• Corpus ID: 249240149

Computing expectation values of adaptive Fourier density matrices for quantum anomaly detection in NISQ devices

@inproceedings{Useche2022ComputingEV,
  title={Computing expectation values of adaptive Fourier density matrices for quantum anomaly detection in NISQ devices},
  author={Diego H. Useche and Oscar A. Bustos-Brinez and Joseph A. Gallego and Fabio A. Gonz'alez},
  year={2022}
}
. This article presents a novel classical-quantum anomaly detection model based on the expected values of density matrices and a new data embedding called adaptive Fourier features. The method works by estimating a probability density function of training data and classifying new samples as anomalies if they lie below a certain probability density threshold. As a core subroutine, we present a new method to estimate the expected value of a density matrix based on its spectral decomposition on a… 

Figures and Tables from this paper

References

SHOWING 1-10 OF 54 REFERENCES
Quantum anomaly detection with density estimation and multivariate Gaussian distribution
TLDR
A quantum procedure for efficiently estimating the determinant of any Hermitian operators with time complexity $O(poly\log N)$ which forms an important subroutine in the authors' quantum anomaly detection with multivariate Gaussian distribution.
Quantum machine learning for quantum anomaly detection
TLDR
It is shown that kernel principal component analysis and one-class support vector machine can be performed using resources logarithmic in the dimensionality of quantum states, which makes these algorithms potentially applicable to big quantum data applications.
Quantum Algorithms for Anomaly Detection Using Amplitude Estimation
TLDR
A new quantum ADDE algorithm based on amplitude estimation is proposed and it is shown that the algorithm can achieves exponential speedup on the number M of training data points compared with the classical counterpart.
Variational quantum anomaly detection: Unsupervised mapping of phase diagrams on a physical quantum computer
TLDR
Variational quantum anomaly detection is proposed, an unsupervised quantum machine learning algorithm to analyze quantum data from quantum simulation to extract the phase diagram of a system with no prior physical knowledge and can be performed end-to-end on the same quantum device where the system is simulated on.
Learning with Density Matrices and Random Features
TLDR
One of the main results of the paper is to show that density matrices coupled with random Fourier features could approximate arbitrary probability distributions over R.
A rigorous and robust quantum speed-up in supervised machine learning
TLDR
A rigorous quantum speed-up for supervised classification using a quantum learning algorithm that only requires classical access to data and achieves high accuracy, robust against additive errors in the kernel entries that arise from finite sampling statistics.
Quantum Measurement Classification with Qudits
TLDR
A hybrid classical-quantum program for density estimation and supervised classification and the proposed quantum protocols allow to estimate probability density functions and to make predictions in a supervised learning manner can be generalized to find expected values of density matrices in highdimensional quantum computers.
Optimisation-free Classification and Density Estimation with Quantum Circuits
TLDR
A variational quantum circuit approach that could leverage quantum advantage for the implementation of a novel machine learning framework for probability density estimation and classification using quantum circuits is discussed.
Learning the quantum algorithm for state overlap
TLDR
This work finds algorithms that have shorter depths than the Swap Test, including one that has constant depth (independent of problem size) and applies this approach to the hardware-specific connectivity and gate alphabets used by Rigetti's and IBM's quantum computers.
Quantum speed-up for unsupervised learning
TLDR
It is explained how it is possible to accelerate learning algorithms by quantizing some of their subroutines by giving quantized versions of clustering via minimum spanning tree, divisive clustering and k-medians that are faster than their classical analogues.
...
...