Explore advanced tensor network methods and their applications in quantum computing, machine learning, and many-body physics through this comprehensive workshop from the Institute for Pure & Applied Mathematics. Delve into the fundamental challenge of representing quantum mechanical systems with n particles, where states exist in exponentially growing Hilbert spaces H1⊗⋯⊗Hn, making naive computational approaches intractable. Discover how tensor network states address this complexity by restricting to physically reasonable tensor subsets that can be parameterized with manageable numbers of parameters using decorated graph structures. Learn about the entanglement properties that become apparent when approximating states through tensor networks rather than physical coordinate systems, and examine recent developments where classical tensor network computations have shown advantages over quantum computers like Google's quantum processor. Engage with cutting-edge research presentations covering tensor networks for machine learning and quantum simulation, border subrank analysis, Hamiltonian simulation and learning, high-dimensional PDEs with convex optimization, arbitrary tensor network algorithms, negative sign problems, Trotterized entanglement renormalization, tensor geometry and invariants, conservative adaptive rank integrators, optimal control problems, coupled cluster theory with matrix product states, NISQ and quantum error correction benchmarking, topological dualities from matchgate networks, matrix product ground state energy spectra, hybrid variational algorithms, monogamy of symmetric states, small ball probabilities for random tensors, asymptotic tensor rank discreteness, memory-efficient tensor measurements, and defective tensor network varieties. Compare computational advantages between quantum computing and tensor networks while investigating theoretical and practical implications for many-body physics, quantum information theory, and high-dimensional probability applications.

Syllabus

Roman Orus - News on tensor Networks for machine learning and quantum computing simulation
Chia-Yu Chang - Border subrank of tensors - IPAM at UCLA
Di Fang - Numerical Analysis for Hamiltonian Simulation and Hamiltonian Learning - IPAM at UCLA
Yuehaw Khoo - High-dimensional PDEs, tensor-network, and convex optimization - IPAM at UCLA
Feng Pan - Arbitrary Tensor Network Algorithm: Theory, Methods and Applications - IPAM at UCLA
Norbert Schuch - Tensor networks and the negative sign problem - IPAM at UCLA
Thomas Barthel - Quantum sim of condensed matter using Trotterized entanglement renormalization
Joseph Landsberg - Geometry of tensor networks and tensor invariants - IPAM at UCLA
Jingmei Qiu - Conservative Adaptive Rank Integrators for Nonlinear Kinetic Models - IPAM at UCLA
Mathias Oster - Solving High-Dimensional Optimal Control Problems w/ Empirical Tensor Train Approx.
Fabian Faulstich - Tailoring coupled cluster theory with matrix product states - IPAM at UCLA
Benjamin Villalonga - Benchmarking NISQ and QEC experiments with tensor networks - IPAM at UCLA
Carolin Wille - Topological Dualities from Matchgate Tensor Networks - IPAM at UCLA
Steve White - The strange energy spectrum of approximate matrix product ground states - IPAM at UCLA
Elisa Ercolessi - Hybrid Variational Algorithms for Classical and Quantum Complex Systems
Ion Nechita - Monogamy of highly symmetric states - IPAM at UCLA
Grigoris Paouris - Small ball probabilities for random tensors and analysis of tensor decompositions
Jeroen Zuiddam - Discreteness of asymptotic tensor ranks - IPAM at UCLA
Liza Rebrova - Memory-efficient modewise measurements for tensor compression and recovery
Alessandra Bernardi - Defective tensor network varieties - IPAM at UCLA