arXiv subjects

Hua Xiang

Publications and source records attributed to Hua Xiang.

At least 19 recordsLinked to original sources

arXiv2026

Quantum algorithm for PageRank computation through multistep quantum resonant transitions

We present a quantum algorithm for obtaining a quantum state that encodes the PageRank vector of the Google matrix through multistep quantum resonant transition (mQRT). In the algorithm, the PageRank vector is encoded in the ground state of a problem Hamiltonian associated with the Google matrix. By dividing the web graph corresponding to the Google matrix into a series of subgraphs with nested structure, we construct a sequence of Hamiltonians based on the subgraphs to form a Hamiltonian evolution path from a simple initial Hamiltonian to the problem Hamiltonian. The ground state of the problem Hamiltonian is obtained by going through ground states of the intermediate Hamiltonians via QRT step by step. This algorithm requires only one ancillary qubit, and the runtime of the algorithm is proportional to the number of steps. It provides a new way for efficiently obtaining the quantum state of the PageRank vector of large-scale networks.

quant-ph↗

arXiv2026

Saving resources through repeat-until-success positive-operator-valued-measure measurements in quantum computation

We present a quantum computation approach in which computation is guided by positive-operator-valuedmeasure (POVM) measurements following a given computation path in multisteps. In this approach, one ancillary qubit is coupled to a register of working qubits, and a POVM measurement is implemented effectively on the working qubits by applying a unitary operation on the whole system followed by a projective measurement performed on the ancillary qubit. Each step of the computation is a repeat-until-success procedure such that the desired state of the step is obtained deterministically on the working qubits via POVM measurements. The principle of deferred measurement states that measurements can always be moved from an intermediate stage of a quantum circuit to the end of the circuit without affecting the efficiency of the computation.We demonstrate that in our approach, by introducing intermediate measurements on the ancillary qubit in the computation process, both the number of qubits and unitary operations can be reduced polynomially, compared to the case where the intermediate measurements are deferred to the end of the computation. We also provide a method for implementation of the approach.

quant-ph↗

arXiv2026

A Practical Semi-Quantum Signature Protocol with Improved Eavesdropping Detection

Semi-quantum signature (SQS) schemes aim to enable quantum signature functionality in scenarios where only a subset of participants possess full quantum capabilities, thereby improving practical deployability while preserving quantum security advantages. Within this framework, we present a practical SQS protocol based on Bell states. The protocol is designed so that only the signer requires full quantum capability, significantly alleviating the quantum burden on the remaining participants. To strengthen security in semi-quantum environments, we incorporate an improved eavesdropping-detection mechanism that more effectively detects tampering. Compared with many existing schemes, which do not explicitly consider tampering of already generated signatures in their unforgeability analyses, the proposed protocol is designed to remain secure in the presence of such tampering.

quant-ph↗

arXiv2026

MorphOPC: Advancing Mask Optimization with Multi-scale Hierarchical Morphological Learning

As feature sizes shrink to the nanometer scale, accurately transferring circuit patterns from photomasks to silicon wafers becomes increasingly challenging. Optical proximity correction (OPC) is widely used to ensure pattern fidelity and manufacturability. Recent generative mask optimization models based on encoder-decoder architecture can synthesize near-optimal masks, serving as fast machine learning (ML) surrogates for traditional OPC. However, these models often fail to capture the geometric transformations from target layouts to mask patterns, leading to suboptimal quality. In this work, we formulate mask generation as a sequence of morphological operations on local layout features and propose \textit{MorphOPC}, a multi-scale hierarchical model with neural morphological modules to learn these transformations. Experiments on edge-based OPC and ILT benchmarks across metal and via layers show that \textit{MorphOPC} consistently outperforms state-of-the-art methods, achieving higher printing fidelity and lower manufacturing cost, demonstrating strong potential for scalable mask optimization.

cs.CV↗

arXiv2025

MaskOpt: A Large-Scale Mask Optimization Dataset to Advance AI in Integrated Circuit Manufacturing

As integrated circuit (IC) dimensions shrink below the lithographic wavelength, optical lithography faces growing challenges from diffraction and process variability. Model-based optical proximity correction (OPC) and inverse lithography technique (ILT) remain indispensable but computationally expensive, requiring repeated simulations that limit scalability. Although deep learning has been applied to mask optimization, existing datasets often rely on synthetic layouts, disregard standard-cell hierarchy, and neglect the surrounding contexts around the mask optimization targets, thereby constraining their applicability to practical mask optimization. To advance deep learning for cell- and context-aware mask optimization, we present MaskOpt, a large-scale benchmark dataset constructed from real IC designs at the 45$\mathrm{nm}$ node. MaskOpt includes 104,714 metal-layer tiles and 121,952 via-layer tiles. Each tile is clipped at a standard-cell placement to preserve cell information, exploiting repeated logic gate occurrences. Different context window sizes are supported in MaskOpt to capture the influence of neighboring shapes from optical proximity effects. We evaluate state-of-the-art deep learning models for IC mask optimization to build up benchmarks, and the evaluation results expose distinct trade-offs across baseline models. Further context size analysis and input ablation studies confirm the importance of both surrounding geometries and cell-aware inputs in achieving accurate mask generation.

cs.LG↗

arXiv2025

Cross-platform Product Matching Based on Entity Alignment of Knowledge Graph with RAEA model

Product matching aims to identify identical or similar products sold on different platforms. By building knowledge graphs (KGs), the product matching problem can be converted to the Entity Alignment (EA) task, which aims to discover the equivalent entities from diverse KGs. The existing EA methods inadequately utilize both attribute triples and relation triples simultaneously, especially the interactions between them. This paper introduces a two-stage pipeline consisting of rough filter and fine filter to match products from eBay and Amazon. For fine filtering, a new framework for Entity Alignment, Relation-aware and Attribute-aware Graph Attention Networks for Entity Alignment (RAEA), is employed. RAEA focuses on the interactions between attribute triples and relation triples, where the entity representation aggregates the alignment signals from attributes and relations with Attribute-aware Entity Encoder and Relation-aware Graph Attention Networks. The experimental results indicate that the RAEA model achieves significant improvements over 12 baselines on EA task in the cross-lingual dataset DBP15K (6.59% on average Hits@1) and delivers competitive results in the monolingual dataset DWY100K. The source code for experiments on DBP15K and DWY100K is available at github (https://github.com/Mockingjay-liu/RAEA-model-for-Entity-Alignment).

cs.AI↗

arXiv2025

Generalized quantum singular value transformation with application in quantum conjugate gradient least squares algorithm

Quantum signal processing (QSP) and generalized quantum signal processing (GQSP) are essential tools for implementing the block encoding of matrix functions. The achievable polynomials of QSP have restrictions on parity, while GQSP eliminates these restrictions. But GQSP only constructs functions of unitary matrices. In this paper, we further investigate GQSP and extend it to general matrices. Compared with the quantum singular value transformation (QSVT), our proposed method relaxes the requirements on the parity of polynomials. We refer to this extension as generalized quantum singular value transformation (GQSVT). Subsequently, by utilizing the relationship between generalized matrix functions and standard matrix functions, we propose a classical-quantum hybrid quantum conjugate gradient least squares (CGLS) algorithm using GQSVT.

math.NA↗

arXiv2024

A generalized Nystrom method with column sketching for low-rank approximation of nonsymmetric matrices

This paper is concerned with the low-rank approximation for large-scale nonsymmetric matrices. Inspired by the classical Nystrom method, which is a popular method to find the low-rank approximation for symmetric positive semidefinite matrices, we explore an extension of the Nystrom method to approximate nonsymmetric matrices. The proposed method is a generalized Nystrom method with column sketching and shows its advantages in accuracy and speed without sacri cing stability. And the numerical experiments will illustrate the robustness of our new methods in finding a desired low-rank approximation of nonsymmetric matrix.

math.NA↗

arXiv2024

A characterization of entangled two-qubit states via partial-transpose-moments

Although quantum entanglement is an important resource, its characterization is quite challenging. The partial transposition is a common method to detect bipartite entanglement. In this paper, the authors study the partial-transpose(PT)-moments of two-qubit states,and completely describe the whole region, composed of the second and third PT-moments, for all two-qubit states. Furthermore, they determine the accurate region corresponding to all entangled two-qubit states. The states corresponding to those boundary points of the whole region, and to the border lines between separable and entangled states are analyzed. As an application, they characterize the entangled region of PT-moments for the two families of Werner states and Bell-diagonal states. The relations between entanglement and the pairs of PT-moments are revealed from these typical examples. They also numerically plot the whole region of possible PT-moments for all two-qubit X-states, and find that this region is almost the same as the whole region of PT-moments for all two-qubit states. Moreover, they extend their results to detect the entanglement of multiqubit states. By utilizing the PT-moment-based method to characterize the entanglement of the multiqubit states mixed by the GHZ and W states, they propose an operational way of verifying the genuine entanglement in such states.

quant-ph↗

arXiv2023

Visualization of all two-qubit states via partial-transpose-moments

Efficiently detecting entanglement based on measurable quantities is a basic problem for quantum information processing. Recently, the measurable quantities called partial-transpose (PT)-moments have been proposed to detect and characterize entanglement. In the recently published paper [L. Zhang \emph{et al.}, \href{https://doi.org/10.1002/andp.202200289}{Ann. Phys.(Berlin) \textbf{534}, 2200289 (2022)}], we have already identified the 2-dimensional (2D) region, comprised of the second and third PT-moments, corresponding to two-qubit entangled states, and described the whole region for all two-qubit states. In the present paper, we visualize the 3D region corresponding to all two-qubit states by further involving the fourth PT-moment (the last one for two-qubit states). The characterization of this 3D region can finally be achieved by optimizing some polynomials. Furthermore, we identify the dividing surface which separates the two parts of the whole 3D region corresponding to entangled and separable states respectively. Due to the measurability of PT-moments, we obtain a complete and operational criterion for the detection of two-qubit entanglement.

quant-ph↗

arXiv2023

Quantum optimization algorithm based on multistep quantum computation

We present a quantum algorithm for finding the minimum of a function based on multistep quantum computation and apply it for optimization problems with continuous variables, in which the variables of the problem are discretized to form the state space of the problem. Usually the cost for solving the problem increases dramatically with the size of the problem. In this algorithm, the dimension of the search space of the problem can be reduced exponentially step by step. We construct a sequence of Hamiltonians such that the search space of a Hamiltonian is nested in that of the previous one. By applying a multistep quantum computation process, the optimal vector is finally located in a small state space and can be determined efficiently. One of the most difficult problems in optimization is that a trial vector is trapped in a deep local minimum while the global minimum is missed, this problem can be alleviated in our algorithm and the runtime is proportional to the number of the steps of the algorithm, provided certain conditions are satisfied. We have tested the algorithm for some continuous test functions.

quant-ph↗

arXiv2023

Efficient quantum algorithms for solving quantum linear system problems

We transform the problem of solving linear system of equations $A\mathbf{x}=\mathbf{b}$ to a problem of finding the right singular vector with singular value zero of an augmented matrix $C$, and present two quantum algorithms for solving this problem. The first algorithm solves the problem directly by applying the quantum eigenstate filtering algorithm with query complexity of $O\left( sκ\log \left( 1/ε\right) \right) $ for a $s$-sparse matrix $C$, where $κ$ is the condition number of the matrix $A$, and $ε$ is the desired precision. The second algorithm uses the quantum resonant transition approach, the query complexity scales as $O\left[sκ+ \log\left( 1/ε\right)/\log \log \left( 1/ε\right) \right] $. Both algorithms meet the optimal query complexity in $κ$, and are simpler than previous algorithms.

quant-ph↗

arXiv2023

Quantum radial basis function method for the Poisson equation

The radial basis function (RBF) method is used for the numerical solution of the Poisson problem in high dimension. The approximate solution can be found by solving a large system of linear equations. Here we investigate the extent to which the RBF method can be accelerated using an efficient quantum algorithm for linear equations. We compare the theoretical performance of our quantum algorithm with that of a standard classical algorithm, the conjugate gradient method. We find that the quantum algorithm can achieve a polynomial speedup.

quant-ph↗

arXiv2022

Quantum-inspired algorithm for truncated total least squares solution

Total least squares (TLS) methods have been widely used in data fitting. Compared with the least squares method, for TLS problem we takes into account not only the observation errors, but also the errors in the measurement matrix. This is more realistic in practical applications. For the large-scale discrete ill-posed problem $Ax \approx b$, we introduce the quantum-inspired techniques to approximate the truncated total least squares (TTLS) solution. We analyze the accuracy of the quantum-inspired truncated total least squares algorithm and perform numerical experiments to demonstrate the efficiency of our method.

math.NA↗

arXiv2022

A quantum-inspired algorithm for approximating statistical leverage scores

Suppose a matrix $A \in \mathbb{R}^{m \times n}$ of rank $r$ with singular value decomposition $A = U_{A}Σ_{A} V_{A}^{T}$, where $U_{A} \in \mathbb{R}^{m \times r}$, $V_{A} \in \mathbb{R}^{n \times r}$ are orthonormal and $Σ_{A} \in \mathbb{R}^{r \times r}$ is a diagonal matrix. The statistical leverage scores of a matrix $A$ are the squared row-norms defined by $\ell_{i} = \|(U_{A})_{i,:}\|_2^2$, where $i \in [m]$, and the matrix coherence is the largest statistical leverage score. These quantities play an important role in machine learning algorithms such as matrix completion and Nyström-based low rank matrix approximation as well as large-scale statistical data analysis applications, whose usual algorithm complexity is polynomial in the dimension of the matrix $A$. As an alternative to the conventional approach, and inspired by recent development on dequantization techniques, we propose a quantum-inspired algorithm for approximating the statistical leverage scores. We then analyze the accuracy of the algorithm and perform numerical experiments to illustrate the feasibility of our algorithm. Theoretical analysis shows that our novel algorithm takes time polynomial in an integer $k$, condition number $κ$ and logarithm of the matrix size.

math.NA↗

arXiv2022

Efficient quantum algorithm for solving structured problems via multi-step quantum computation

In classical computation, a problem can be solved in multiple steps where calculated results of each step can be copied and used repeatedly. While in quantum computation, it is difficult to realize a similar multi-step computation process because the no-cloning theorem forbids making copies of an unknown quantum state perfectly. We find a method based on quantum resonant transition to protect and reuse an unknown quantum state that encodes calculated results of an intermediate step without making copies of the state, and present a quantum algorithm that solves a problem via a multi-step quantum computation process. This algorithm can achieve an exponential speedup over classical algorithms in solving a type of structured search problems.

quant-ph↗

arXiv2021

Quantum radial basis function methods for scattered data fitting

Scattered data fitting is a frequently encountered problem for reconstructing an unknown function from given scattered data. Radial basis function (RBF) methods have proven to be highly useful to deal with this problem. We describe two quantum algorithms to efficiently fit scattered data based on globally and compactly supported RBFs respectively. For the globally supported RBF method, the core of the quantum algorithm relies on using coherent states to calculate the radial functions and a nonsparse matrix exponentiation technique for efficiently performing a matrix inversion. A quadratic speedup is achieved in the number of data over the classical algorithms. For the compactly supported RBF method, we mainly use the HHL algorithm as a subroutine to design an efficient quantum procedure that runs in time logarithmic in the number of data, achieving an exponential improvement over the classical methods.

math.NA↗

arXiv2021

Quantum Algorithm for Matrix Logarithm by Integral Formula

The matrix logarithm is one of the important matrix functions. Recently, a quantum algorithm that computes the state $|f\rangle$ corresponding to matrix-vector product $f(A)b$ is proposed in [Takahira, et al. Quantum algorithm for matrix functions by Cauchy's integral formula, QIC, Vol.20, No.1\&2, pp.14-36, 2020]. However, it can not be applied to matrix logarithm. In this paper, we propose a quantum algorithm, which uses LCU method and block-encoding technique as subroutines, to compute the state $|f\rangle = \log(A)|b\rangle / \|\log(A)|b\rangle\|$ corresponding to $\log(A)b$ via the integral representation of $\log(A)$ and the Gauss-Legendre quadrature rule.

math.NA↗