quantum chaos, targeting a full robust proof that the quantum complexity measures the evolution time of generic quantum chaotic systems even up to very long times. I will finally add the dimension of quantum complexity to the fundamental laws of physics by identifying at which complexity scales quantum processes are allowed to happen. My analysis will be enabled by my recently developed tools in quantum complexity. Overall, my research will push forward the frontiers of quantum information science by developing the crucial supporting theory for near-term applications of quantum computers, as well as by transforming our understanding of many-body phenomena in physics beyond low complexity scales.