arXiv subjects

Yong-Mei Li

Publications and source records attributed to Yong-Mei Li.

4 recordsLinked to original sources

arXiv2024

Variational quantum algorithm-preserving feasible space for solving the uncapacitated facility location problem

The Quantum Alternating Operator Ansatz (QAOA+) is one of the Variational Quantum Algorithm (VQA) specifically developed to tackle combinatorial optimization problems by exploring the feasible space in search of a target solution. For constrained optimization problems with unconstrained variables, which we call Unconstrained-Variables Problems (UVPs), the mixed operators in the QAOA+ circuit are applied to the constrained variables, while the single-qubit rotating gates $R_X$ operate on the unconstrained variables. The expressibility of this circuit is limited by the shortage of two-qubit gates and the parameter sharing in the $R_X$, which consequently impacts the performance of QAOA+ for solving UVPs. Therefore, it is crucial to develop a suitable ansatz for UVPs. In this paper, we propose the Variational Quantum Algorithm-Preserving Feasible Space (VQA-PFS) ansatz, exemplified by the Uncapacitated Facility Location Problem (UFLP), that applies mixed operators on constrained variables while employing Hardware-Efficient Ansatz (HEA) on unconstrained variables. The numerical results demonstrate that VQA-PFS significantly enhances the success probability and exhibits faster convergence compared to QAOA+, Quantum Approximation Optimization Algorithm (QAOA), and HEA. Furthermore, VQA-PFS reduces the circuit depth dramatically in comparison to QAOA+ and QAOA. Our algorithm is general and instructive in tackling UVPs.

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arXiv2023

A general quantum matrix exponential dimensionality reduction framework based on block-encoding

As a general framework, Matrix Exponential Dimensionality Reduction (MEDR) deals with the small-sample-size problem that appears in linear Dimensionality Reduction (DR) algorithms. High complexity is the bottleneck in this type of DR algorithm because one has to solve a large-scale matrix exponential eigenproblem. To address it, here we design a general quantum algorithm framework for MEDR based on the block-encoding technique. This framework is configurable, that is, by selecting suitable methods to design the block-encodings of the data matrices, a series of new efficient quantum algorithms can be derived from this framework. Specifically, by constructing the block-encodings of the data matrix exponentials, we solve the eigenproblem and then obtain the digital-encoded quantum state corresponding to the compressed low-dimensional dataset, which can be directly utilized as input state for other quantum machine learning tasks to overcome the curse of dimensionality. As applications, we apply this framework to four linear DR algorithms and design their quantum algorithms, which all achieve a polynomial speedup in the dimension of the sample over their classical counterparts.

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arXiv2022

Quantum discriminative canonical correlation analysis

Discriminative Canonical Correlation Analysis (DCCA) is a powerful supervised feature extraction technique for two sets of multivariate data, which has wide applications in pattern recognition. DCCA consists of two parts: (i) mean-centering that subtracts the sample mean from the sample; (ii) solving the generalized eigenvalue problem. The cost of DCCA is expensive when dealing with a large number of high-dimensional samples. To solve this problem, here we propose a quantum DCCA algorithm. Specifically, we devise an efficient method to compute the mean of all samples, then use block-Hamiltonian simulation and quantum phase estimation to solve the generalized eigenvalue problem. Our algorithm achieves a polynomial speedup in the dimension of samples under certain conditions over its classical counterpart.

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arXiv2021

Quantum algorithms for anomaly detection using amplitude estimation

Anomaly detection plays a critical role in fraud detection, health care, intrusion detection, military surveillance, etc. Anomaly detection algorithm based on density estimation (called ADDE algorithm) is one of widely used algorithms. Liang et al. proposed a quantum version of the ADDE algorithm [Phys. Rev. A 99, 052310 (2019)] and it is believed that the algorithm has exponential speedups on both the number and the dimension of training data point over the classical algorithm. In this paper, we find that Liang et al.'s algorithm doesn't actually execute. Then we propose a new quantum ADDE algorithm based on amplitude estimation. It is shown that our algorithm can achieves exponential speedup on the number $M$ of training data points compared with the classical counterpart. Besides, the idea of our algorithm can be applied to optimize the anomaly detection algorithm based on kernel principal component analysis (called ADKPCA algorithm). Different from the quantum ADKPCA proposed by Liu et al. [Phys. Rev. A 97, 042315 (2018)], compared with the classical counterpart, which offer exponential speedup on the dimension $d$ of data points, our algorithm achieves exponential speedup on $M$.

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