用遗传算法研究噪声量子信道相干信息的超可加性
Exploring super-additivity of coherent information of noisy quantum channels through Genetic algorithms
摘要：
机器学习技术越来越多地用于基础研究，以解决各种具有挑战性的问题。在这里，我们探索这样一种技术来解决量子通信场景中的一个重要问题。当通过有噪声的量子信道传输量子信息时，信道的效用由其量子容量来表征。然而，量子信道显示出一种有趣的特性，称为相干信息的超可加性。这使得量子容量的计算成为一个困难的计算问题，涉及在指数增长的搜索空间上的优化。在这项工作中，我们首先利用神经网络模拟器来表示量子态，然后应用进化优化方案来解决这个问题。我们发现在量子位泡利通道的三参数空间中的区域，相干信息表现出这种超加性特征。我们的特点是量子码，实现高相干信息，找到几个非平凡的量子码，优于一些泡利信道的重复码。对于某些泡利通道，这些代码显示出非常高的超加性的顺序为0.01，远远高于在其他研究良好的量子信道中观察到的值。我们进一步比较了神经网络模拟器与原始模拟器的学习性能，发现在三次拍摄的情况下，神经网络模拟器在寻找高相干信息的量子码方面优于原始表示。我们还比较了进化算法的学习性能与一个简单的粒子群优化方案，并显示经验结果表明可比的性能，这表明神经网络animation加上进化方案确实是一个很有前途的方法来寻找非平凡的量子代码的高相干信息。
英文摘要：
Machine learning techniques are increasingly being used in fundamental research to solve various challenging problems. Here we explore one such technique to address an important problem in quantum communication scenario. While transferring quantum information through a noisy quantum channel, the utility of the channel is characterized by its quantum capacity. Quantum channels, however, display an intriguing property called super-additivity of coherent information. This makes the calculation of quantum capacity a hard computational problem involving optimization over an exponentially increasing search space. In this work, we first utilize a neural network ansatz to represent quantum states and then apply an evolutionary optimization scheme to address this problem. We find regions in the three-parameter space of qubit Pauli channels where coherent information exhibits this super-additivity feature. We characterised the quantum codes that achieves high coherent information, finding several non-trivial quantum codes that outperforms the repetition codes for some Pauli channels. For some Pauli channels, these codes displays very high super-additivity of the order of 0.01, much higher than the observed values in other well studied quantum channels. We further compared the learning performance of the Neural Network ansatz with the raw ansatz to find that in the three-shot case, the neural network ansatz outperforms the raw representation in finding quantum codes of high coherent information. We also compared the learning performance of the evolutionary algorithm with a simple Particle Swarm Optimisation scheme and show empirical results indicating comparable performance, suggesting that the Neural Network ansatz coupled with the evolutionary scheme is indeed a promising approach to finding non-trivial quantum codes of high coherent information.
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