Scalable Protocols for Characterization of Correlated non-Markovian Noise in Trapped-Ion Quantum Processors

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Characterizing noise is crucial for improving quantum control and error mitigation protocols as well as designing quantum error-correcting codes and decoders. An important source of errors is the non-Markovian noise which has recently been shown cite{P} to lead to non-trivial dynamics in logical qubits in trapped-ion quantum processors. A less understood source of non-Markovian noise in trapped-ion quantum processors is due to unknown dynamics of interactions between spins and the bosonic bath comprised of the motional states of ions under correlated electric-field noise. Two difficulties arise in characterizing this noise which include the infinite dimensionality of the Fock space of the bosonic bath as well as the non-local nature of the spin-boson dynamics induced by spatially correlated electric field noise. Here, we introduce a scalable protocol to characterize this source of correlated non-Markovian noise, which requires quadratic number of gates for a given number of qubits. We then use the spectroscopic information of this protocol to predict the noise dynamics in a logical qubit. We further introduce a scalable protocol to characterize the correlated non-Markovian noise in a logical qubit and compare the predictions of the first protocol with the second protocol. We discuss a potential route to extend our protocols to characterize the correlated non-Markovian noise in logical gate operations with trapped-ion quantum processors.

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ibitem{P}Pal, A., Schindler, P., Erhard, A., Rivas, Á., Martin-Delgado, M., Blatt, R., Monz, T. & Müller, M. Relaxation times do not capture logical qubit dynamics. {em Quantum}. extbf{6} pp. 632 (2022,1), https://doi.org/10.22331/q-2022-01-24-632

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