arXiv subjects

Yingjian Liu

Publications and source records attributed to Yingjian Liu.

14 recordsLinked to original sources

arXiv2026

Unifying Qubit Routing Across Diverse Quantum ISAs via Canonical Representation

Qubit mapping/routing is a critical stage in compilation for both near-term and fault-tolerant quantum computers, yet existing scalable methods typically impose several times the routing overhead in terms of circuit depth or duration. This inefficiency stems from a fundamental disconnect: compilers rely on an abstract routing model (e.g., three-CX-unrolled SWAP insertion) that completely ignores the idiosyncrasies of native gates supported by physical devices. Recent hardware breakthroughs have enabled high-precision implementations of diverse instruction set architectures (ISAs) beyond standard CX-based gates. Advanced ISAs involving gates such as $\mathrm{\sqrt{iSWAP}}$ and $\mathrm{ZZ}(θ)$ gates offer superior circuit synthesis capabilities and can be realized with higher fidelities. However, systematic compiler optimization strategies tailored to these advanced ISAs are lacking. To address this, we propose Canopus, a unified qubit mapping/routing framework applicable to diverse quantum ISAs. Built upon the canonical representation of two-qubit gates, Canopus centers on qubit routing to perform deep co-optimization in an ISA-aware approach. Canopus leverages the two-qubit canonical representation and the monodromy polytope theory to model the synthesis cost for more intelligent SWAP insertion during qubit routing. We also formalize the commutation relations between two-qubit gates through the canonical form, providing a generalized approach to commutativity-based optimization. Experiments show that Canopus consistently reduces routing overhead by 15%-35% compared to state-of-the-art methods across various backend ISAs and device topologies. More broadly, this work establishes a coherent method for co-exploration of program patterns, quantum ISAs, and hardware topologies, yielding concrete guidelines for hardware-software co-design.

quant-ph↗

arXiv2026

Graph Theoretic Approach to Quantum Nonstabilizerness

Detecting nonstabilizerness requires full tomography and an optimization over exponentially many stabilizer states. A limited Pauli measurement set promises resource-efficient magic certification, yet the resulting reduced stabilizer polytope is generally difficult to characterize. We trace this difficulty into two coupled obstructions: the simultaneous measurability of measurements captured by their frustration graph structure, and the consistency of sign dependencies from stabilizer formalism. We show that the sign dependencies can be discarded exactly whenever active dependencies are absent, and that perfect frustration graphs then make this reduced polytope efficiently solvable. This solvable regime derives a closed form bounded by the clique number of the frustration graph, revealing a tradeoff between witness capacity and simultaneous measurability. Clifford covariance allows rotated measurement sets to enlarge the detectable state space without raising the capacity. Graph structure therefore emerges as both a certificate of tractability and a design principle for scalable magic resource detection.

quant-ph↗

arXiv2026

Regularity of Lyapunov exponents at one-point Lyapunov spectra: the semisimple case

We study the regularity of Lyapunov exponents as functions on the space of compactly supported probability measures on $\mathrm{GL}(d,\mathbb{R})$. We prove that the Lyapunov exponents are pointwise log-Hölder continuous with respect to the Wasserstein distance, at semisimple probability measures with one-point Lyapunov spectrum. The proof relies on a decomposition of the action into virtually conformal subspaces and a Berry-Esseen type estimate for the random walk towards these subspaces.

math.DS↗

arXiv2025

A Convolutional Hierarchical Deep-learning Neural Network (C-HiDeNN) Framework for Non-linear Finite Element Analysis

We present a framework for the Convolutional Hierarchical Deep-learning Neural Network (C-HiDeNN) tailored for nonlinear finite element analysis. Building upon the structured foundation of HiDeNN, C-HiDeNN introduces a convolution operator to enhance numerical approximation. A distinctive feature of C-HiDeNN is its higher-order accurate approximation achieved through an expanded set of parameters, such as the polynomial order 'p,' dilation parameter 'a,' patch size 's,' and nodal position 'X'. These parameters function as the functional equivalents of weights and biases within each C-HiDeNN patch. In addition, C-HiDeNN can be selectively applied to regions requiring high resolution to adaptively improve local prediction accuracy. To demonstrate the effectiveness of this framework, we provide numerical examples in the context of nonlinear finite element analysis. The results show that our approach achieves significantly higher accuracy than conventional Finite Element Method (FEM) while substantially reducing computational costs.

math.NA↗

arXiv2025

Quantum Algorithm for Reversing Unknown Unitary Evolutions

Reversing an unknown quantum evolution is of central importance to quantum information processing and fundamental physics, yet it remains a formidable challenge as conventional methods necessitate an infinite number of queries to fully characterize the quantum process. Here we introduce the Quantum Unitary Reversal Algorithm (QURA), a deterministic and exact approach to universally reverse arbitrary unknown unitary transformations using $\mathcal{O}(d^2)$ calls of the unitary, where $d$ is the system dimension. Our quantum algorithm resolves a fundamental problem of time-reversal simulations for closed quantum systems by confirming the feasibility of reversing any unitary evolution without knowing the exact process. The algorithm also provides the construction of a key oracle for unitary inversion in many quantum algorithm frameworks, such as quantum singular value transformation. It notably reveals a sharp boundary between the quantum and classical computing realms and unveils a quadratic quantum advantage in computational complexity for this foundational task.

quant-ph↗

arXiv2025

Sample-Efficient Estimation of Nonlinear Quantum State Functions

Efficient estimation of nonlinear functions of quantum states is crucial for various key tasks in quantum computing, such as entanglement spectroscopy, fidelity estimation, and feature analysis of quantum data. Conventional methods using state tomography and estimating numerous terms of the series expansion are computationally expensive, while alternative approaches based on a purified query oracle impose practical constraints. In this paper, we introduce the quantum state function (QSF) framework by extending the SWAP test via linear combination of unitaries and parameterized quantum circuits. Our framework enables the implementation of arbitrarily normalized degree-$n$ polynomial functions of quantum states with precision $\varepsilon$ using $\mathcal{O}(n/\varepsilon^2)$ copies. We further apply QSF for developing quantum algorithms for fundamental tasks, including entropy, fidelity, and eigenvalue estimations. Specifically, for estimating von Neumann entropy, quantum relative entropy, and quantum state fidelity, where $κ$ and $γ$ represent the minimal nonzero eigenvalue and normalized factor, respectively, we achieve a sample complexity of $\tilde{\mathcal{O}}(γ^2/(\varepsilon^2κ))$. Our work establishes a concise and unified paradigm for estimating and realizing nonlinear functions of quantum states, paving the way for the practical processing and analysis of quantum data.

quant-ph↗

arXiv2025

Quantum Algorithms for Inverse Participation Ratio Estimation in multi-qubit and multi-qudit systems

Inverse Participation Ratios (IPRs) and the related Participation Entropies quantify the spread of a quantum state over a selected basis of the Hilbert space, offering insights into the equilibrium and non-equilibrium properties of the system. In this work, we propose three quantum algorithms to estimate IPRs on multi-qubit and multi-qudit quantum devices. The first algorithm allows for the estimation of IPRs in the computational basis by single-qubit measurements, while the second one enables measurement of IPR in the eigenbasis of a selected Hamiltonian, without the knowledge about the eigenstates of the system. Next, we provide an algorithm for IPR in the computational basis for a multi-qudit system. We discuss resources required by the algorithms and benchmark them by investigating the one-axis twisting protocol, the thermalization in a deformed PXP model, and the ground state of a spin-$1$ AKLT chain in a transverse field.

quant-ph↗

arXiv2025

Hypothesis testing of symmetry in quantum dynamics

Symmetry plays a crucial role in quantum physics, dictating the behavior and dynamics of physical systems. In this paper, we develop a hypothesis-testing framework for quantum dynamics symmetry using a limited number of queries to the unknown unitary operation and establish the quantum max-relative entropy lower bound for the type-II error. We construct optimal ancilla-free protocols that achieve optimal type-II error probability for testing time-reversal symmetry (T-symmetry) and diagonal symmetry (Z-symmetry) with limited queries. Contrasting with the advantages of indefinite causal order strategies in various quantum information processing tasks, we show that parallel, adaptive, and indefinite causal order strategies have equal power for our tasks. We establish optimal protocols for T-symmetry testing and Z-symmetry testing for 6 and 5 queries, respectively, from which we infer that the type-II error exhibits a decay rate of $\mathcal{O}(m^{-2})$ with respect to the number of queries $m$. This represents a significant improvement over the basic repetition protocols without using global entanglement, where the error decays at a slower rate of $\mathcal{O}(m^{-1})$.

quant-ph↗

arXiv2025

Parameterized quantum comb and simpler circuits for reversing unknown qubit-unitary operations

Quantum combs play a vital role in characterizing and transforming quantum processes, with wide-ranging applications in quantum information processing. However, obtaining the explicit quantum circuit for the desired quantum comb remains a challenging problem. We propose PQComb, a novel framework that employs parameterized quantum circuits (PQCs) or quantum neural networks to harness the full potential of quantum combs for diverse quantum process transformation tasks. This method is well-suited for near-term quantum devices and can be applied to various tasks in quantum machine learning. As a notable application, we present two streamlined protocols for the time-reversal simulation of unknown qubit unitary evolutions, reducing the ancilla qubit overhead from six to three compared to the previous best-known method. We also extend PQComb to solve the problems of qutrit unitary transformation and channel discrimination. Furthermore, we demonstrate the hardware efficiency and robustness of our qubit unitary inversion protocol under realistic noise simulations of IBM-Q superconducting quantum hardware, yielding a significant improvement in average similarity over the previous protocol under practical regimes. PQComb's versatility and potential for broader applications in quantum machine learning pave the way for more efficient and practical solutions to complex quantum tasks.

quant-ph↗

arXiv2025

Optimizer-Dependent Generalization Bound for Quantum Neural Networks

Quantum neural networks (QNNs) play a pivotal role in addressing complex tasks within quantum machine learning, analogous to classical neural networks in deep learning. Ensuring consistent performance across diverse datasets is crucial for understanding and optimizing QNNs in both classical and quantum machine learning tasks, but remains a challenge as QNN's generalization properties have not been fully explored. In this paper, we investigate the generalization properties of QNNs through the lens of learning algorithm stability, circumventing the need to explore the entire hypothesis space and providing insights into how classical optimizers influence QNN performance. By establishing a connection between QNNs and quantum combs, we examine the general behaviors of QNN models from a quantum information theory perspective. Leveraging the uniform stability of the stochastic gradient descent algorithm, we propose a generalization error bound determined by the number of trainable parameters, data uploading times, dataset dimension, and classical optimizer hyperparameters. Numerical experiments validate this comprehensive understanding of QNNs and align with our theoretical conclusions. As the first exploration into understanding the generalization capability of QNNs from a unified perspective of design and training, our work offers practical insights for applying QNNs in quantum machine learning.

quant-ph↗

arXiv2024

CFN-ESA: A Cross-Modal Fusion Network with Emotion-Shift Awareness for Dialogue Emotion Recognition

Multimodal emotion recognition in conversation (ERC) has garnered growing attention from research communities in various fields. In this paper, we propose a Cross-modal Fusion Network with Emotion-Shift Awareness (CFN-ESA) for ERC. Extant approaches employ each modality equally without distinguishing the amount of emotional information in these modalities, rendering it hard to adequately extract complementary information from multimodal data. To cope with this problem, in CFN-ESA, we treat textual modality as the primary source of emotional information, while visual and acoustic modalities are taken as the secondary sources. Besides, most multimodal ERC models ignore emotion-shift information and overfocus on contextual information, leading to the failure of emotion recognition under emotion-shift scenario. We elaborate an emotion-shift module to address this challenge. CFN-ESA mainly consists of unimodal encoder (RUME), cross-modal encoder (ACME), and emotion-shift module (LESM). RUME is applied to extract conversation-level contextual emotional cues while pulling together data distributions between modalities; ACME is utilized to perform multimodal interaction centered on textual modality; LESM is used to model emotion shift and capture emotion-shift information, thereby guiding the learning of the main task. Experimental results demonstrate that CFN-ESA can effectively promote performance for ERC and remarkably outperform state-of-the-art models.

cs.CL↗

arXiv2024

EmotionIC: emotional inertia and contagion-driven dependency modeling for emotion recognition in conversation

Emotion Recognition in Conversation (ERC) has attracted growing attention in recent years as a result of the advancement and implementation of human-computer interface technologies. In this paper, we propose an emotional inertia and contagion-driven dependency modeling approach (EmotionIC) for ERC task. Our EmotionIC consists of three main components, i.e., Identity Masked Multi-Head Attention (IMMHA), Dialogue-based Gated Recurrent Unit (DiaGRU), and Skip-chain Conditional Random Field (SkipCRF). Compared to previous ERC models, EmotionIC can model a conversation more thoroughly at both the feature-extraction and classification levels. The proposed model attempts to integrate the advantages of attention- and recurrence-based methods at the feature-extraction level. Specifically, IMMHA is applied to capture identity-based global contextual dependencies, while DiaGRU is utilized to extract speaker- and temporal-aware local contextual information. At the classification level, SkipCRF can explicitly mine complex emotional flows from higher-order neighboring utterances in the conversation. Experimental results show that our method can significantly outperform the state-of-the-art models on four benchmark datasets. The ablation studies confirm that our modules can effectively model emotional inertia and contagion.

cs.CL↗

arXiv2024

ERNetCL: A novel emotion recognition network in textual conversation based on curriculum learning strategy

Emotion recognition in conversation (ERC) has emerged as a research hotspot in domains such as conversational robots and question-answer systems. How to efficiently and adequately retrieve contextual emotional cues has been one of the key challenges in the ERC task. Existing efforts do not fully model the context and employ complex network structures, resulting in limited performance gains. In this paper, we propose a novel emotion recognition network based on curriculum learning strategy (ERNetCL). The proposed ERNetCL primarily consists of temporal encoder (TE), spatial encoder (SE), and curriculum learning (CL) loss. We utilize TE and SE to combine the strengths of previous methods in a simplistic manner to efficiently capture temporal and spatial contextual information in the conversation. To ease the harmful influence resulting from emotion shift and simulate the way humans learn curriculum from easy to hard, we apply the idea of CL to the ERC task to progressively optimize the network parameters. At the beginning of training, we assign lower learning weights to difficult samples. As the epoch increases, the learning weights for these samples are gradually raised. Extensive experiments on four datasets exhibit that our proposed method is effective and dramatically beats other baseline models.

cs.CL↗

arXiv2023

Watch the Speakers: A Hybrid Continuous Attribution Network for Emotion Recognition in Conversation With Emotion Disentanglement

Emotion Recognition in Conversation (ERC) has attracted widespread attention in the natural language processing field due to its enormous potential for practical applications. Existing ERC methods face challenges in achieving generalization to diverse scenarios due to insufficient modeling of context, ambiguous capture of dialogue relationships and overfitting in speaker modeling. In this work, we present a Hybrid Continuous Attributive Network (HCAN) to address these issues in the perspective of emotional continuation and emotional attribution. Specifically, HCAN adopts a hybrid recurrent and attention-based module to model global emotion continuity. Then a novel Emotional Attribution Encoding (EAE) is proposed to model intra- and inter-emotional attribution for each utterance. Moreover, aiming to enhance the robustness of the model in speaker modeling and improve its performance in different scenarios, A comprehensive loss function emotional cognitive loss $\mathcal{L}_{\rm EC}$ is proposed to alleviate emotional drift and overcome the overfitting of the model to speaker modeling. Our model achieves state-of-the-art performance on three datasets, demonstrating the superiority of our work. Another extensive comparative experiments and ablation studies on three benchmarks are conducted to provided evidence to support the efficacy of each module. Further exploration of generalization ability experiments shows the plug-and-play nature of the EAE module in our method.

cs.CL↗