Core Concepts
Quantum Normalizing Flows can achieve competitive performance for anomaly detection compared to classical methods, while providing an efficient quantum implementation.
Abstract
This work introduces Quantum Normalizing Flows (QNFs) for anomaly detection. QNFs compute a bijective mapping from an arbitrary data distribution to a predefined (e.g. normal) distribution using quantum gates. The deviation from the expected normal distribution is then used as an anomaly score.
The authors optimize the QNF architecture using quantum architecture search, minimizing the Kullback-Leibler divergence or cosine dissimilarity between the transformed data distribution and the target normal distribution. Experiments on the iris and wine datasets show that the optimized QNF models achieve competitive performance for anomaly detection compared to classical methods like isolation forests, local outlier factor (LOF), and single-class SVMs.
The authors also demonstrate how the QNF can be used as a generative model by sampling from the normal distribution and inverting the flow to generate new samples in the original data space.
Importantly, the authors provide an efficient quantum implementation of the QNF-based anomaly detection, where the input data is encoded into a quantum state, the optimized QNF is applied, and the similarity to the target normal distribution is evaluated using a quantum swap test. This allows the entire anomaly detection pipeline to be executed on a quantum computer.
Stats
The iris dataset has 4 dimensions, which are encoded into 12-dimensional binary vectors. The wine dataset has 14 dimensions, encoded into 28-dimensional binary vectors.
Quotes
"Quantum Normalizing Flows can achieve competitive performance for anomaly detection compared to classical methods, while providing an efficient quantum implementation."
"The deviation from the expected normal distribution is then used as an anomaly score."
"The authors also demonstrate how the QNF can be used as a generative model by sampling from the normal distribution and inverting the flow to generate new samples in the original data space."