Modeling Low-Frequency Hamiltonian Noise*

The ability to precisely and completely characterize the behavior of as-built quantum computing hardware is essential to the development of next-generation quantum computers. Tomographic protocols, such as gate set tomography (GST), produce incredibly detailed descriptions of the noise in a system, but do so under the assumption that the noise is markovian. Non-markovian noise sources (e.g. leakage, crosstalk and temporal correlations) are common in real systems, and are pernicious in that we not only do not capture them with most existing characterization protocols, but they can in fact corrupt our estimates for the markovian noise in a device.

In this work we introduce a method for modeling and characterizing non-markovianity due to temporally correlated fluctuating hamiltonians in the quasi-static DC/low-frequency limit and demonstrate its performance in simulation. While not fully general,

this limit captures many important forms of non-markovianity, such as non-markovian dephasing. Moreover, this demonstrates an essential first step in the development of models for non-markovianity arising from hamiltonians fluctating according to arbitrary noise spectra.