I was quite confused about the definition of physical error rate in the paper Topological quantum memory, which is famous because it estimate the accurate threshold by using Ising model.
In this paper, the author said that Let us imagine that, in a single time step, we will execute a measurement of each stabilizer operator at each site and each plaquette of the lattice. During each time step, new qubit errors might occur. To be concrete and to simplify the discussion, we assume that all qubit errors are stochastic, and so can be assigned probabilities. (For example, errors that arise from decoherence have this property.) We will also assume that the errors acting on different qubits are independent, that bit-flip (X) errors and phase (Z) errors are uncorrelated with one another, and that X and Z errors are equally likely. Thus the error in each time step acting on a qubit with state ρ can be represented by the quantum channel. [located in Sec4.A]
And the result of this paper is 11% if perfect measurement and 1.1% if imperfect measurement.
So, my question is:
What does this error rate mean? The probability of occuring error in the whole stabilizer measurement or the probability of occuring error in just one gate time which might be in the order of 1/8 less than the previous one if using the standard X(Z) stabilizer measurement circuit.
