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Measurement-based quantum computation cannot avoid byproducts

Measurement-based quantum computation is a novel model of quantum computing where universal quantum computation can be done with only local measurements on each particle of a quantum many-body state, which is called a resource state. One large difference of the measurement-based model from the circuit model is the existence of byproducts. In the circuit model, a desired unitary U can be implemented deterministically, whereas the measurement-based model implements BU, where B is an additional operator, which is called a byproduct. In order to compensate byproducts, following measurement angles must be adjusted. Such a feed-forwarding requires some classical processing and tuning of the measurement device, which cause the delay of computation and the additional decoherence. Is there any byproduct-free resource state? Here we show that if we respect the no-signaling principle, which is one of the most fundamental principles of physics, no universal resource state can avoid byproducts.