In this talk, I will cover recent results in two areas: 1) Using quantum-inspired methods in machine learning, including using low-entanglement states (matrix product states/tensor train decompositions) for different regression and classification tasks. 2) Using machine learning methods for efficient classical simulation of quantum systems. I will cover our results on simulating quantum circuits on parallel computers using graph-based algorithms, and also efficient numerical methods for optimization using tensor-trains for the computational of large number (up to B=100) on GPUs. The code is a combination of classical linear algebra algorithms, Riemannian optimization methods and efficient software implementation in TensorFlow.

1. Rakhuba, M., Novikov, A. and Oseledets, I., 2019. Low-rank Riemannian eigensolver for high-dimensional Hamiltonians. Journal of Computational Physics, 396, pp.718-737.
2. Schutski, Roman, Danil Lykov, and Ivan Oseledets. Adaptive algorithm for quantum circuit simulation. Physical Review A 101, no. 4 (2020): 042335.
3. Khakhulin, Taras, Roman Schutski, and Ivan Oseledets. Graph Convolutional Policy for Solving Tree Decomposition via Reinforcement Learning Heuristics. arXiv preprint arXiv:1910.08371 (2019).