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. Owing to these time correlations, 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, specifically a multimode Bosonic bath, on qubit randomized benchmarking experiments. We apply unitary operations on the qubits, interspersed with brief interactions with the environment governed by a Hamiltonian. 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. The Markovian model’s decay is exponential as expected whereas the model with non-Markovian interactions displays a much slower, power-law times exponential decay. We support our theoretical results with numerical simulations, and developed efficient methods for the same. These results inform efforts on incorporating quantum non-Markovian noise in the characterization and benchmarking of quantum devices.