Quantum algorithm for support matrix machines

Duan, Bojia; Yuan, Jian; Liu, Ying; Li, Dan

doi:10.1103/physreva.96.032301

Cited by 64 publications

(37 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…are all initialized by |0⟩, the register B is initialized by the threshold |τ ⟩, the register M is initialized by the quantum state |ψ A0 ⟩. Then using Gram-Schmidt decomposition, we have [6]…”

Section: A Initializationmentioning

confidence: 99%

“…Time complexity: Now we study the time complexity of U P E . The Hamilton simulation e 2πiρt0 , with t 0 = O(κ/ϵ) (κ is the condition number of the matrix A, ϵ is the error of the Hamilton simulation), can be simulated by using O(t 2 0 ϵ −1 ) copies of e 2πiρ∆t for the time slice ∆t [6]. Based on (11), the time complexity of each of the above copies is determined by the time complexity of preparing |ψ A0 ⟩, which is O(log(pq)).…”

Section: B Phase Estimation I ⊗ U P Ementioning

confidence: 99%

“…This small trick makes the total number of phase estimations down to three. As the runtime of the phase estimations dominates other that of other operations [6], the proposed qPCA achieves a runtime of roughly 3 5 of that of [5]. This paper is organized as follows: In Section II, we review the qPCA algorithm proposed by Lin et al.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Low-Complexity Quantum Principal Component Analysis Algorithm

He¹,

Li²,

Liu³

et al. 2022

IEEE Trans. Quantum Eng.

View full text Add to dashboard Cite

In this paper, we propose a low complexity quantum principal component analysis (qPCA) algorithm. Similar to the state-of-the-art qPCA, it achieves dimension reduction by extracting principal components of the data matrix, rather than all components of the data matrix, to quantum registers, so that the samples of measurement required can be reduced considerably. Both our qPCA and Lin's qPCA are based on the quantum singular value thresholding (QSVT). The key of Lin's qPCA is to combine QSVT and modified QSVT (MQSVT) to obtain the superposition of the principle components. The key of our algorithm, however, is to modify QSVT by replacing the rotation controlled operation of QSVT with the controllednot operation, to obtain the superposition of the principal components. As a result, this small trick makes the circuit much simpler. Particularly, the proposed qPCA requires 3 phase estimations, while the the state-of-the-art qPCA requires 5. Since the runtime of qPCA mainly comes from phase estimations, the proposed qPCA achieves a runtime of roughly 3 5 of that of the state-of-the-art. We simulate the proposed qPCA on the IBM quantum computing platform, and the simulation result verifies that the proposed qPCA yields the expected quantum state.

show abstract

Section: A Initializationmentioning

confidence: 99%

Section: B Phase Estimation I ⊗ U P Ementioning

confidence: 99%

See 1 more Smart Citation

A Low-Complexity Quantum Principal Component Analysis Algorithm

He¹,

Li²,

Liu³

et al. 2022

IEEE Trans. Quantum Eng.

View full text Add to dashboard Cite

show abstract

“…This significant reduction in the time complexity is due to the introduction of the approximation concept. While the classical algorithms always provide an exact solution (x), the quantum HHL algorithm in an approximate solution [80].…”

Section: Approximate Computingmentioning

confidence: 99%

Resource Optimal Executable Quantum Circuit Generation Using Approximate Computing

Adarsh

Möller

2021

2021 IEEE International Conference on Quantum Computing and Engineering (QCE)

View full text Add to dashboard Cite

“…The quantum state preparation algorithms [32]- [36], quantum phase estimation [37] and quantum Hamiltonian simulations [38]- [45] have been used as the base toolkits for above quantum machine learning algorithms. For example, the quantum phase estimation and quantum Hamiltonian simulations can be performed for solving linear systems of equations [20]- [25], quantum support vector or matrix machines [26], [27], quantum dimensionality reduction algorithms [18], [28], and so forth. Quantum ridge regression algorithms were proposed in [29] and [30].…”

Section: Introductionmentioning

confidence: 99%

Quantum Algorithm for Spectral Regression for Regularized Subspace Learning

Meng

Xiang

et al. 2019

IEEE Access

View full text Add to dashboard Cite

In this paper, we propose an efficient quantum algorithm for spectral regression which is a dimensionality reduction framework based on the regression and spectral graph analysis. The quantum algorithm involves two core subroutines: the quantum principal eigenvectors analysis and the quantum ridge regression algorithm. The quantum principal eigenvectors analysis can be performed by an efficient sparse Hamiltonian simulation. For the ridge regression, we propose a quantum algorithm that is derived from the quantum singular value decomposition method. Our quantum ridge regression algorithm is more suitable for data matrices that are non-sparse and skewed. Our analysis demonstrates that the quantum subroutines can be implemented with an approximatively polynomial speedup on a quantum computer over their classical counterparts. INDEX TERMS Spectral regression, dimensionality reduction, quantum principal eigenvectors analysis, quantum ridge regression.

show abstract

Quantum algorithm for support matrix machines

Cited by 64 publications

References 18 publications

A Low-Complexity Quantum Principal Component Analysis Algorithm

A Low-Complexity Quantum Principal Component Analysis Algorithm

Resource Optimal Executable Quantum Circuit Generation Using Approximate Computing

Quantum Algorithm for Spectral Regression for Regularized Subspace Learning

Contact Info

Product

Resources

About