Table 3 Description of noisy gates in Table 2

M_PP(p, η)

Measurement of Pauli Product PP on a pair of qubits:

 • independently register incorrect measurement result with probability p,

 • apply a two-qubit Z-biased noise channel with total error probability p and noise bias η after measurement, i.e., apply:

 - the trivial identity operator (II) with a probability 1 − p,

 - ZI, IZ, and ZZ operators, each with probability ζp/3,

 - the remaining Pauli operators, each with probability (1 − ζ)p/12, where \(\zeta =\frac{3}{5}{\left(\frac{\eta }{1+\eta }\right)}^{2}+\frac{2}{5}\left(\frac{\eta }{1+\eta }\right)\).

Init(p,η)

Qubit initialization in some Pauli basis, followed by applying a single-qubit Z-biased noise channel with total error probability p and noise bias η after the reset, i.e., apply:

 • the trivial identity operator (I) with a probability 1 − p,

 • Pauli Z operator with probability pη/(η + 1),

 • Pauli X and Y operators, each with probability p/[2(η + 1)].

M(p)

Measure the qubit in some Pauli basis and register the incorrect measurement result with probability p.