Multi-time quantum process tomography on a superconducting qubit

The characterisation of noise is a critical requirement for advancing quantum technologies. Noise is present in all current quantum devices as they interact with their environment; for many devices, this includes non-Markovian noise due to temporal correlations across a multi-time process. While most current techniques assume Markovian noise, this assumption fails in realistic quantum devices, and non-Markovian noise has been reported in state-of-the-art quantum computing devices (such as IBM and Google) [1,2].

Past general approaches to capture non-Markovian noise only provide access to two times of a quantum process through dynamical maps. Recently, a formalism was developed that constructs a process matrix [3,4], which encodes all multi-time correlations and investigates its nature (classical or quantum) and amount [5].

Here, we present the first implementation of full process tomography of a multi-time quantum process on a superconducting qubit and obtain measures of non-Markovianity. We implement mid-circuit measurements and overcome the need for a feed-forward mechanism with a post-processing trick. We use in-house and cloud-based quantum processors to measure general and quantum non-Markovian noise and build a theoretical model to compare our findings. Our work offers a robust method for fully characterising non-Markovian noise, significantly advancing both our theoretical understanding and the development of noise mitigation techniques.

[1] J. Morris, F. A. Pollock, and K. Modi, Open Systems & Information Dynamics 29, 10.1142/S123016122250007X (2022).

[2] M. McEwen et al., Nature Communications 12, 10.1038/s41467-021-21982-y (2021).

[3] O. Oreshkov, F. Costa, and Č. Brukner, Nat. Commun. 3, 1092 (2012).

[4] O. Oreshkov and C. Giarmatzi, New J. Phys. 18, 093020 (2016).

[5] C. Giarmatzi and F. Costa, Quantum 5, 440 (2021).