I've read contradictory information: on the Wikipedia page for BQP, it is written without proof that "APPROX-QCIRCUIT-PROB is a BQP-complete problem", while I have read elsewhere (don't remember) that "it is usually assumed that are no BQP-complete problems". There is a chapter in the 'Handbook of Natural Computing' entitled "BQP-complete problems" but it contains no BQP-complete problems, only PromiseBQP-complete problems.
So is APPROX-QCIRCUIT-PROB a BQP-complete problem? If not, shouldn't the page be corrected? is it a PromiseBQP-complete problem?
There is a similar question about Hamiltonian simulation where there are answers stating that it is BQP-complete and others that it is not, but only PromiseBQP-complete, so the clarification probably would be useful there too. What is promised exactly?