BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jonas Haferkamp (FU Berlin) DTSTART:20210708T130000Z DTEND:20210708T140000Z DTSTAMP:20260423T011111Z UID:hep-tn/2 DESCRIPTION:Title: L inear growth of quantum circuit complexity\nby Jonas Haferkamp (FU Ber lin) as part of Tensor Networks in High-Energy Physics\n\n\nAbstract\nTitl e: Linear growth of quantum circuit complexity\n\nAbstract: Quantifying qu antum states' complexity is a key problem in various subfields of science\ , from quantum computing to black-hole physics. We prove a prominent conje cture by Brown and Susskind about how random quantum circuits' complexity increases. Consider constructing a unitary from Haar-random two-qubit quan tum gates. Implementing the unitary exactly requires a circuit of some min imal number of gates - the unitary's exact circuit complexity. We prove th at this complexity grows linearly in the number of random gates\, with uni t probability\, until saturating after exponentially many random gates. Ou r proof is surprisingly short\, given the established difficulty of lower- bounding the exact circuit complexity. Our strategy combines differential topology and elementary algebraic geometry with an inductive construction of Clifford circuits.\n\nZoom link: https://mpi-aei.zoom.us/j/93184951966\ n LOCATION:https://researchseminars.org/talk/hep-tn/2/ END:VEVENT END:VCALENDAR