Fig. 3: MEADD circuits used to characterize the entangling parameters of CZ gates.

a The circuits are composed of three steps. Prepare \(\left\vert +0\right\rangle\) with a microwave gate (blue), or similarly \(\left\vert 0+\right\rangle\) (not shown), interleave X ⊗ X dynamical decoupling gates (yellow) with the repeated CZ gates for even repetitions 2n, and finally measure both qubits in the X and Y bases (green). As explained in the main text, combining the resulting measurement bits for different depths n yields an estimate of the controlled phase ϕ that is robust to both low-frequency noise and DD gate imperfections. b Similarly, for the swapping angle θ and phase χ, we prepare \(\left\vert 10\right\rangle\) (or \(\left\vert 01\right\rangle\), not shown), use X ⊗ X and Y ⊗ X as DD gates, and measure either in the computational basis of both qubits (top circuit) or in the Bell basis of the odd parity subspace (bottom circuit), where \({X}_{{\rm{odd}}}=\left\vert 10\right\rangle \left\langle 01\right\vert +\left\vert 01\right\rangle \left\langle 10\right\vert\) and \({Y}_{{\rm{odd}}}=i\left\vert 10\right\rangle \left\langle 01\right\vert -i\left\vert 01\right\rangle \left\langle 10\right\vert\).