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3

Peter Shor has two error correcting methods. One is the bit flip method and the other is the phase shift method. The bit flip method is similar to what you could use in classical computing, and is what I would recommend you use when comparing the two. The phase shift method is unique to quantum computing. This is a great link describing it. This circuit ...

5

Can implementing error correction in this case be any easier than in the case of a general quantum circuit? Yes, for example you could use a classical error correcting code such as a repetition code. Or, and I really want to emphasize how much more efficient this would be as a strategy for running the computation, you could throw the quantum computer into a ...

2

As you say, $$\mathrm{Tr}[\rho_{XB} \log \rho_{XB}] = -S(X) + \sum_{x} p(x) \mathrm{Tr}[\rho_{B}^x \log \rho_B^x].$$ But if you can prove the above statement, then the exact same derivation gives you $$\mathrm{Tr}[\rho_{XB} \log \sigma_{XB}] = - S(X) + \sum_{x} p(x) \mathrm{Tr}[\rho_B^x \log \sigma_B^x].$$ If you put both together then you get  \begin{...

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