arXiv subjects

Yanying Liang

Publications and source records attributed to Yanying Liang.

11 recordsLinked to original sources

arXiv2026

iSWAP maximises the second-moment spectral gap in random quantum circuits

We prove that the $\mathrm{iSWAP}$ gate maximises the spectral gap of the Hermitian second-moment operator on every connected graph with at least three vertices, among all two-local unitary circuit ensembles. We further prove that the polyhedral cone defined by asymmetric four-point inequalities is invariant under the transpose of the $\mathrm{iSWAP}$ semigroup, yielding a componentwise comparison certificate for its positive Perron--Frobenius eigenvector. These results resolve a conjecture of Kong, Li, and Liu.

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arXiv2026

Spectral gaps of ironed two-qubit gadgets matching the iSWAP gap

We prove that every ironed two-qubit gadget whose KAK-derived parameter satisfies $a=5/9$ has, on the complete graph $K_n$ with $n\geqslant 5$, the same second-moment spectral gap as the iSWAP gadget. The central step is a representation-theoretic localisation theorem: the largest strictly negative eigenvalue of the associated $\mathfrak S_n$-invariant operator always occurs in the highest-spin $\mathrm{SU}(2)$ summand. A local positive-semidefinite decomposition separates every spin sector except the two highest. This settles a conjecture of Kong, Li, and Liu.

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arXiv2026

A Dynamical Lie-Algebraic Framework for Hamiltonian Engineering and Quantum Control

Determining the unitary dynamics accessible from finite Hamiltonian resources is a central problem in Hamiltonian engineering and quantum control. Dynamical Lie algebras (DLAs) connect available control Hamiltonians with the reachable dynamics, but their use as a design tool for modifying Hamiltonian generator sets remains less developed. In this work, we develop a finite-dimensional DLA framework for three generator-set operations: composition, invariance, and reduction. For composition, we construct direct sums of component DLAs using spectral projectors on an auxiliary register. For invariance, we analyze when modifications of Pauli-string generating sets preserve the generated Lie algebra, and introduce algebraic diagnostics for added generators. For reduction, we consider compact reductive DLAs and show how projection onto selected simple ideals gives reduced generating sets whose Lie closures are the corresponding ideal sums. We illustrate these results with finite-dimensional examples and numerical checks, including direct-sum dimension addition, central-spin invariance diagnostics, and DLA-based ansatz reduction for block-local Hamiltonians. The results show how DLA structure can be used to diagnose controllability and guide Hamiltonian generator design under explicit algebraic assumptions.

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arXiv2025

Entangled mixed-state datasets generation by quantum machine learning

The advancement of classical machine learning is inherently linked to the establishment and progression of classical dataset. In quantum machine learning (QML), there is an analogous imperative for the development of quantum entangled datasets comprised with huge quantity and high quality. Especially for multipartite mixed-state datasets, due to the lack of suitable entanglement criteria, previous researchers often could only perform classification tasks on datasets extended based on Werner states or other well-structured states. This paper is dedicated to provide a method for generating mixed-state datasets for entangled-separable classification tasks. This method is based on supervised quantum machine learning and the concentratable entanglement measures. It furthers the assembly of quantum entangled datasets, inspires the discovery of new entanglement criteria with both classical and quantum machine learning, and provides a valuable resource for benchmarking QML models, thereby opening new avenues for exploring the rich structure of quantum entanglement in mixed states. Additionally, we benchmark several machine learning models using this dataset, offering guidance and suggestions for the selection of QML models.

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arXiv2024

Enhancing Variational Quantum Circuit Training: An Improved Neural Network Approach for Barren Plateau Mitigation

Combining classical optimization with parameterized quantum circuit evaluation, variational quantum algorithms (VQAs) are among the most promising algorithms in near-term quantum computing. Similar to neural networks (NNs), VQAs iteratively update circuit parameters to optimize a cost function. However, the training of variational quantum circuits (VQCs) is susceptible to a phenomenon known as barren plateaus (BPs). Various methods have been proposed to mitigate this issue, such as using neural networks to generate VQC parameters. In this paper, we improve the NN-based BP mitigation approach by refining the neural network architecture and extend its applicability to a more generalized scenario that includes random quantum inputs and VQC structures. We evaluate the effectiveness of this approach by comparing the convergence speed before and after it is utilized. Furthermore, we give an explanation for the effectiveness of this method by utilizing a loss landscape visualization technique and the expressibility metric of VQC. The smoothness of the loss landscape offers an intuitive insight into the method's utility, while the reduction in expressibility accounts for the enhanced trainability. Our research highlights the universal applicability of the NN-based BP mitigation approach, underscoring its potential to drive progress in the development of VQAs across diverse domains.

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arXiv2024

Learnability of a hybrid quantum-classical neural network for graph-structured quantum data

Graph-structured data commonly arise in many real-world applications, and this extends naturally into the quantum setting, where quantum data with inherent graph structures are frequently generated by typical quantum data sources. However, existing state-of-the-art models often lack training and evaluation on deeper quantum neural networks. In this work, we design a hybrid quantum-classical neural network with deep residual learning, termed Res-HQCNN, specifically designed to handle graph-structured quantum data.Building upon this architecture, we systematically explore the interplay between residual block structures and graph information in both training and testing phases. Through extensive experiments, we demonstrate that incorporating graph structure information into the quantum data significantly improves learning efficiency compared to the existing model. Additionally, we conduct comparative experiments to evaluate the effectiveness of residual blocks. Our results show that the residual structure enables deeper Res-HQCNN models to learn graph-structured quantum data more efficiently and accurately.

quant-ph↗

arXiv2024

Polygamy relations for tripartite and multipartite quantum systems

We study the polygamy property for tripartite and multipartite quantum systems. In tripartite system, we build a solution set for polygamy in tripartite system and find a lower bound of the set, which can be a sufficient and necessary condition for any quantum entanglement of assistance $Q$ to be polygamous. In multipartite system, we firstly provide generalized definitions for polygamy in two kind of divisions of $n$-qubit systems, and then build polygamy inequalities with a polygamy power $β$, repectively. Moreover, we use right triangle and tetrahedron to explain our polygamy relations according to the new definitions.

quant-ph↗

arXiv2021

A hybrid quantum-classical neural network with deep residual learning

Inspired by the success of classical neural networks, there has been tremendous effort to develop classical effective neural networks into quantum concept. In this paper, a novel hybrid quantum-classical neural network with deep residual learning (Res-HQCNN) is proposed. We firstly analysis how to connect residual block structure with a quantum neural network, and give the corresponding training algorithm. At the same time, the advantages and disadvantages of transforming deep residual learning into quantum concept are provided. As a result, the model can be trained in an end-to-end fashion, analogue to the backpropagation in classical neural networks. To explore the effectiveness of Res-HQCNN , we perform extensive experiments for quantum data with or without noisy on classical computer. The experimental results show the Res-HQCNN performs better to learn an unknown unitary transformation and has stronger robustness for noisy data, when compared to state of the arts. Moreover, the possible methods of combining residual learning with quantum neural networks are also discussed.

cs.LG↗

arXiv2020

Monogamy relations and upper bounds for the generalized $W$-class states using Rényi-$α$ entropy

We investigate monogamy relations and upper bounds for generalized $W$-class states related to the Rényi-$α$ entropy. First, we present an analytical formula on Rényi-$α$ entanglement (R$α$E) and Rényi-$α$ entanglement of assistance (REoA) of a reduced density matrix for a generalized $W$-class states. According to the analytical formula, we show monogamy and polygamy relations for generalized $W$-class states in terms of R$α$E and REoA. Then we give the upper bounds for generalized $W$-class states in terms of R$α$E. Next, we provide tighter monogamy relations for generalized $W$-class states in terms of concurrence and convex-roof extended negativity and obtain the monogamy relations for R$α$E by the analytical expression between R$α$E and concurrence. Finally, we apply our results into quantum games and present a new bound of the nonclassicality of quantum games restricting to generalized $W$-class states.

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arXiv2019

Tighter monogamy and polygamy relations using Rényi-$α$ entropy

We investigate monogamy relations related to the Rényi-$α$ entanglement and polygamy relations related to the Rényi-$α$ entanglement of assistance. We present new entanglement monogamy relations satisfied by the $μ$-th power of Rényi-$α$ entanglement with $α\in[\sqrt{7}-1)/2,(\sqrt{13}-1)/2]$ for $μ\geqslant2$, and polygamy relations satisfied by the $μ$-th power of Rényi-$α$ entanglement of assistance with $α\in[\sqrt{7}-1)/2,(\sqrt{13}-1)/2]$ for $0\leqμ\leq1$. These relations are shown to be tighter than the existing ones.

quant-ph↗

arXiv2017

General Monogamy Relations for Multiqubit W-class States in terms of negativity and squared Rényi-$α$ entanglement

For multipartite entangled states, entanglement monogamy is an important property. We investigate the monogamy relations for multiqubit generalized W-class states. We present new analytical monogamy inequalities satisfied by the $x$-th power of the dual of convex-roof extended negativity, namely CRENOA, for $x\geq2$ and $x\leq0$. As for The squared Rényi-$α$ entanglement (SR$α$E) with $α$ in the region $[(\sqrt 7 - 1)/2,(\sqrt {13} - 1)/2]$, we show the upper bound of SR$α$E.

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