So, the paper describes how some logical operations can be performed relatively easily, while a few others require manipulations of the error correction scheme in order to work. (These manipulations have names like lattice surgery and magic state distillation, which are good signs that the field doesn’t take itself that seriously.)
So, in sum, Microsoft feels that it has identified an error correction scheme that is fairly compact, can be implemented efficiently on hardware that stores qubits in photons, atoms, or trapped ions, and enables universal computation. What it hasn’t done, however, is show that it actually works. And that’s because it simply doesn’t have the hardware right now.
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