Filter Functions for Quantum Processes under Correlated Noise

Physical Review Letters, vol. 127, pp. 170403

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 us 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.

Authors 3

1. Pascal Cerfontaine Aachen JARA-FIT Institute for Quantum Information

   RWTH Aachen University · Forschungszentrum Jülich · Jülich Aachen Research Alliance

   Affiliation as printed

   JARA-FIT Institute for Quantum Information, Forschungszentrum Jülich GmbH and RWTH Aachen University, 52074 Aachen, Germany

2. Tobias Hangleiter Aachen JARA-FIT Institute for Quantum Information

   RWTH Aachen University · Forschungszentrum Jülich · Jülich Aachen Research Alliance

   Affiliation as printed

   JARA-FIT Institute for Quantum Information, Forschungszentrum Jülich GmbH and RWTH Aachen University, 52074 Aachen, Germany

3. Hendrik Bluhm Aachen JARA-FIT Institute for Quantum Information

   RWTH Aachen University · Forschungszentrum Jülich · Jülich Aachen Research Alliance

   Affiliation as printed

   JARA-FIT Institute for Quantum Information, Forschungszentrum Jülich GmbH and RWTH Aachen University, 52074 Aachen, Germany