HEP-TN Seminar: Jonas Haferkamp "Linear growth of quantum circuit complexity" скачать в хорошем качестве

HEP-TN Seminar: Jonas Haferkamp "Linear growth of quantum circuit complexity"

Quantifying quantum states' complexity is a key problem in various subfields of science, from quantum computing to black-hole physics. In this talk, Jonas Haferkamp (Free University of Berlin) shows a proof of a prominent conjecture by Brown and Susskind about how random quantum circuits' complexity increases. Consider constructing a unitary from Haar-random two-qubit quantum gates. Implementing the unitary exactly requires a circuit of some minimal number of gates - the unitary's exact circuit complexity. Jonas proves that this complexity grows linearly in the number of random gates, with unit probability, until saturating after exponentially many random gates. The proof is surprisingly short, given the established difficulty of lower-bounding the exact circuit complexity. Jonas' strategy combines differential topology and elementary algebraic geometry with an inductive construction of Clifford circuits. This seminar is part of an online series on Tensor Networks in High Energy Physics (HEP-TN). For more details, and schedule of upcoming talks, visit: www.heptnseminar.org. This talk was recorded on July 8, 2020 at the Albert Einstein Institute in Potsdam-Golm.