Complexity classification of general quantum compilation

Determine the complexity class of general quantum compilation, including whether the problem is NP-complete.

Background

The paper situates its Poly-Z min-depth circuit synthesis problem within the broader quantum-compilation literature. Although several restricted compilation and routing problems have known complexity results, the authors state that the complexity of quantum compilation in general has not been established. This unresolved issue provides motivation for studying complexity results for specialized compilation problems.

References

In general, the -completeness of quantum compilation is an open problem.

— Circuit Design Problems in Binary Polynomial Quantum Optimization  (2610.13283 - Mermoud et al., 9 Oct 2026) in Section 1, subsection “Related work”