Quantum algorithms for anomaly detection using amplitude estimation

Guo, Ming-Chao; Liu, Hai-Ling; Li, Yong-Mei; Li, Wen-Min; Qin, Su-Juan; Wen, Qiao-Yan; Gao, Fei

doi:10.48550/arxiv.2109.13820

Cited by 2 publications

(2 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Herr et al [167] used parameterized quantum circuits to model the generator used in AnoGan [295] for anomaly detection. Quantum amplitude estimation (Section 4.4) was utilized to enhance density-estimation-based anomaly detection [155]. There also exist quantum variants of common clustering methods, such as k-means (Section 7.3), that could be useful for anomaly detection.…”

Section: Anomaly Detectionmentioning

confidence: 99%

A Survey of Quantum Computing for Finance

Herman¹,

Googin²,

Liu³

et al. 2022

Preprint

View full text Add to dashboard Cite

Quantum computers are expected to surpass the computational capabilities of classical computers during this decade and have transformative impact on numerous industry sectors, particularly finance. In fact, finance is estimated to be the first industry sector to benefit from quantum computing, not only in the medium and long terms, but even in the short term. This survey paper presents a comprehensive summary of the state of the art of quantum computing for financial applications, with particular emphasis on Monte Carlo integration, optimization, and machine learning, showing how these solutions, adapted to work on a quantum computer, can help solve more efficiently and accurately problems such as derivative pricing, risk analysis, portfolio optimization, natural language processing, and fraud detection. We also discuss the feasibility of these algorithms on near-term quantum computers with various hardware implementations and demonstrate how they relate to a wide range of use cases in finance. We hope this article will not only serve as a reference for academic researchers and industry practitioners but also inspire new ideas for future research.

show abstract

Section: Anomaly Detectionmentioning

confidence: 99%

A Survey of Quantum Computing for Finance

Herman¹,

Googin²,

Liu³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Recently, quantum computing has exhibited potential acceleration advantages over classical computing by exploiting the unique properties of supposition and entanglement in quantum mechanics in solving certain problems, such as factoring integers [7], unstructured database searching [8], solving equations [9][10][11], regression [12][13][14], dimensionality reduction [15][16][17], anomaly detection [18,19] and neural network [20]. Therefore, some scholars have proposed employing quantum algorithm to solve eigenproblem of the Laplacian matrix.…”

Section: Introductionmentioning

confidence: 99%

A quantum algorithm for solving eigenproblem of the Laplacian matrix of a fully connected weighted graph

Liu¹,

Qin²,

Wan³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

Solving eigenproblem of the Laplacian matrix of a fully connected graph has wide applications in data science, machine learning, and image processing, etc. However, it is very challenging because it involves expensive matrix operations. Here, we propose an efficient quantum algorithm to solve it based on a general assumption that the element of each vertex and its norms can be accessed via a quantum random access data structure. Specifically, we propose in detail how to construct the block-encodings of operators containing the information of the weight matrix and the degree matrix respectively, and further obtain the block-encoding of the Laplacian matrix. This enables us to implement the quantum simulation of the Laplacian matrix by employing the optimal Hamiltonian simulation technique based on the block-encoding framework. Afterwards, the eigenvalues and eigenvectors of the Laplacian matrix are extracted by the quantum phase estimation algorithm. Compared with its classical counterpart, our algorithm has a polynomial speedup on the number of vertices and an exponential speedup on the dimension of each vertex over its classical counterpart. We also show that our algorithm can be extended to solve the eigenproblem of symmetric (nonsymmetric) normalized Laplacian matrix.

show abstract

Quantum algorithms for anomaly detection using amplitude estimation

Cited by 2 publications

References 34 publications

A Survey of Quantum Computing for Finance

A Survey of Quantum Computing for Finance

A quantum algorithm for solving eigenproblem of the Laplacian matrix of a fully connected weighted graph

Contact Info

Product

Resources

About