Figure 1

The Bloch sphere is defined at the point labeled ${\epsilon }_{BS}$, where we have plotted the energy levels as a function of $\epsilon$ the gate voltage. The $z$ basis corresponds to the energy eigenstates of the Hamiltonian at the point ${\epsilon }_{BS}$.Reuse & Permissions

Figure 2

Schematic illustration of the $\epsilon$ pulse sequence for the $z$ preparation and measurement as a function of time $t$. The pulse starts at the measurement point ${\epsilon }_M$ and rapidly but adiabatically ramps down to the qubit point ${\epsilon }_{BS}$. See Ref. [11] for details.Reuse & Permissions

Figure 3

Schematic illustration of the pulse sequence for the (a) $+x$ and (b) $+y$ preparation and measurement.Reuse & Permissions

Figure 4

Comparison of state and measurement reconstruction for methods A (green), B (blue), and C (red). (a) The convergence of a systematic error for the measurement $E_x$. Here, $\alpha$ is the angular separation between the vector $R_i^2$ and the true measurement with respect to the total number of measurements $N$. (b) The infidelity $1-F$ between the true state ${\rho }_1$ and reconstructed state ${\rho }_1^{est}$. The data have been averaged over 10 runs per point in order to highlight the difference in average-case performance of methods B and C.Reuse & Permissions

Figure 5

Process fidelities for the Hadamard gate, reconstructed using states and measurements characterized from methods A (green), B (blue), and C (red). (a), (b) the infidelity between the ideal unitary ${\rho }_U$ and the reconstructed process ${\rho }_{{\mathcal{E}}_{est}}$ based on state and measurement tomography obtained for $N_{\mathrm{SPAM}}={10}^6$ (a) and $N_{\mathrm{SPAM}}={10}^9$ (b) total measurements, respectively. The solid line represents the fidelity between the true process and the ideal Hadamard gate; process tomography estimates should converge to this line. (c), (d) the fidelity between the true $\mathcal{E}$ and reconstructed process ${\mathcal{E}}_{\mathrm{est}}$, again for $N_{\mathrm{SPAM}}={10}^6$ (c) and $N_{\mathrm{SPAM}}={10}^9$ (d) total measurements, respectively. These process tomography estimates should improve continuously as $1/\sqrt{N}$. The data have been averaged over 10 runs per point.Reuse & Permissions