Thema der Dissertation:
Randomness and complexity in random complex quantum systems
Randomness and complexity in random complex quantum systems
Abstract: The interaction of complexity theory and quantum physics touches a wide range of topics from emerging technologies such as quantum computers to the physics of black holes. Tools from quantum information theory can help to answer questions in theoretical computer science and, conversely, the ideas developed for analysing the power of computers can shed light on physical phenomena. New methods in the theory of random matrices with locality restrictions lead to several advances in the complexity theory of local quantum physics. This includes new results on the average-case complexity of tensor network contraction, contributions to the foundation of verifiable quantum supremacy experiments as well as novel bounds on the generation of quantum pseudorandomness. In particular, we show that unitary t-designs can be generated with a system-size independent number of non-Clifford resources and that random quantum circuits generate unitary t-designs in depth O(n t^{5+o(1)}). These bounds have numerous applications including the best known bounds on the growth of operational notions of quantum circuit complexity. Moreover, we provide a proof of the Brown-Susskind conjecture for the linear growth of exact circuit complexity in random quantum circuits. Random quantum circuits provide – among other applications – a rigorous toy model for the disordered quantum dynamics in black holes. In this context, quantum circuit complexity was conjectured to be the holographic dual of volume. Therefore, the lower bounds proven in this thesis provide rigorous evidence for quantum models of black hole dynamics.
Zeit & Ort
20.03.2023 | 16:30
Hörsaal A (1.3.14)
Fachbereich Physik, Arnimallee 14, 14195 Berlin