论文标题
更快的随机一阶方法，用于最大样品量子层造影
Faster Stochastic First-Order Method for Maximum-Likelihood Quantum State Tomography
论文作者
论文摘要
在最大似然量子层析成像中，样本量和尺寸均随量子数的数量而成倍增长。因此，需要开发一种随机的一阶方法，就像现代机器学习的随机梯度下降一样，以计算最大样品估计。为此，我们提出了一种带有Burg熵的称为随机镜下降的算法。它的预期优化错误以$ o（\ sqrt {（1 / t）d \ log t}）$ rate的速率消失，其中$ d $和$ t $分别表示迭代的尺寸和数量。它的触电时间复杂性为$ O（d^3）$，与样本量无关。据我们所知，目前，这是最大样品量子层造影的计算最快的随机一阶方法。
In maximum-likelihood quantum state tomography, both the sample size and dimension grow exponentially with the number of qubits. It is therefore desirable to develop a stochastic first-order method, just like stochastic gradient descent for modern machine learning, to compute the maximum-likelihood estimate. To this end, we propose an algorithm called stochastic mirror descent with the Burg entropy. Its expected optimization error vanishes at a $O ( \sqrt{ ( 1 / t ) d \log t } )$ rate, where $d$ and $t$ denote the dimension and number of iterations, respectively. Its per-iteration time complexity is $O ( d^3 )$, independent of the sample size. To the best of our knowledge, this is currently the computationally fastest stochastic first-order method for maximum-likelihood quantum state tomography.
