Partial characterization of quantum gates using character eigenvalue estimation

In experimental quantum systems, an accurate understanding of underlying noise processes is pivotal for implementing targeted calibration strategies. One common approach for characterizing errors is quantum phase estimation; however, existing schemes for phase estimation are not entirely robust to state prep errors and are limited to characterizing specific types of noise, i.e coherent errors. To overcome these limitations, we introduce a technique that harnesses tools from representation theory to robustly and precisely estimate parameters of general Markovian noise processes, which call character eigenvalue estimation (CEE). CEE uses linear combinations of circuit outcomes to isolate individual eigenvalues of a noisy gate, which can then be learned to high precision with a simple fitting routine. We validate our method's efficacy through simulations with error models encompassing both coherent and stochastic noise. We also discuss how to use CEE to perform gate set tomography without computationally intensive maximum-likelihood estimation, which offers a pathway towards robust and scalable partial tomography of quantum gate sets.