I'm studying quantum error correction on Nielsen's Quantum Computation and Quantum Information, but I don't understand how it identifies the number of places where an error may occur.

It uses approximations and does not show how to identify those places.

I'm referencing pages 479 and 480, how does he know the values of the c and c0, c1, etc.


Each of the itemized steps specifies the part of a quantum circuit where a single error occurs. So, for that part of the circuit, essentially what you want to do is write out the circuit diagram. Then, you "slice up" the circuit, i.e. put in vertical lines that just subdivide the circuit into distinct slices where all the gates in the slice can be performed simultaneously. So, you know the number of time steps required, $T$ and the number of qubits involved, $Q$. So, the number of places an error can occur is $c_0= QT$.

  • $\begingroup$ Does the error only happen on qubits that are being affected by a gate on the step? Or on any qubit on the step? $\endgroup$
    – Nillmer
    Sep 17 '20 at 16:21
  • 1
    $\begingroup$ It's any qubit. $\endgroup$
    – DaftWullie
    Sep 17 '20 at 17:51

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