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- Title
Quantum locality preserving projection algorithm.
- Authors
He, Xiaoyun; Zhang, Anqi; Zhao, Shengmei
- Abstract
In this paper, we propose a quantum algorithm to efficiently perform locality preserving projection (LPP) for dimensionality reduction, named quantum locality preserving projection (QLPP). We present QLPP in 4 steps and give their corresponding quantum circuits. Furthermore, we give an improved algorithm to construct the density matrix proportional to the Hermitian/non-Hermitian chain product composed of multiple Hermitian/non-Hermitian matrices in QLPP. The analysis results show that the computation complexity of QLLP is O (d κ eff 10 m polylog (m) / ε 7) for m ≫ n , where κ eff is a predefined condition number, m is the number of training data with dimension n, d is the dimension of reduced dimension feature space, and ε denotes the tolerance error. It is polynomial speedup in m compared to classical LPP algorithm, whose complexity is O (m 2 n) .
- Subjects
DENSITY matrices; ALGORITHMS; HERMITIAN forms
- Publication
Quantum Information Processing, 2022, Vol 21, Issue 3, p1
- ISSN
1570-0755
- Publication type
Article
- DOI
10.1007/s11128-022-03424-w