"Isn't this just post-selection bias?" Yes, absolutely. It is intentional statistical conditioning toward lower-energy states. The thesis I am exploring is whether that structural bias survives deep into hardware decoherence when global expectation values fail.
"Does this actually improve VQE convergence?" I haven't run a full 500-step optimizer loop on 133 qubits to prove full convergence, because doing so on IBM's Pay-As-You-Go tier would cost roughly $100,000. This data is from a single-shot, unoptimized ansatz to prove the filter successfully extracts a cooling delta from the infinite-temperature limit.
I'm currently looking at ways to calculate tighter bootstrap confidence intervals on the retained subset to further prove non-random structure. Open to any critiques on the physics or the statistical boundaries here!