Filter Functions for Quantum Processes under Correlated Noise

Abstract

Many qubit implementations are afflicted by correlated noise not captured by standard theoretical tools that are based on Markov approximations. While independent gate operations are a key concept for quantum computing, it is actually not possible to fully describe noisy gates locally in time if noise is correlated on times longer than their duration. To address this issue, we develop a method based on the filter function formalism to perturbatively compute quantum processes in the presence of correlated classical noise. We derive a composition rule for the filter function of a sequence of gates in terms of those of the individual gates. The joint filter function allows to efficiently compute the quantum process of the whole sequence. Moreover, we show that correlation terms arise which capture the effects of the concatenation and thus yield insight into the effect of noise correlations on gate sequences. Our generalization of the filter function formalism enables both qualitative and quantitative studies of algorithms and state-of-the-art tools widely used for the experimental verification of gate fidelities like randomized benchmarking, even in the presence of noise correlations.

qopt: An experiment-oriented Qubit Simulation and Quantum Optimal Control Package

“…The filter function formalism is an approximate and efficient method to calculate the infidelity caused by fast non-Markovian noise of small amplitude. It outperforms Monte Carlo simulations for small systems, while Monte Carlo methods scale better with an increasing number of qubits [45,46]. The numerical routines for the calculation of filter functions and their derivatives with respect to the control amplitudes ∂Fα ∂u k (t) are provided by the software package filter functions [47].…”