MPS energy landscapes lack poor local minima because gauge freedom induces overparametrization that concentrates local minima near the global minimum, with the local minimum distribution proven invariant under orthogonality center moves.
Or \' u s ,\ title Tensor networks for complex quantum systems ,\ 10.1038/s42254-019-0086-7 journal journal Nature Reviews Physics \ volume 1 ,\ pages 538 ( year 2019 ) NoStop
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A commutativity-based dynamic ansatz within DMET enables ground-state simulations of molecules up to 144 qubits using at most 20 qubits at a time with improved accuracy and lower gate counts than standard approaches.
Fault-tolerant Iceberg code on trapped-ion hardware achieves beyond-break-even error detection for Toffoli and Bell circuits by filtering errors, yielding higher fidelity than unencoded versions.
A tensor-network solver extended with jump-counting computes electron currents in up to 50 quantum dots, matching traditional solvers for small systems but with orders of magnitude less memory and time.
A 50-qubit quantum processor produces dynamical structure factors for KCuF3 that quantitatively match neutron-scattering measurements of its spinon spectrum.
Spectral bounds relate graph Laplacian eigenvalues to the congestion of binary-tree embeddings, with an efficient spectral-ordering algorithm and applications to tensor-network contraction complexity.
Reshetikhin-Turaev knot polynomials are fixed-parameter tractable in the treewidth of the input diagram via tensor network contraction, yielding e^{O(sqrt n)} time.
Tensor networks developed for quantum states are reviewed as tools for machine learning models, with assessment of their potential computational, explanatory, and privacy advantages alongside remaining challenges.
Introductory lecture notes on tensor networks with emphasis on matrix-product states, their algorithms, higher-dimensional generalizations, and applications to mixed states and open quantum systems, accompanied by Julia code.
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