Title | Quantum state tomography via non-convex Riemannian gradient descent |

Publication Type | Journal Article |

Year of Publication | 2022 |

Authors | Hsu, M-C, Kuo, E-J, Yu, W-H, Cai, J-F, Hsieh, M-H |

Date Published | 10/10/2022 |

Keywords | FOS: Physical sciences, Quantum Physics (quant-ph) |

Abstract | The recovery of an unknown density matrix of large size requires huge computational resources. The recent Factored Gradient Descent (FGD) algorithm and its variants achieved state-of-the-art performance since they could mitigate the dimensionality barrier by utilizing some of the underlying structures of the density matrix. Despite their theoretical guarantee of a linear convergence rate, the convergence in practical scenarios is still slow because the contracting factor of the FGD algorithms depends on the condition number κ of the ground truth state. Consequently, the total number of iterations can be as large as O(κ−−√ln(1ε)) to achieve the estimation error ε. In this work, we derive a quantum state tomography scheme that improves the dependence on κ to the logarithmic scale; namely, our algorithm could achieve the approximation error ε in O(ln(1κε)) steps. The improvement comes from the application of the non-convex Riemannian gradient descent (RGD). The contracting factor in our approach is thus a universal constant that is independent of the given state. Our theoretical results of extremely fast convergence and nearly optimal error bounds are corroborated by numerical results. |

URL | https://arxiv.org/abs/2210.04717 |

DOI | 10.48550/ARXIV.2210.04717 |