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

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 five to six 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.

9 pages, 3 figures

References in corpus (10)

• Randomized Benchmarking of Quantum Gates
• Quantum Process Tomography: Resource Analysis of Different Strategies
• Randomized benchmarking and process tomography for gate errors in a solid-state qubit
• Process tomography of ion trap quantum gates
• Compressed sensing quantum process tomography for superconducting quantum gates
• Optimal two-qubit tomography based on local and global measurements: Maximal robustness against errors as described by condition numbers
• Projected Least-Squares Quantum Process Tomography
• Experimental adaptive process tomography
• Implementing efficient selective quantum process tomography of superconducting quantum gates on the IBM quantum processor
• Effective quantum state reconstruction using compressive sensing in NMR quantum computing

Cited by in corpus (4)

• Direct tomography of quantum states and processes via weak measurements of Pauli spin operators on an NMR quantum processor
• Neural network assisted quantum state and process tomography using limited data sets
• Deterministic generation of frequency-bin-encoded microwave photons
• Experimental quantum state transfer of an arbitrary single-qubit state on a cycle with four vertices using a coined quantum random walk