Sinkhorn-based synthesis of an arbitrary quantum circuit
Alexis De Vos, Stijn De Baerdemacker · arXiv (Cornell University) · 2015
Given an arbitrary $2^\omega \times 2^w$ unitary matrix, a powerful matrix decomposition can be applied, leading to the synthesis of a w-qubit quantum circuit performing the unitary transformation. The demonstration is based on a recent theorem by F\uhr and Rzeszotnik, generalizing the scaling of single-bit unitary gates $(\omega=1)$ to gates with arbitrary value of $\omega$. The synthesized circuit consists of controlled 1-qubit gates, such as NEGATOR gates and PHASOR gates. We propose a numerical approach to compute the design using a generalization of the Sinkhorn algorithm to scale unitary matrices.