While the quantum operations formalism provides a natural framework for describing the con- catenation of quantum processes, it is of limited use when describing the effect of non-Markovian noise. We address this issue with an extension of the filter-function formalism, which so far has mostly been used to model gate fidelities and the effects of dynamical decoupling sequences. Our extension allows the efficient, perturbative calculation of full quantum processes in the presence of correlated noise, e.g., the $1/f$ -like noise found in many solid-state qubit systems [1, 2]. We show that a simple composition rule arises for the filter functions of gate sequences. This enables the investigation of quantum algorithms in the presence of correlated noise with moderate computa- tional resources. Moreover, it allows for singling out correlation terms between different gates in a sequence, capturing for instance the dynamical error suppression of spin echos. Lastly, we present the fast and easy-to-use, open-source filter functions software framework  which facilitates the calculation of quantum processes and fidelities for arbitrary system dimensions using filter functions. Other features include the efficient concatenation of several operations, an optimized treatment of periodic Hamiltonians, as well as integration with qopt, a software package for quantum robust control [4, 5].
 T. Hangleiter, P. Cerfontaine, and H. Bluhm, Filter- function formalism and software package to compute quantum processes of gate sequences for classical non- Markovian noise, Physical Review Research 3, 043047.
 P. Cerfontaine, T. Hangleiter, and H. Bluhm, Filter Func- tions for Quantum Processes under Correlated Noise, Physical Review Letters 127, 170403.
 https://github.com/qutech/filter functions/.
 J. D. Teske, P. Cerfontaine, and H. Bluhm, Qopt: An Experiment-Oriented Software Package for Qubit Simu- lation and Quantum Optimal Control, Physical Review Applied 17, 034036.
 I. N. M. Le, J. D. Teske, T. Hangleiter, P. Cerfontaine, and H. Bluhm, Analytic Filter-Function Derivatives for Quantum Optimal Control, Physical Review Applied 17, 024006.