Seminarium Wydziału Matematyki, Fizyki i Informatyki UG 04.03.2022 | FTiMS - Politechnika Gdańska

4 marca (piątek) o godz. 12.15 w formie online poprzez aplikację Zoom (link znajduje się na końcu wiadomości) 
dr Sergii Strelchuk- Department of Applied Mathematics and Theoretical Physics, University of Cambridge
wygłosi wykład p.t."Speeding up Learning Quantum States with the help of Group Equivariant Convolutional Quantum Ansätze”
 

We demonstrate how to effectively apply the celebrated Okounkov-Vershik's representation theory in machine learning and quantum physics :  (1) we show how to gain a super-exponential speedup in computing the matrix elements of Sn-Fourier coefficients compared to the best known classical Fast Fourier Transform (FFT) over the symmetric group. (2) we prove that Sn Convolutional Quantum Ansätze are dense, thus expressible within each Sn-irrep block, which may serve as a universal model for potential future quantum machine learning and optimization applications. (3) we get a new proof (which is of distinctly representation-theoretic flavour) of the universality of the Quantum Approximate Optimization Algorithm. (4) our framework can be naturally applied to a wide array of problems with global SU(d) (for any integer d) symmetry. (5) We show that our ansätze are highly effective numerically by providing numerical solutions to the problem of the sign structure of the ground state of the J1-J2 antiferromagnetic Heisenberg model on the rectangular and Kagome lattices.