Scaling of contraction costs for multi-scale entanglement renormalization including tensor Trotterization and variational Monte Carlo
| Autor: | Barthel, Thomas, Miao, Qiang |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | The multi-scale entanglement renormalization ansatz (MERA) is a hierarchical class of tensor network states motivated by the real-space renormalization group, and it is used to simulate strongly correlated quantum many-body systems. For prominent MERA structures in one and two spatial dimensions, we determine the optimal scaling of contraction costs as well as corresponding contraction sequences and algorithmic phase diagrams. This is motivated by recent efforts to employ MERA in hybrid quantum-classical algorithms, where the MERA tensors are Trotterized, i.e., chosen as brickwall circuits of two-qubit gates, and observables as well as energy gradients are evaluated by sampling causal-cone states. We investigate whether tensor Trotterization and/or variational Monte Carlo sampling can lead to quantum-inspired classical MERA algorithms that perform better than the traditional alternating least-squares optimization of full MERA. Algorithmic phase diagrams indicate the best MERA method depending on the scaling of the energy accuracy and the number of Trotter steps with the bond dimension. Comment: 10 pages main text, 7 pages appendix, 9 figures, 3 tables |
| Databáze: | arXiv |
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