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The quantum circuit model allows gates between any pair of qubits yet physical instantiations allow only limited interactions.
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There is an asymptotically better algorithm with overhead O ( log n ) O(\log n) on the hypercube. However, we will not consider it here since it is based on the AKS sorting algorithm [ 3 , 4 ] which has constant ≈ 6,100 \approx 6,100 [ 5 ]
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D. Hucul, I. Inlek, G. Vittorini, C. Crocker, S. Debnath, S. Clark and C. Monroe, Modular entanglement of atomic qubits using photons and phonons, Nature Physics 11, 37–42 (2015)
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