.png){kind=icon}
返回
Resource-efficient quantum principal component analysis
.png){kind=icon}
PRE
AI
DOI：10.1088/2058-9565/ad466c.png)
.png){kind=icon}
原文求助.png){kind=icon}
分享.png){kind=icon}
收藏
摘要
En 中文
Principal component analysis (PCA) is an important dimensionality reduction method in machine learning and data analysis. Recently, the quantum version of PCA has been established to diagonalize quantum states. Although these quantum algorithms promise quantum advantages, they require substantial resources beyond the reach of state-of-the-art quantum technologies. This work aims to reduce resource requirements and improve the efficiency of quantum PCA. Assuming that the quantum state is accessed through a purified quantum query model and a sampling model, we propose quantum algorithms that use minimal resource requirements for ancillary qubits to reveal properties of eigenvectors and eigenvalues of a state. In particular, we show that estimating eigenvalue lambda with error epsilon and success probability larger than lambda(1 - eta) requests a query complexity (O) over tilde(epsilon(- 1)) and a sample complexity (O) over tilde(epsilon(-2) eta(- 1)) , respectively. To our knowledge, our result is the first quantum speedup that achieves asymptotic linear scaling in 1 / epsilon for quantum PCA. As applications, we discuss estimating the minimum relative entropy of entanglement of bipartite pure-states and performing quantum state discrimination tasks. We show that quantum speedups are maintained when the pure state has a low Schmidt number and states of discrimination have a low rank. This study opens up a new quantum PCA method for high-dimensional quantum data analysis and discusses its application in quantum information processing tasks.
Keyword:
quantum computing
quantum machine learning
principal component analysis
期刊
IF:
5
论文数:
1.4K
被引数:
5.1K
机构
引用论文
.png){kind=icon}
查看更多内容