Ladies and Gentlemen. Due to the coronavirus epidemic in Poland, the CTP PAS is operating in a limited way. In particular, until further notice the CTP PAS administration will be opened only in Tuesday and Thursday. On other days contact with the administration will be possible only by an e-mail. We are sorry for any inconvenience.

## Seminar details

 Name Quantum Information and Quantum Computing working group Title Efficient unitary t-designs with few non-Clifford gates Details THIS IS REMOTE MEETING (DETAILS BELOW)Many quantum information protocols require the implementation of random unitaries. Because it takes exponential resources to produce Haar-random unitaries drawn from the full n-qubit group, one often resorts to t-designs. Unitary t-designs mimic the Haar-measure up to t-th moments. It is known that Clifford operations can implement at most 3-designs. In this work, we quantify the non-Clifford resources required to break this barrier. We find that it suffices to inject $O(t^4log^2(t)log(1/ε))$ many non-Clifford gates into a polynomial-depth random Clifford circuit to obtain an ε-approximate t-design. Strikingly, the number of non-Clifford gates required is independent of the system size asymptotically, the density of non-Clifford gates is allowed to tend to zero. We also derive novel bounds on the convergence time of random Clifford circuits to the t-th moment of the uniform distribution on the Clifford group. Our proofs exploit a recently developed variant of Schur-Weyl duality for the Clifford group, as well as bounds on restricted spectral gaps of averaging operators.The talk will be based on the paper: arxiv:2002.09524ZOOM INFORMATIONTopic: Quantum Information and Quantum Computing Working GroupTime: Apr 1, 2020, 10:30 AM WarsawJoin Zoom Meeting link:QIQCWG-ZOOMMeeting ID: 640 279 690Password: tp4C,;kERxIf you encounter any problems with connecting to the Zoom meeting, please email filip.b.maciejewski@gmail.com directly. Time Wednesday, 1 April 2020, at 10:30 CEST The seminar was held! Speaker Mgr Jonas Haferkamp  (Freie Universitat Berlin) Seminar Language English Organisers Michał Oszmaniec; Filip Maciejewski;