Filter Function Formalism for Unitary Quantum Operations

While the quantum process formalism provides a natural framework for describing the concatenation of quantum operations, it is of limited use when describing the effects of non-Markovian noise. In my talk, I will first present 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 facilitates 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. I will then 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 computational resources. Lastly, we present a fast and easy-to-use open source software framework (quantuminfo.physik.rwth-aachen.de/code) which facilitates the calculation of (first order) quantum processes and fidelities for arbitrary system dimensions. Other features include the efficient concatenation of several operations, and an optimized treatment of periodic Hamiltonians.