基于隐含子群量子自编码器的信息压缩
Information compression via hidden subgroup quantum autoencoders
AI总结：
本研究提出基于隐含子群量子算法的量子自编码器信息压缩方法，可指数级快于经典算法，实验优于经典自编码器，展现量子计算在特定数据压缩上的应用潜力。
摘要：
我们设计了一种利用隐含子群量子算法实现经典信息压缩的量子方法。我们研究数据库中具有先验未知的隐含子群型对称性的序列数据。我们证明，具有给定群结构的数据可以达到与隐含子群问题相同的查询复杂度，其速度比已知最优的经典算法呈指数级提升。此外，我们设计了一种量子算法，能够以变分方式找到群结构并利用其压缩数据。该算法遵循量子自编码器的范式，包含编码器和解码器。训练完成后，编码器输出压缩后的数据串以及隐含子群对称性的描述，解码器可据此恢复输入数据。在示例验证中，我们的算法在测试数据的均方误差指标上优于经典自编码器。这种信息压缩能力上的经典-量子差异具有热力学意义：量子智能体赋予系统的自由能可能远高于经典智能体。综上，我们的结果表明，量子计算机的一个潜在应用是高效压缩某些当前经典计算机方法无法高效压缩的数据类型。
英文摘要：
We design a quantum method for classical information compression that exploits the hidden subgroup quantum algorithm. We consider sequence data in a database with a priori unknown symmetries of the hidden subgroup type. We prove that data with a given group structure can be compressed with the same query complexity as the hidden subgroup problem, which is exponentially faster than the best known classical algorithms. We moreover design a quantum algorithm that variationally finds the group structure and uses it to compress the data. There is an encoder and a decoder, along the paradigm of quantum autoencoders. After the training, the encoder outputs a compressed data string and a description of the hidden subgroup symmetry, from which the input data can be recovered by the decoder. In illustrative examples, our algorithm outperforms the classical autoencoder on the mean squared value of test data. This classical-quantum separation in information compression capability has thermodynamical significance: the free energy assigned by a quantum agent to a system can be much higher than that of a classical agent. Taken together, our results show that a possible application of quantum computers is to efficiently compress certain types of data that cannot be efficiently compressed by current methods using classical computers.
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