Abstract
We show that the set of observables \(\{Z\otimes X, (\cos\theta) X + (\sin\theta) Y \ {\rm all} \ \theta \in [0,2\pi)\}\) with one ancillary qubit is universal for quantum computation. The set is simpler than a previous one in the sense that one-qubit projective measurements described by the observables in the set are ones only in the (X,Y) plane of the Bloch sphere. The proof of the universality implies a simple set of observables that is approximately universal for quantum computation. Moreover, it implies a simple set of observables for efficient graph state preparation.
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Takahashi, Y. (2011). Simple Sets of Measurements for Universal Quantum Computation and Graph State Preparation. In: van Dam, W., Kendon, V.M., Severini, S. (eds) Theory of Quantum Computation, Communication, and Cryptography. TQC 2010. Lecture Notes in Computer Science, vol 6519. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18073-6_3
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DOI: https://doi.org/10.1007/978-3-642-18073-6_3
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