Self-guaranteed measurement-based quantum computation
  In order to guarantee the output of a quantum computation, we usually assume that the component devices are trusted. However, when the total computation process is large, it is not easy to guarantee the whole system when we have scaling effects, unexpected noise, or unaccounted correlations between several subsystems. If we do not trust the measurement basis nor the prepared entangled state, we do need to be worried about such uncertainties. To this end, we proposes a "self-guaranteed" protocol for verification of quantum computation under the scheme of measurement-based quantum computation where no prior-trusted devices (measurement basis nor entangled state) are needed. The approach we present enables the implementation of verifiable quantum computation using the measurement-based model in the context of a particular instance of delegated quantum computation where the server prepares the initial computational resource and sends it to the client who drives the computation by single-qubit measurements. Applying self-testing procedures we are able to verify the initial resource as well as the operation of the quantum devices, and hence the computation itself. The overhead of our protocol scales as the size of the initial resource state to the power of 4 times the natural logarithm of the initial state's size. 
Masahito Hayashi and Michal Hajdusek
quant-ph