Fast Tensor Disentangling Algorithm

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.

8+4 pages, 3 figures; v3 improves the extended algorithm in Appendix B

References in corpus (6)

• A class of quantum many-body states that can be efficiently simulated
• Synthesis of Quantum Logic Circuits
• Encoding of Matrix Product States into Quantum Circuits of One- and Two-Qubit Gates
• Riemannian optimization of isometric tensor networks
• Optimization schemes for unitary tensor-network circuit
• MERACLE: Constructive layer-wise conversion of a Tensor Train into a MERA

Cited by in corpus (1)

• Locally Purified Maximally Mixed States At Scale: Entanglement Pruning and Symmetries