Scaling a unitary matrix
Mathematical Physics
2015-02-09 v2 math.MP
Quantum Physics
Abstract
The iterative method of Sinkhorn allows, starting from an arbitrary real matrix with non-negative entries, to find a so-called 'scaled matrix' which is doubly stochastic, i.e. a matrix with all entries in the interval (0, 1) and with all line sums equal to 1. We conjecture that a similar procedure exists, which allows, starting from an arbitrary unitary matrix, to find a scaled matrix which is unitary and has all line sums equal to 1. The existence of such algorithm guarantees a powerful decomposition of an arbitrary quantum circuit.
Cite
@article{arxiv.1401.7883,
title = {Scaling a unitary matrix},
author = {Alexis De Vos and Stijn De Baerdemacker},
journal= {arXiv preprint arXiv:1401.7883},
year = {2015}
}
Comments
A proof of the conjecture is now provided by Idel & Wolf (http://arxiv.org/abs/1408.5728)