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Is there any recent review on the state of the art NMR quantum computing? there are some reviews but they are not complete. for example does not give the data for the gate times and so on.

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Not as far as I know. NMR quantum computing isn't a particularly active area of research these days for a few reasons including:

  • You're not working with a single qubit, but rather an ensemble of roughly Avogadro's number of copies of your qubits in parallel which are averaged over
  • You don't deterministically start with a known state, but rather with a statistical polarization which becomes exponentially smaller with the number of qubits
  • You also only have nearest neighbor interactions, which also makes scaling the number of qubits up impractical

Also, as for how long gates take on NMR systems, this demonstration of Shor's algorithm with NMR qubits mentions gate times on the order of a 100us-1ms timescale.

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