Variational quantum multidimensional scaling algorithm

被引:0
作者
Xinglan Zhang
Feng Zhang
Yankun Guo
Fei Chen
机构
[1] Beijing University of Technology,Faculty of Information Technology
[2] Beijing Key Laboratory of Trusted Computing,undefined
来源
Quantum Information Processing | / 23卷
关键词
Quantum multidimensional scaling; Quantum dimensionality reduction; Variational quantum algorithm; Variational quantum multidimensional scaling; Qiskit;
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摘要
Quantum multidimensional scaling is a quantum dimensionality reduction algorithm. Its complex quantum circuit design structure and excessive qubits consumption make it difficult to run on the current quantum computers. In order to solve this problem, this paper proposes the variational quantum multidimensional scaling algorithm based on the variational quantum algorithm. Utilizing the parallel advantages of quantum computing to quickly compute low-dimensional embeddings of high-dimensional data, the variational quantum multidimensional scaling algorithm can provide lower time complexity; compared with the non-variational quantum multidimensional scaling algorithm, the variational quantum multidimensional scaling algorithm provides a simpler quantum circuit. In the noisy intermediate scale quantum era, the algorithm can run on a quantum computer. In addition, the article finally implemented the variational quantum multidimensional scaling algorithm on the Qiskit framework, proving the correctness of the algorithm.
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共 172 条
[1]  
Daley AJ(2022)Practical quantum advantage in quantum simulation Nature 607 667-676
[2]  
Bloch I(2019)Quantum data compression by principal component analysis Quantum Inf. Process. 18 1-20
[3]  
Kokail C(1987)Principal component analysis Chemom. Intell. Lab. Syst. 2 37-52
[4]  
Flannigan S(2000)Nonlinear dimensionality reduction by locally linear embedding Science 290 2323-2326
[5]  
Pearson N(2001)Quantum computation and quantum information Phys. Today 54 60-371
[6]  
Troyer M(2009)Quantum algorithm for linear systems of equations Phys. Rev. Lett. 103 359-633
[7]  
Zoller P(2007)Efficient quantum algorithms for simulating sparse hamiltonians Commun. Math. Phys. 270 631-21
[8]  
Yu C-H(2014)Quantum principal component analysis Nat. Phys. 10 1-17
[9]  
Gao F(2016)Quantum discriminant analysis for dimensionality reduction and classification New J. Phys. 18 79-644
[10]  
Lin S(2019)Quantum algorithm and quantum circuit for a-optimal projection: Dimensionality reduction Phys. Rev. A 99 1-2830