Browsing by Author "Kalev, Amir"

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Fast Quantum State Reconstruction via Accelerated Non-Convex Programming
    (MDPI, 2023) Kim, Junhyung Lyle; Kollias, George; Kalev, Amir; Wei, Ken X.; Kyrillidis, Anastasios
    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 (MiFGD), extends the applicability of quantum tomography for larger systems. Despite being a non-convex method, MiFGD converges provably close to the true density matrix at an accelerated linear rate asymptotically in the absence of experimental and statistical noise, under common assumptions. With this manuscript, we present the method, prove its convergence property and provide the 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 (noisy) experiments, performed on the IBM’s quantum processing unit. We find that the proposed algorithm performs orders of magnitude faster than the state-of-the-art approaches, with similar or better accuracy. In both synthetic and real experiments, we observed accurate and robust reconstruction, despite the presence of experimental and statistical noise in the tomographic data. Finally, we provide a ready-to-use code for state tomography of multi-qubit systems.
  • Thumbnail Image
    Item
    Provable compressed sensing quantum state tomography via non-convex methods
    (Springer Nature, 2018) Kyrillidis, Anastasios; Kalev, Amir; Park, Dohyung; Bhojanapalli, Srinadh; Caramanis, Constantine; Sanghavi, Sujay
    With nowadays steadily growing quantum processors, it is required to develop new quantum tomography tools that are tailored for high-dimensional systems. In this work, we describe such a computational tool, based on recent ideas from non-convex optimization. The algorithm excels in the compressed sensing setting, where only a few data points are measured from a low-rank or highly-pure quantum state of a high-dimensional system. We show that the algorithm can practically be used in quantum tomography problems that are beyond the reach of convex solvers, and, moreover, is faster and more accurate than other state-of-the-art non-convex approaches. Crucially, we prove that, despite being a non-convex program, under mild conditions, the algorithm is guaranteed to converge to the global minimum of the quantum state tomography problem; thus, it constitutes a provable quantum state tomography protocol.