Thema der Dissertation:
Unitary designs, complexity, and information dynamics in random and noisy quantum systems
Unitary designs, complexity, and information dynamics in random and noisy quantum systems
Abstract: Quantum many-body dynamics lies at the intersection of physics and information theory. It raises questions about how quantum systems generate randomness, how complex quantum states become under time evolution, and how much quantum information can be transmitted through noisy dynamics. In this talk, I will present the main results of my PhD thesis on these information-theoretic aspects of quantum many-body dynamics.
First, I will discuss randomness generation in random quantum circuits from the perspective of unitary designs. I show that structured random gates can lead to faster randomness generation than unstructured Haar-random gates, and obtain exact results for the second-moment spectrum via a mapping to free fermions. Second, I will discuss monitored random circuits, where unitary gates and measurements compete. I prove that the circuit complexity of quantum states exhibits a measurement-induced phase transition. It quickly saturates above a critical measurement rate, while below the threshold it grows at least linearly for exponentially long times. Finally, I will discuss communication tasks for noisy multi-time quantum processes using quantum combs. I introduce notions of simulation and capacity of quantum combs, derive SDP lower bounds on the simulation error under constraints such as PPT preservation, and apply them to concrete examples such as depolarizing dynamics.
First, I will discuss randomness generation in random quantum circuits from the perspective of unitary designs. I show that structured random gates can lead to faster randomness generation than unstructured Haar-random gates, and obtain exact results for the second-moment spectrum via a mapping to free fermions. Second, I will discuss monitored random circuits, where unitary gates and measurements compete. I prove that the circuit complexity of quantum states exhibits a measurement-induced phase transition. It quickly saturates above a critical measurement rate, while below the threshold it grows at least linearly for exponentially long times. Finally, I will discuss communication tasks for noisy multi-time quantum processes using quantum combs. I introduce notions of simulation and capacity of quantum combs, derive SDP lower bounds on the simulation error under constraints such as PPT preservation, and apply them to concrete examples such as depolarizing dynamics.
Zeit & Ort
02.07.2026 | 16:30
FB-Raum (1.1.16)
(Fachbereich Physik, Arnimallee 14, 14195 Berlin)