Fixed-Depth Two-Qubit Circuits and the Monodromy Polytope
Rigetti Quantum Computing, 2919 Seventh St, Berkeley, CA 94710
Published: | 2020-03-26, volume 4, page 247 |
Eprint: | arXiv:1904.10541v3 |
Doi: | https://doi.org/10.22331/q-2020-03-26-247 |
Citation: | Quantum 4, 247 (2020). |
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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 ``$\mathrm{XY}$--family'' for which this subspace is particularly large, i.e., for which many two-qubit programs admit expression as low-depth circuits.

Featured image: Two-qubit programs which admit circuits using 3 (red), 4 (yellow), and 5 (blue) applications of √CZ.
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