  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.
