Universal resources for approximate and stochastic measurement-based quantum computation

          @misc{ pirsa_PIRSA:08050021,
            doi = {10.48660/08050021},
            url = {https://pirsa.org/08050021},
            author = {},
            keywords = {Quantum Information},
            language = {en},
            title = {Universal resources for approximate and stochastic measurement-based quantum computation },
            publisher = {Perimeter Institute},
            year = {2008},
            month = {may},
            note = {PIRSA:08050021 see, \url{https://pirsa.org}}
          }
          

Abstract

We investigate which families of quantum states can be used as resources for approximate and/or stochastic universal measurement-based quantum computation, in the sense that single-qubit operations and classical communication are sufficient to prepare (with some fixed precision and/or probability) any quantum state from the initial resource. We find entanglement-based criteria for non-universality in the approximate and/or stochastic case. By applying them, we are able to discard some families of states as not universal also in this weaker sense. Finally, we show that any family $Sigma$ of states that is \'close\' to an (approximate and/or stochastic) universal family $Gamma$ is approximate and stochastic universal, and we prove that if $Gamma$ was efficiently universal then also $Sigma$ is.