Exploring exotic configurations with anomalous features with deep learning: Application of classical and quantum-classical hybrid anomaly detection

We present the application of classical and quantum-classical hybrid anomaly detection schemes to explore exotic configurations with anomalous features. We consider the Anderson model as a prototype, where we define two types of anomalies—a high conductance in the presence of strong impurity and a low conductance in the presence of weak impurity—as a function of random impurity distribution. Such anomalous outcome constitutes an imperceptible fraction of the data set and is not a part of the training process. These exotic configurations, which can be a source of rich new physics, usually remain elusive to conventional classification or regression methods and can be tracked only with a suitable anomaly detection scheme. We also present a systematic study of the performance of the classical and the quantum-classical hybrid anomaly detection method and show that the inclusion of a quantum circuit significantly enhances the performance of anomaly detection, which we quantify with suitable performance metrics. Our approach is quite generic in nature and can be used for any system that relies on a large number of parameters to find their new configurations, which can hold exotic new features.

Figure 1

Distribution of conductance and schematic of the device configuration. (a) Distribution of conductance for $V_0=0.9$ (red) and $V_0=0.3$ (blue) for 2000 random configurations. Inset: the variation of average conductance (solid black line, gray region shows the rms deviation), with vertical red line denoting $V_0=0.3,0.9$. (b),(c) Two configurations for $V_0=0.9$, with LDOS (in gray scale) and conductance (in legend). The green regions show the electrodes. The red dots denote the impurities which are confined within the central region marked by a black dashed line.

Figure 2

Schematic representation of an autoencoder. The input data are compressed by the encoder and the decoder expands the compress data to its original size. The intermediate space with compressed dimension is called the latent space.

Figure 3

A schematic diagram of a hybrid classical-quantum autoencoder (HAE) architecture [32]. The data coming from the classical encoder are embedded into the PQC. In PQC, the $U_1\left({\theta }_{ij}\right)$ and $U_2\left({\varphi }_{ij}\right)$ are the blocks of quantum circuits containing different rotation gates with rotation parameters $\theta ,\varphi$. After the blocks of quantum circuits, there are measurements followed by the postmeasurement processing block (denoted as Post Process). After postprocessing, the information is fed into the classical decoder.

Figure 4

Visualization of anomalies (red) and nominal data (light blue). (a)–(d) $V_0=0.9$ and (e)–(h) $V_0=0.3$ data sets with respect to two arbitrary input dimensions. (a) and (e) show the original input data. (b) and (f) show the PCA of the original data. (c) and (g) show the output from the classical encoder, and (d) and (h) show the output from the PQC.