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Efficient experimental characterization of quantum processes via compressed sensing on an NMR quantum processor

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Abstract

We employ the compressed sensing (CS) algorithm and a heavily reduced data set to experimentally perform true quantum process tomography (QPT) on an NMR quantum processor. We obtain the estimate of the process matrix \(\chi \) corresponding to various two- and three-qubit quantum gates with a high fidelity. The CS algorithm is implemented using two different operator bases, namely the standard Pauli basis and the Pauli-error basis. We experimentally demonstrate that the performance of the CS algorithm is significantly better in the Pauli-error basis, where the constructed \(\chi \) matrix is maximally sparse. We compare the standard least square (LS) optimization QPT method with the CS-QPT method and observe that, provided an appropriate basis is chosen, the CS-QPT method performs significantly better as compared to the LS-QPT method. In all the cases considered, we obtained experimental fidelities greater than 0.9 from a reduced data set, which was approximately 5–6 times smaller in size than a full data set. We also experimentally characterized the reduced dynamics of a two-qubit subsystem embedded in a three-qubit system and used the CS-QPT method to characterize processes corresponding to the evolution of two-qubit states under various J-coupling interactions.

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The data sets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

All the experiments were performed on a Bruker Avance-III 600 MHz FT-NMR spectrometer at the NMR Research Facility of IISER Mohali. Arvind acknowledges financial support from DST/ICPS/QuST/Theme-1/2019/Q-68. K. D. acknowledges financial support from DST/ICPS/QuST/Theme-2/2019/Q-74.

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  1. Department of Physical Sciences, Indian Institute of Science Education and Research (IISER) Mohali, Sector 81 SAS Nagar, Ajitgarh, Punjab, 140306, India

    Akshay Gaikwad,  Arvind & Kavita Dorai

  2. Punjabi University Patiala, Patiala, Punjab, 147002, India

    Arvind

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Gaikwad, A., Arvind & Dorai, K. Efficient experimental characterization of quantum processes via compressed sensing on an NMR quantum processor. Quantum Inf Process 21, 388 (2022). https://doi.org/10.1007/s11128-022-03695-3

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