论文标题
分布式量子状态层析成像的局部随机分类梯度下降
Local Stochastic Factored Gradient Descent for Distributed Quantum State Tomography
论文作者
论文摘要
我们提出了一个分布式量子状态断层扫描（QST）协议，称为局部随机分类的梯度下降（局部SFGD），以学习一组本地机器的密度矩阵的低级别因子。 QST是表征量子系统状态的规范过程，我们将其作为随机非凸平滑优化问题提出。从物理上讲，对低级别密度矩阵的估计有助于表征量子计算引入的噪声量。从理论上讲，我们证明了一类限制的强凸/平滑损耗功能的局部SFGD的局部收敛，即，局部SFGD在本地收敛到恒定步长的线性速率上的全局最佳速率的一小部分，而稳定的台阶大小，而本地汇聚在局部性速度较小的速度率降低的情况下，则在本地收敛。通过适当的初始化，局部收敛结果意味着全局收敛。我们通过在Greenberger-Horne-Zeilinger（GHz）状态上对QST进行数值模拟来验证我们的理论发现。
We propose a distributed Quantum State Tomography (QST) protocol, named Local Stochastic Factored Gradient Descent (Local SFGD), to learn the low-rank factor of a density matrix over a set of local machines. QST is the canonical procedure to characterize the state of a quantum system, which we formulate as a stochastic nonconvex smooth optimization problem. Physically, the estimation of a low-rank density matrix helps characterizing the amount of noise introduced by quantum computation. Theoretically, we prove the local convergence of Local SFGD for a general class of restricted strongly convex/smooth loss functions, i.e., Local SFGD converges locally to a small neighborhood of the global optimum at a linear rate with a constant step size, while it locally converges exactly at a sub-linear rate with diminishing step sizes. With a proper initialization, local convergence results imply global convergence. We validate our theoretical findings with numerical simulations of QST on the Greenberger-Horne-Zeilinger (GHZ) state.
