Fixed-Depth Two-Qubit Circuits and the Monodromy Polytope
Abstract
For a native gate set which includes all single-qubit gates, we apply results from symplectic geometry to analyze the spaces of two-qubit programs accessible within a fixed number of gates. These techniques yield an explicit description of this subspace as a convex polytope, presented by a family of linear inequalities themselves accessible via a finite calculation. We completely describe this family of inequalities in a variety of familiar example cases, and as a consequence we highlight a certain member of the "XY-family" for which this subspace is particularly large, i.e., for which many two-qubit programs admit expression as low-depth circuits.
Cite
@article{arxiv.1904.10541,
title = {Fixed-Depth Two-Qubit Circuits and the Monodromy Polytope},
author = {Eric C. Peterson and Gavin E. Crooks and Robert S. Smith},
journal= {arXiv preprint arXiv:1904.10541},
year = {2021}
}
Comments
Updated after initial publication to fix increasing/decreasing conventions and an incorrect Figure 6