Compressed sensing quantum process tomography for superconducting quantum gates

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We apply the method of compressed sensing (CS) quantum process tomography (QPT) to characterize quantum gates based on superconducting Xmon and phase qubits.

• Using experimental data for a two-qubit controlled-Z gate, we obtain an estimate for the process matrix $\chi$ with reasonably high fidelity compared to full QPT, but using a significantly reduced set of initial states and measurement configurations.
• We show that the CS method still works when the amount of used data is so small that the standard QPT would have an underdetermined system of equations.
• We also apply the CS method to the analysis of the three-qubit Toffoli gate with numerically added noise, and similarly show that the method works well for a substantially reduced set of data.