Scaling a unitary matrix

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.

A proof of the conjecture is now provided by Idel & Wolf (http://arxiv.org/abs/1408.5728)

Cited by in corpus (5)

• The block-ZXZ synthesis of an arbitrary quantum circuit
• Certainty relations, mutual entanglement and non-displacable manifolds
• The Birkhoff theorem for unitary matrices of arbitrary dimensions
• Product states and Schmidt rank of mutually unbiased bases in dimension six
• Constructive quantum scaling of unitary matrices