I don't think it will ever be possible to prove that given piece of hardware contains no malware. Still, there is demand for transparency and product that comes with manufacturer's warranty that says "malware not included". People believe this could lead to some good results, such as better hardware and lower probability of bugged computer.

It's theoretically possible, provided you have a small trusted circuit. It's an active research area. The basic idea is to use multiple separate, untrusted chips and have them do multiparty computation, coordinated by the small trusted circuit.

With testing amplification, you can then set an upper bound on the probability that the chip will run a backdoor.