一组物理变换的最大似然估计

Gradient-based stopping rules for maximum-likelihood quantum-state tomography

When performing maximum-likelihood quantum-state tomography, one must find the quantum state that maximizes the likelihood of the state given observed measurements on identically prepared systems. The optimization is usually performed with iterative algorithms. This paper provides a gradient-based upper bound on the ratio of the true maximum likelihood and the likelihood of the state of the current iteration, regardless of the particular algorithm used. This bound is useful for formulating stopping rules for halting iterations of maximization algorithms. We discuss such stopping rules in the c…

基于高效鲁棒量子似然梯度的最大似然估计哈密顿量学习

Maximum-Likelihood-Estimate Hamiltonian learning via efficient and robust quantum likelihood gradient

提出结合最大似然估计、梯度下降与量子多体算法的高效哈密顿量学习方法，沿量子似然梯度优化，具有负半定保证，尊重局域性，可扩展至大系统，且在噪声、波动和温度下准确性和稳定性更优。

Hedged maximum likelihood estimation

This paper proposes and analyzes a new method for quantum state estimation, called hedged maximum likelihood (HMLE). HMLE is a quantum version of Lidstone's Law, also known as the "add beta" rule. A straightforward modification of maximum likelihood estimation (MLE), it can be used as a plugin replacement for MLE. The HMLE estimate is a strictly positive density matrix, slightly less likely than the ML estimate, but with much better behavior for predictive tasks. Single-qubit numerics indicate that HMLE beats MLE, according to several metrics, for nearly all "true" states. For nearly-pure stat…