Persistent Khovanov homology and quantum complexity

Investigate whether the quantum computational complexity results known for persistence in clique homology (e.g., BQP_1-hardness with BQP containment) extend to persistent Khovanov homology, and characterize the precise complexity of determining persistence in this setting.

Background

Persistent Khovanov homology has recently been introduced. For clique homology, related persistence problems are tightly linked to quantum computation and admit exponential quantum speedups (BQP_1-hard and in BQP). Determining whether analogous results hold for persistent Khovanov homology would connect categorified knot invariants to quantum complexity in the persistence regime.