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

TL;DR

This paper demonstrates that compressed sensing enables accurate quantum process tomography on an NMR quantum processor using significantly fewer measurements, especially when employing the Pauli-error basis, achieving high fidelity results.

Contribution

The study introduces a practical implementation of compressed sensing for quantum process tomography, showing improved performance over traditional methods in an NMR setting with reduced data requirements.

Findings

High-fidelity process matrices (>0.9) with 5-6 times less data

Compressed sensing outperforms least squares in basis-dependent scenarios

Effective characterization of two- and three-qubit quantum processes

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.