Fast Tensor Disentangling Algorithm
arXiv:2104.08283 · doi:10.21468/SciPostPhys.11.3.056
Abstract
Many recent tensor network algorithms apply unitary operators to parts of a tensor network in order to reduce entanglement. However, many of the previously used iterative algorithms to minimize entanglement can be slow. We introduce an approximate, fast, and simple algorithm to optimize disentangling unitary tensors. Our algorithm is asymptotically faster than previous iterative algorithms and often results in a residual entanglement entropy that is within 10 to 40% of the minimum. For certain input tensors, our algorithm returns an optimal solution. When disentangling order-4 tensors with equal bond dimensions, our algorithm achieves an entanglement spectrum where nearly half of the singular values are zero. We further validate our algorithm by showing that it can efficiently disentangle random 1D states of qubits.
arXiv comment8+4 pages, 3 figures; v3 improves the extended algorithm in Appendix B
References in corpus (25)
- A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
- A class of quantum many-body states that can be efficiently simulated
- Synthesis of Quantum Logic Circuits
- Tensor networks for complex quantum systems
- Optimal Quantum Circuits for General Two-Qubit Gates
- Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)
- Hand-waving and Interpretive Dance: An Introductory Course on Tensor Networks
- Tensor Network Renormalization
- Algorithms for entanglement renormalization
- A universal quantum circuit for two-qubit transformations with three CNOT gates
- Lecture Notes of Tensor Network Contractions
- Encoding of Matrix Product States into Quantum Circuits of One- and Two-Qubit Gates
- Isometric Tensor Network States in Two Dimensions
- Tensor network renormalization yields the multi-scale entanglement renormalization ansatz
- Algorithms for tensor network renormalization
- Efficient variational diagonalization of fully many-body localized Hamiltonians
- A class of highly entangled many-body states that can be efficiently simulated
- Riemannian optimization of isometric tensor networks
- Efficient representation of fully many-body localized systems using tensor networks
- Finding purifications with minimal entanglement
- GHZ extraction yield for multipartite stabilizer states
- Conversion of projected entangled pair states into a canonical form
- Tripartite Entanglement in Qudit Stabilizer States and Application in Quantum Error Correction
- Optimization schemes for unitary tensor-network circuit
- MERACLE: Constructive layer-wise conversion of a Tensor Train into a MERA