论文标题
软贝斯的最大型量子层析成像
Maximum-Likelihood Quantum State Tomography by Soft-Bayes
论文作者
论文摘要
量子状态断层扫描（QST）是估计未知量子状态给定测量结果的任务，对于构建可靠的量子计算设备至关重要。尽管计算最大样品（ML）估计值对应于解决有限的凸出优化问题，但目标函数并不光滑，也不是Lipschitz，因此大多数现有的凸优化方法都缺乏样品复杂性的保证；此外，样本量和维度都随QST实验中的Qubit数量而成倍增长，因此所需的算法相对于尺寸和样本大小，就像随机梯度下降一样。 In this paper, we propose a stochastic first-order algorithm that computes an $\varepsilon$-approximate ML estimate in $O( ( D \log D ) / \varepsilon ^ 2 )$ iterations with $O( D^3 )$ per-iteration time complexity, where $D$ denotes the dimension of the unknown quantum state and $\varepsilon$ denotes the optimization 错误。我们的算法是量子设置的软膜的扩展。
Quantum state tomography (QST), the task of estimating an unknown quantum state given measurement outcomes, is essential to building reliable quantum computing devices. Whereas computing the maximum-likelihood (ML) estimate corresponds to solving a finite-sum convex optimization problem, the objective function is not smooth nor Lipschitz, so most existing convex optimization methods lack sample complexity guarantees; moreover, both the sample size and dimension grow exponentially with the number of qubits in a QST experiment, so a desired algorithm should be highly scalable with respect to the dimension and sample size, just like stochastic gradient descent. In this paper, we propose a stochastic first-order algorithm that computes an $\varepsilon$-approximate ML estimate in $O( ( D \log D ) / \varepsilon ^ 2 )$ iterations with $O( D^3 )$ per-iteration time complexity, where $D$ denotes the dimension of the unknown quantum state and $\varepsilon$ denotes the optimization error. Our algorithm is an extension of Soft-Bayes to the quantum setup.
