Fast Tensor Disentangling Algorithm

TL;DR

This paper presents a new fast and simple algorithm for optimizing disentangling unitary tensors in tensor networks, significantly reducing computation time while maintaining low residual entanglement.

Contribution

The authors introduce an approximate, asymptotically faster algorithm for tensor disentangling that often approaches optimal solutions and outperforms previous iterative methods.

Findings

Algorithm is asymptotically faster than previous methods.

Residual entanglement entropy is within 10-40% of the minimum.

Effectively disentangles random 1D qubit states.

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.