Table 1.

A complete basis for the learnable linear functions of log Pauli fidelities and Pauli error rates for a single CNOT/SWAP gate

Gate	CNOT	SWAP
(a) Cycle basis	lII, lZI, lIX, lZX, lXZ, lYY, lXY, lYZ,  lIZ + lZZ, lIY + lZY, lIZ + lZY,  lXI + lXX, lYI + lYX, lXI + lYX	lII, lXX, lXY, lXZ, lYX, lYY, lYZ, lZX, lZY,  lZZ, lIX + lXI, lIY + lYI, lIZ + lZI,  lXI + lIY, lXI + lIZ
(b) Learnable Pauli fidelities	λII, λZI, λIX, λZX, λXZ, λYY, λXY, λYZ,  λIZ ⋅ λZZ, λIY ⋅ λZY, λIZ ⋅ λZY,  λXI ⋅ λXX, λYI ⋅ λYX, λXI ⋅ λYX	λII, λXX, λXY, λXZ, λYX, λYY, λYZ, λZX, λZY,  λZZ, λIX ⋅ λXI, λIY ⋅ λYI, λIZ ⋅ λZI,  λXI ⋅ λIY, λXI ⋅ λIZ
(c) Learnable Pauli errors	pII, pZI, pIX, pZX, pXZ, pYY, pXY, pYZ,  pIZ + pZZ, pIY + pZY, pIZ + pZY,  pXI + pXX, pYI + pYX, pXI + pYX	pII, pXX, pXY, pXZ, pYX, pYY, pYZ, pZX, pZY,  pZZ, pIX + pXI, pIY + pYI, pIZ + pZI,  pXI + pIY, pXI + pIZ
(d) Unlearnable degrees of freedom	λXI, λIZ	λXI