Tensor Network Algorithms for Quantum Simulation //

We review recent advances in the development of efficient tree tensor network algorithms and their applications to quantum simulation, benchmarking, and theoretical interpretation. In particular, we present results on two- and three-dimensional systems, both in and out of equilibrium, including scattering processes and induced false vacuum decay in the two-dimensional quantum Ising model. We further highlight the use of tree tensor network methods beyond traditional quantum simulation, such as addressing hard classical combinatorial problems through mappings to many-body quantum Hamiltonians, optimizing quantum compilation tasks, and enabling quantum equational reasoning. Refs: Scattering and induced false vacuum decay in the two-dimensional quantum Ising model Luka Pavešić, Marco Di Liberto, Simone Montangero, arXiv:2509.02702 Quantum algorithms for equational reasoning Davide Rattacaso, Daniel Jaschke, Marco Ballarin, Ilaria Siloi, Simone Montangero, arXiv:2508.21122   Simone Montangero is Full Professor at University of Padua where he directs the Quantum Computing and Simulation Center. He is Honorary Professor at Ulm University and co-leads the Quantum Computing Spoke of the Italian National Center for HPC, Big-Data and Quantum Computer. He has been a Heisenberg Fellow of the German Science Foundation, a Humboldt Fellow and a IQOQI visiting fellow of the Institute for Quantum Optics and Quantum Information of the Austrian Academy of Science. He has been a member of the Science and Engineering Board of the Quantum Flagship. He authored more than 150 scientific publications pioneering the development and application of quantum optimal control and of tensor network methods for quantum technologies and lattice gauge theories in one and more dimensions.