SAMOP 2021 – scientific programme

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QI: Fachverband Quanteninformation

QI 2: Quantum Computing and Algorithms I

QI 2.2: Talk

Monday, September 20, 2021, 11:00–11:15, H5

Linear growth of quantum circuit complexity — •Jonas Haferkamp¹, Philippe Faist¹, Naga Kothakonda¹, Jens Eisert¹, and Nicole Yunger Halpern² — ¹Freie Universität Berlin — ²Harvard-Smithsonian, ITAMP

Quantifying quantum states' complexity is a key problem in various subfields of science, from quantum computing to black-hole physics. We prove 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. We prove that this complexity grows linearly in the number of random gates, with unit probability, until saturating after exponentially many random gates. Our 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.