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Fast Tensor Disentangling Algorithm

by Kevin Slagle

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Kevin Slagle
Submission information
Preprint Link:  (pdf)
Code repository:
Date accepted: 2021-09-06
Date submitted: 2021-06-25 02:40
Submitted by: Slagle, Kevin
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Computational
  • Quantum Physics
Approach: Computational


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.

Author comments upon resubmission

We thank the referees for the very helpful reviews of our work, which has led to useful improvements in our draft.

List of changes

A detailed diff showing changes can be found here:

In addition to the changes suggested by the referees, we improved the extended algorithm in Appendix B.

Published as SciPost Phys. 11, 056 (2021)

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