Potential for improved circuit designs using alternative universal gate sets

Investigate whether circuit designs for generalized extreme channels can be improved—either in gate count, accuracy, or practical implementability—by employing alternative universal gate sets such as Householder reflections, rather than Givens rotations and their controlled versions.

Background

The paper’s circuit constructions primarily use Givens rotations and controlled Givens rotations. The authors note that other universal gate sets, such as Householder reflections, exist and may lead to better designs.

This open question invites exploration of alternative gate sets to reduce circuit cost or improve fidelity, potentially impacting both theoretical optimization and practical implementations.

References

Our circuit construction employs Givens rotation and its controlled version, while other universal set of gates also exist, such as Householder reflections. It remains to investigate whether better circuit design can be achieved using other set of gates and other methods.

— Convex decomposition of dimension-altering quantum channels  (1510.01040 - Wang, 2015) in Section 6 (Discussion and conclusion)