Quantum non-Markovian noise effects in randomized benchmarking

In non-Markovian systems, the current state of the system depends on the full or partial history of its past evolution. Non-Markovian noise violates common assumptions in gate characterization protocols such as randomized benchmarking and gate-set tomography. Here, we perform a case study of the effects of a quantum non-Markovian bath on single-qubit randomized benchmarking experiments. We consider a model consisting of a qubit coupled to a multimode Bosonic bath. We apply unitary operations on the qubit, interspersed with interactions with the environment. Allowing for non-Markovianity in the interactions leads to clear differences in the randomized benchmarking decay curves in this model, which we analyze in detail.