Fast quantum state reconstruction via accelerated non-convex programming
This work addresses the challenge of scalable quantum tomography for researchers and practitioners in quantum computing, offering a faster and accurate method for reconstructing multi-qubit states, though it is incremental as it builds on existing compressed sensing and optimization techniques.
The authors tackled the problem of quantum state reconstruction for larger systems by proposing a new algorithm called Momentum-Inspired Factored Gradient Descent (MiFGD), which converges provably close to the true density matrix at an accelerated linear rate and performs orders of magnitude faster than state-of-the-art approaches with the same or better accuracy in synthetic and real experiments.
We propose a new quantum state reconstruction method that combines ideas from compressed sensing, non-convex optimization, and acceleration methods. The algorithm, called Momentum-Inspired Factored Gradient Descent (\texttt{MiFGD}), extends the applicability of quantum tomography for larger systems. Despite being a non-convex method, \texttt{MiFGD} converges \emph{provably} close to the true density matrix at an accelerated linear rate, in the absence of experimental and statistical noise, and under common assumptions. With this manuscript, we present the method, prove its convergence property and provide Frobenius norm bound guarantees with respect to the true density matrix. From a practical point of view, we benchmark the algorithm performance with respect to other existing methods, in both synthetic and real experiments performed on an IBM's quantum processing unit. We find that the proposed algorithm performs orders of magnitude faster than state of the art approaches, with the same or better accuracy. In both synthetic and real experiments, we observed accurate and robust reconstruction, despite experimental and statistical noise in the tomographic data. Finally, we provide a ready-to-use code for state tomography of multi-qubit systems.