# InQMAD: Incremental Quantum Measurement Anomaly Detection

arXiv: https://arxiv.org/abs/2210.05061 · HTML: https://mlsanity.com/paper/2210.05061/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 43 references that are in the map.
- First posted on arXiv 11 Oct 2022.

## Builds on (most cited first, 8 of 8)

- [A Unifying Review of Deep and Shallow Anomaly Detection](https://mlsanity.com/paper/2009.11732/) (2020)
- [Anomaly Detection using One-Class Neural Networks](https://mlsanity.com/paper/1802.06360/) (2018)
- [Extended Isolation Forest](https://mlsanity.com/paper/1811.02141/) (2018)
- [MSTREAM: Fast Anomaly Detection in Multi-Aspect Streams](https://mlsanity.com/paper/2009.08451/) (2020)
- [Learning with Density Matrices and Random Features](https://mlsanity.com/paper/2102.04394/) (2021)
- [MemStream: Memory-Based Streaming Anomaly Detection](https://mlsanity.com/paper/2106.03837/) (2021)
- [Supervised Learning with Quantum Measurements](https://mlsanity.com/paper/2004.01227/) (2020)
- [Quantum Adaptive Fourier Features for Neural Density Estimation](https://mlsanity.com/paper/2208.00564/) (2022)

## Built on by (most cited first, 2 of 2)

- [Quorum: Zero-Training Unsupervised Anomaly Detection using Quantum Autoencoders](https://mlsanity.com/paper/2504.13113/) (2025)
- [MEMO-QCD: Quantum Density Estimation through Memetic Optimisation for Quantum Circuit Design](https://mlsanity.com/paper/2406.08591/) (2024)

## Abstract (arXiv)

Streaming anomaly detection refers to the problem of detecting anomalous data samples in streams of data. This problem poses challenges that classical and deep anomaly detection methods are not designed to cope with, such as conceptual drift and continuous learning. State-of-the-art flow anomaly detection methods rely on fixed memory using hash functions or nearest neighbors that may not be able to constrain high-frequency values as in a moving average or remove seamless outliers and cannot be trained in an end-to-end deep learning architecture. We present a new incremental anomaly detection method that performs continuous density estimation based on random Fourier features and the mechanism of quantum measurements and density matrices that can be viewed as an exponential moving average density. It can process potentially endless data and its update complexity is constant O(1). A systematic evaluation against 12 state-of-the-art streaming anomaly detection algorithms using 12 streaming datasets is presented.