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Characterizing noisy quantum processes is important to quantum computation and communication (QCC), since quantum systems are generally open.
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All stabilizer measurements and error correction operations can be implemented using one- and two-body interactions [ 19 ] . To see that such interactions suffice to implement U U and S + S^{+} , consider the unitary version of QEC, which requires only one- and two-body interactions and can be represented as: ∀ J , a [ ( F a | J ⟩ ) | 0 ⟩ S → ( F a | J ⟩ ) | a ⟩ S → | J ⟩ | a ⟩ ] , \forall_{J,a}\left[(F_{a}|J\rangle)|0\rangle_{S}\rightarrow(F_{a}|J\rangle)|a\rangle_{S}\rightarrow|J\rangle|a\rangle\right], where the first register is the computer and the second holds the syndrome register. To implement U ( a , b ) U(a,b) , one prepares the second register (an ancilla) in the state 1 2 ( | a ⟩ + | b ⟩ ) \frac{1}{\sqrt{2}}(|a\rangle+|b\rangle) and reverses the above operation. To implement S + S^{+} one corrects the state of the quantum computer, applies the phase gate | a ⟩ ⟶ e i θ a | a ⟩ |a\rangle\longrightarrow e^{i\theta_{a}}|a\rangle on the second register, and then “uncorrects” the resulting composite system. For the last step, we invoke the result that single qubit gates and CNOT are universal for quantum computation [ 1 ]
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