论文标题
基于子系统净化的各种编码器的降低性降低
Dimensionality reduction with variational encoders based on subsystem purification
论文作者
论文摘要
编码和压缩的有效方法可能会在更高维的希尔伯特空间上克服贫瘠的高原问题上的有效训练性问题铺平道路。在这里,我们提出了一种替代方法,以减少更高维希尔伯特空间中代表的状态的维度。为此,我们构建了一个基于变异的自动编码器电路,该电路将作为输入数据集,并优化参数化量子电路(PQC)ANSATZ的参数,以产生输出状态,通过最小化TR(ρ^2),可以将其表示为2个子系统的张量产物。该电路的输出通过一系列受控的交换门和测量值,以输出量子数量的一半的状态,同时保留起始状态的特征,其精神与经典算法中使用的任何降低技术相同。获得的输出用于监督学习,以确保如此开发的编码程序的工作。我们利用条形和条纹数据集(BAS)进行8x8网格,以创建有效的编码状态,并在同一网格上报告95%的分类精度。因此,所展示的示例显示了该方法在减少较大希尔伯特空间中表示的状态中工作的证明,同时保持了随后的任何进一步的机器学习算法所需的功能。
Efficient methods for encoding and compression are likely to pave way towards the problem of efficient trainability on higher dimensional Hilbert spaces overcoming issues of barren plateaus. Here we propose an alternative approach to variational autoencoders to reduce the dimensionality of states represented in higher dimensional Hilbert spaces. To this end we build a variational based autoencoder circuit that takes as input a dataset and optimizes the parameters of Parameterized Quantum Circuit (PQC) ansatz to produce an output state that can be represented as tensor product of 2 subsystems by minimizing Tr(ρ^2). The output of this circuit is passed through a series of controlled swap gates and measurements to output a state with half the number of qubits while retaining the features of the starting state, in the same spirit as any dimension reduction technique used in classical algorithms. The output obtained is used for supervised learning to guarantee the working of the encoding procedure thus developed. We make use of Bars and Stripes dataset (BAS) for an 8x8 grid to create efficient encoding states and report a classification accuracy of 95% on the same. Thus the demonstrated example shows a proof for the working of the method in reducing states represented in large Hilbert spaces while maintaining the features required for any further machine learning algorithm that follow.