# Spectral Quantum Tomography

## TL;DR

Spectral quantum tomography is a resource-efficient method for extracting eigenvalues of noisy quantum gates, providing detailed diagnostics beyond traditional fidelity measures, and is applicable to real superconducting qubit systems.

## Contribution

We introduce spectral quantum tomography, a novel SPAM-resistant technique for eigenvalue extraction of quantum gates using minimal resources.

## Key findings

- Successfully applied to superconducting qubits on cloud platforms.
- Revealed effects of cross-talk, leakage, and non-Markovian errors.
- Provides detailed gate diagnostics beyond fidelity measures.

## Abstract

We introduce spectral quantum tomography, a simple method to extract the eigenvalues of a noisy few-qubit gate, represented by a trace-preserving superoperator, in a SPAM-resistant fashion, using low 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 gate diagnostic tool. We apply our method to one- and two-qubit gates on two different superconducting systems available in the cloud, namely the QuTech Quantum Infinity and the IBM Quantum Experience. We discuss how cross-talk, leakage and non-Markovian errors affect the eigenvalue data.