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Page 10 of 13
Minimal resources for Measurement-based Quantum Computing.
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Simon Perdrix
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Projective measurements are universal for Quantum Computation. Since projective measurements are destructive, some ancillary qubits are required to simulate a reversible transformation like a unitary transformation. How many projective measurements and how many ancillas are required to simulate any unitary transformation? Successive improvements have been done to minimize the resources of Measurement-based QC [1,2,3]. We improve the existing results by proving that a set composed of 3 projective measurements, including 1 two-qubit measurement and 2 one-qubit measurements, requires only one ancilla to be universal. Moreover we exhibit non trivial lower bounds for this kind of universal resources.
References
[1] M. A. Nielsen. Universal quantum computation using only projective measurement, quantum memory, and preparation of the 0 state, arXiv.org reportquant-ph/0108020, 2001.
[2] D. W. Leung. Two-qubit projective measurements are universal for quantum computation, arXiv.org report quant-ph/0111077, 2001.
[3] S. Perdrix. State Transfer instead of Teleportation in Measurement-based QuantumComputation , arXiv.org report quant-ph/0402204, 2004.
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