基于深度学习LDAMP网络的量子状态估计

设计出一种基于学习去噪的近似消息传递(Learned denoising-based approximate message passing, LDAMP)的深度学习网络,将其应用于量子状态的估计.该网络将去噪卷积神经网络与基于去噪的近似消息传递算法相结合,利用量子系统输出的测量值作为网络输入,通过设计出的带有去噪卷积神经网络的LDAMP网络重构出原始密度矩阵,从大量的训练样本中提取各种不同类型密度矩阵的结构特征,来实现对量子本征态、叠加态以及混合态的估计.在对4个量子位的量子态估计的具体实例中,分别在无和有测量噪声干扰情况下,对基于LDAMP网络的量子态估计进行了仿真实验性能研究,并与基于压缩感知的交替方向乘子法和三维块匹配近似消息传递等算法进行估计性能对比研究.数值仿真实验结果表明,所设计的LDAMP网络可以在较少的测量的采样率下,同时完成对4种量子态的更高精度估计.

Quantum State Estimation Based on Deep Learning LDAMP Networks

A learned denoising-based approximate message passing (LDAMP) deep learning network is proposed and trained in this paper, which is applied to the estimation of quantum states. This network combines denoising convolutional neural network with denoising-based approximate message passing algorithm. Using the measured output of the quantum system as the network input, the original density matrix was reconstructed by the designed LDAMP network with denoising convolutional neural network, and the structural features of various density matrices were extracted from a large number of training samples to realize the estimation of superposition and mixed states of quantum eigenstates. In the specific examples of quantum state estimation of four qubits, we study the performance of the quantum state estimation based on the LDAMP networks in the absence and presence of measurement interference, respectively, and compare the estimation performance with other algorithms which is based on compressed sensing such as alternating direction multiplier method and block matching 3D AMP. The numerical simulation results show that the LDAMP network can simultaneously estimate the four quantum states with higher accuracy in a small number of measurements.