Spectral Quantum Tomography

We introduce spectral quantum tomography, a simple method to extract the eigenvalues of a noisyfew-qubit gate, represented by a trace-preserving superoperator, in a SPAM-resistant fashion, usinglow resources in terms of gate sequence length. The eigenvalues provide detailed gate information,supplementary to known gate-quality measures such as the gate fidelity, and can be used as a gatediagnostic tool. We apply our method to one- and two-qubit gates on two different superconduct-ing systems available in the cloud, namely the QuTech Quantum Infinity and the IBM QuantumExperience. We discuss how cross-talk, leakage and non-Markovian errors affect the eigenvalue data.