Exact mapping of generalized extreme channels to the cosine–sine decomposition-based circuit ansatz

Determine a rigorous, exact procedure to decompose any generalized extreme channel into the cosine–sine decomposition-based ansatz circuits introduced in this work, providing a constructive mapping from channel parameters to circuit parameters without reliance on numerical optimization.

Background

The authors present several circuit ansatz constructions for generalized extreme channels based on cosine–sine decomposition (CSD), using them within numerical optimization to approximate arbitrary channels. However, they explicitly note the absence of an exact decomposition procedure that maps a channel to their circuit ansatz without approximation.

Establishing such an exact mapping would strengthen the theoretical foundations of their approach and potentially lead to deterministic implementations of channel decompositions.

References

Our quantum circuits used in this work are constructed {\em a priori} based on cosine-sine decomposition, hence {\em Ansatz}, which means it is not known how to exactly decompose a generalized extreme channel into our quantum circuit.

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