Machine Learning Versus Semidefinite Programming Approach to a Particular Problem of the Theory of Open Quantum Systems

[1]  Li Fei-Fei,et al.  ImageNet: A large-scale hierarchical image database , 2009, CVPR.

[2]  E. Hairer,et al.  Geometric Numerical Integration: Structure Preserving Algorithms for Ordinary Differential Equations , 2004 .

[3]  E. Sudarshan,et al.  Completely Positive Dynamical Semigroups of N Level Systems , 1976 .

[4]  Leonid Khachiyan,et al.  Computing integral points in convex semi-algebraic sets , 1997, Proceedings 38th Annual Symposium on Foundations of Computer Science.

[5]  Michael M. Wolf,et al.  The Complexity of Relating Quantum Channels to Master Equations , 2009, 0908.2128.

[6]  Jian Sun,et al.  Deep Residual Learning for Image Recognition , 2015, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[7]  Elsi-Mari Laine,et al.  Colloquium: Non-Markovian dynamics in open quantum systems , 2015, 1505.01385.

[8]  G. Lindblad On the generators of quantum dynamical semigroups , 1976 .

[9]  Natalia Gimelshein,et al.  PyTorch: An Imperative Style, High-Performance Deep Learning Library , 2019, NeurIPS.

[10]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[11]  Naftali Tishby,et al.  Machine learning and the physical sciences , 2019, Reviews of Modern Physics.

[12]  A. Kolmogoroff Zur Theorie der Markoffschen Ketten , 1936 .

[13]  S. Blanes,et al.  The Magnus expansion and some of its applications , 2008, 0810.5488.

[14]  Isaac L. Chuang,et al.  Quantum Computation and Quantum Information: Frontmatter , 2010 .

[15]  M. Garey Johnson: computers and intractability: a guide to the theory of np- completeness (freeman , 1979 .

[16]  Peter Hänggi,et al.  Calculating Floquet states of large quantum systems: A parallelization strategy and its cluster implementation , 2015, Comput. Phys. Commun..

[17]  Konstantin Stefanov,et al.  Supercomputer Lomonosov-2: Large Scale, Deep Monitoring and Fine Analytics for the User Community , 2019, Supercomput. Front. Innov..

[18]  E. Hairer,et al.  Geometric Numerical Integration , 2022, Oberwolfach Reports.

[19]  J Eisert,et al.  Assessing non-Markovian quantum dynamics. , 2007, Physical review letters.

[20]  David J. Schwab,et al.  A high-bias, low-variance introduction to Machine Learning for physicists , 2018, Physics reports.

[21]  Gaël Varoquaux,et al.  Scikit-learn: Machine Learning in Python , 2011, J. Mach. Learn. Res..