arXiv subjects

Junxu Li

Publications and source records attributed to Junxu Li.

14 recordsLinked to original sources

arXiv2026

Bridge the Gap between Classical and Quantum Neural Networks with Residual Connections

We introduce a Hybrid Quantum Residual Network (HQRN) and establish an exact functional correspondence between its state evolution and the dynamics of classical networks with residual connections. When inputs are restricted to the computational basis, the HQRN reduces to its classical analog, enabling the direct translation of optimized classical weights into quantum unitary operations, effectively inheriting the landscape benefits of classical optimization. Conversely, when processing general mixed states, the HQRN leverages off-diagonal quantum correlations to resolve features inaccessible to its classical analog. We validate this framework through digit recognition and bipartite entanglement classification. Notably, HQRN achieves high classification accuracy even for adversarial separable states that mimic the marginal measurement statistics of entangled pairs. Our results bridge the gap between classical and quantum residual learning, paving a scalable pathway for deep quantum architectures.

quant-ph↗

arXiv2025

PR-CapsNet: Pseudo-Riemannian Capsule Network with Adaptive Curvature Routing for Graph Learning

Capsule Networks (CapsNets) show exceptional graph representation capacity via dynamic routing and vectorized hierarchical representations, but they model the complex geometries of real\-world graphs poorly by fixed\-curvature space due to the inherent geodesical disconnectedness issues, leading to suboptimal performance. Recent works find that non\-Euclidean pseudo\-Riemannian manifolds provide specific inductive biases for embedding graph data, but how to leverage them to improve CapsNets is still underexplored. Here, we extend the Euclidean capsule routing into geodesically disconnected pseudo\-Riemannian manifolds and derive a Pseudo\-Riemannian Capsule Network (PR\-CapsNet), which models data in pseudo\-Riemannian manifolds of adaptive curvature, for graph representation learning. Specifically, PR\-CapsNet enhances the CapsNet with Adaptive Pseudo\-Riemannian Tangent Space Routing by utilizing pseudo\-Riemannian geometry. Unlike single\-curvature or subspace\-partitioning methods, PR\-CapsNet concurrently models hierarchical and cluster or cyclic graph structures via its versatile pseudo\-Riemannian metric. It first deploys Pseudo\-Riemannian Tangent Space Routing to decompose capsule states into spherical\-temporal and Euclidean\-spatial subspaces with diffeomorphic transformations. Then, an Adaptive Curvature Routing is developed to adaptively fuse features from different curvature spaces for complex graphs via a learnable curvature tensor with geometric attention from local manifold properties. Finally, a geometric properties\-preserved Pseudo\-Riemannian Capsule Classifier is developed to project capsule embeddings to tangent spaces and use curvature\-weighted softmax for classification. Extensive experiments on node and graph classification benchmarks show PR\-CapsNet outperforms SOTA models, validating PR\-CapsNet's strong representation power for complex graph structures.

cs.LG↗

arXiv2025

Knowledge Distillation Inspired Variational Quantum Eigensolver with Virtual Annealing

In this paper, we propose a Knowledge Distillation Inspired Variational Quantum Eigensolver (KD-VQE). Inspired by the virtual distillation process in knowledge distillation (KD), KD-VQE introduces a virtual annealing mechanism to the variational quantum eigensolver (VQE) framework. In KD-VQE, measurement resources (shots) are dynamically allocated among multiple trial wavefunctions, each weighted according to a Boltzmann distribution with a virtual temperature. As the temperature decreases gradually, the algorithm progressively reallocates resources toward lower-energy candidates, effectively filtering out suboptimal states and steering the system toward the global minimum. Moreover, we demonstrate the effectiveness of KD-VQE by applying it to the two-site Fermi-Hubbard model. Compared to standard VQE framework, KD-VQE explores a broader region of the solution space, and offers improved convergence behavior and increased reliability.

quant-ph↗

arXiv2024

A Feasible Design of Elementary Quantum Arithmetic Logic Units for Near-Term Quantum Computers

Quantum arithmetic logic units (QALUs) constitute a fundamental component of quantum computing. However, the implementation of QALUs on near-term quantum computers remains a substantial challenge, largely due to the limited connectivity of qubits. In this paper, we propose feasible QALUs, including quantum binary adders, subtractors, multipliers, and dividers, which are designed for near-term quantum computers with qubits arranged in two-dimensional arrays. Additionally, we introduce a feasible quantum arithmetic operation to compute the two's complement representation of signed integers. The proposed QALUs utilize only Pauli-X gates, CNOT gates, and $C\sqrt{X}$ (CSX) gates, and all two-qubit gates are operated between nearest neighbor qubits. Our work demonstrates a viable implementation of QALUs on near-term quantum computers, advancing towards scalable and resource-efficient quantum arithmetic operations.

quant-ph↗

arXiv2024

Quantum Circuit for High Order Perturbation Theory Corrections

Perturbation theory (PT) might be one of the most powerful and fruitful tools for both physicists and chemists, which has led to a wide variety of applications. Over the past decades, advances in quantum computing provide opportunities for alternatives to classical methods. Recently, a general quantum circuit estimating the low order PT corrections has been proposed. In this article, we revisit the quantum circuits for PT calculations, and develop the methods for higher order PT corrections of eigenenergy, especially the 3rd and 4th order corrections. We present the feasible quantum circuit to estimate each term in these PT corrections. There are two the fundamental operations in the proposed circuit. One approximates the perturbation terms, the other approximates the inverse of unperturbed energy difference. The proposed method can be generalized to higher order PT corrections.

quant-ph↗

arXiv2024

An Iterative Method to Improve the Precision of Quantum Phase Estimation Algorithm

Here we revisit the quantum phase estimation (QPE) algorithm, and devise an iterative method to improve the precision of QPE with propagators over a variety of time spans. For a given propagator and a certain eigenstate as input, QPE with propagator is introduced to estimate the phase corresponding to an eigenenergy. Due to the periodicity of the complex exponential, we can pinpoint the eigenenergy in a branch of comb-like ranges by applying QPE with propagators over longer time spans. Thus, by picking up appropriate time spans, the iterative QPE with corresponding propagators can enable us to pinpoint the eigenenergy more precisely. Moreover, even if there are only few qubits as ancilla qubits, high precision is still available by the proposed iterative method. Our work provides a feasible and promising means toward precise estimations of eigenvalue on noisy intermediate-scale quantum (NISQ) devices.

quant-ph↗

arXiv2023

Møller-Plesset Perturbation Theory Calculations on Quantum Devices

Accurate electronic structure calculations might be one of the most anticipated applications of quantum computing.The recent landscape of quantum simulations within the Hartree-Fock approximation raises the prospect of substantial theory and hardware developments in this context.Here we propose a general quantum circuit for Møller-Plesset perturbation theory (MPPT) calculations, which is a popular and powerful post-Hartree-Fock method widly harnessed in solving electronic structure problems. MPPT improves on the Hartree-Fock method by including electron correlation effects wherewith Rayleigh-Schrodinger perturbation theory. Given the Hartree-Fock results, the proposed circuit is designed to estimate the second order energy corrections with MPPT methods. In addition to demonstration of the theoretical scheme, the proposed circuit is further employed to calculate the second order energy correction for the ground state of Helium atom, and the total error rate is around 2.3%. Experiments on IBM 27-qubit quantum computers express the feasibility on near term quantum devices, and the capability to estimate the second order energy correction accurately. In imitation of the classical MPPT, our approach is non-heuristic, guaranteeing that all parameters in the circuit are directly determined by the given Hartree-Fock results. Moreover, the proposed circuit shows a potential quantum speedup comparing to the traditional MPPT calculations. Our work paves the way forward the implementation of more intricate post-Hartree-Fock methods on quantum hardware, enriching the toolkit solving electronic structure problems on quantum computing platforms.

quant-ph↗

arXiv2023

Towards Perturbation Theory Methods on a Quantum Computer

Perturbation theory (PT) might be one of the most powerful and fruitful tools for both physicists and chemists, which evoked an explosion of applications with the blooming of atomic and subatomic physics. Even though PT is well-used today, techniques for PT are significantly lacking in quantum computing. Here we present a quantum circuit estimating both the energy and eigenstates corrections with PT methods, which we claim is far superior to the classical version when estimating the second order energy correction. Our approach is further demonstrated with an application on the extended Hubbard model, where numerical simulation based on qiskit is also presented. Unlike the popular quantum variational circuit, there is no training or optimizing process in our circuit, and all parameters are derived from the unperturbed Hamiltonian. Our work offers a new approach to studying complex systems with quantum devices, which might shed light on the quantum implementation of the more intricate methods based on PT.

quant-ph↗

arXiv2022

Quantum Machine Learning for Chemistry and Physics

Machine learning (ML) has emerged into formidable force for identifying hidden but pertinent patterns within a given data set with the objective of subsequent generation of automated predictive behavior. In the recent years, it is safe to conclude that ML and its close cousin deep learning (DL) have ushered unprecedented developments in all areas of physical sciences especially chemistry. Not only the classical variants of ML , even those trainable on near-term quantum hardwares have been developed with promising outcomes. Such algorithms have revolutionzed material design and performance of photo-voltaics, electronic structure calculations of ground and excited states of correlated matter, computation of force-fields and potential energy surfaces informing chemical reaction dynamics, reactivity inspired rational strategies of drug designing and even classification of phases of matter with accurate identification of emergent criticality. In this review we shall explicate a subset of such topics and delineate the contributions made by both classical and quantum computing enhanced machine learning algorithms over the past few years. We shall not only present a brief overview of the well-known techniques but also highlight their learning strategies using statistical physical insight. The objective of the review is to not only to foster exposition to the aforesaid techniques but also to empower and promote cross-pollination among future-research in all areas of chemistry which can benefit from ML and in turn can potentially accelerate the growth of such algorithms.

physics.chem-ph↗

arXiv2021

A Universal Quantum Circuit Design for Periodical Functions

We propose a universal quantum circuit design that can estimate any arbitrary one-dimensional periodic functions based on the corresponding Fourier expansion. The quantum circuit contains N-qubits to store the information on the different N-Fourier components and $M+2$ auxiliary qubits with $M = \lceil{\log_2{N}}\rceil$ for control operations. The desired output will be measured in the last qubit $q_N$ with a time complexity of the computation of $O(N^2\lceil \log_2N\rceil^2)$. We illustrate the approach by constructing the quantum circuit for the square wave function with accurate results obtained by direct simulations using the IBM-QASM simulator. The approach is general and can be applied to any arbitrary periodic function.

quant-ph↗

arXiv2021

Statistical correlation between quantum entanglement and spin-orbit coupling in crossed beam molecular dynamics

Non-classical features like interference is already being harnessed to control the output of chemical reactions. However quantum entanglement which is an equally enigmatic many-body quantum correlation can also be used as a powerful resource yet have eluded explicit attention. In this report, we propose an experimental scheme under the crossed beam molecular dynamical setup, with the F+HD reaction, aiming to study the possible influence of entanglement within reactant pairs on the angular features of the product distribution. The aforesaid reaction has garnered interest recently as an unusual horseshoe shape pattern in the product (HF) distribution was observed, which has been attributed to the coupling of spin and orbital degrees of freedom. We propose an experimental scheme aiming to study the possible influence of entanglement on the necessity for the inclusion of such spin-orbit characteristics, under circumstances wherein the existence of entanglement and spin-orbit interaction is simultaneously detectable. We further numerically simulate the attainable results highlighting specific patterns corresponding to various possibilities. Such studies if extended can provide unforeseen mechanistic insight in analogous reactions too from the lens of quantum information.

quant-ph↗

arXiv2021

Quantum Cluster Algorithm for Data classification

We present a quantum algorithm for data classification based on the nearest-neighbor learning algorithm. The classification algorithm is divided into two steps: Firstly, data in the same class is divided into smaller groups with sublabels assisting building boundaries between data with different labels. Secondly we construct a quantum circuit for classification that contains multi control gates. The algorithm is easy to implement and efficient in predicting the labels of test data. To illustrate the power and efficiency of this approach, we construct the phase transition diagram for the metal-insulator transition of $VO_2$, using limited trained experimental data, where $VO_2$ is a typical strongly correlated electron materials, and the metallic-insulating phase transition has drawn much attention in condensed matter physics. Moreover, we demonstrate our algorithm on the classification of randomly generated data and the classification of entanglement for various Werner states, where the training sets can not be divided by a single curve, instead, more than one curves are required to separate them apart perfectly. Our preliminary result shows considerable potential for various classification problems, particularly for constructing different phases in materials.

quant-ph↗

arXiv2021

A practical quantum encryption protocol with varying encryption configurations

Quantum communication is an important application that derives from the burgeoning field of quantum information and quantum computation. Focusing on secure communication, quantum cryptography has two major directions of development, namely quantum key distribution and quantum encryption. In this work we propose a quantum encryption protocol that utilizes a quantum algorithm to create blocks of ciphertexts based on quantum states. The main feature of our quantum encryption protocol is that the encryption configuration of each block is determined by the previous blocks, such that additional security is provided. We then demonstrate our method by an example model encrypting the English alphabet, with numerical simulation results showing the large error rate of a mock attack by a potential adversary. With possible future improvements in mind, our quantum encryption protocol is a capable addition to the toolbox of quantum cryptography.

quant-ph↗

arXiv2019

Entanglement Classifier in Chemical Reactions

Ever since the appearance of the seminal work of Einstein, Podolsky and Rosen (The EPR-paradox), the phenomenon of entanglement, which features the essential difference between classical and quantum physics, has received wide theoretical and experimental attentions. Recently the desire to understand and create quantum entanglement between particles such as spins, photons, atoms and molecules is fueled by the development of quantum teleportation, quantum communication, quantum cryptography and quantum computation. Although most of the work has focused on showing that entanglement violates the famous Bell's inequality and its generalization for discrete measurements, few recent attempts focus on continuous measurement results. Here, we have developed a general practical inequality to test entanglement for continuous measurement results, particularly scattering of chemical reactions. After we explain how to implement this new inequality to classify entanglement in scattering experiments, we propose a specific chemical reaction to test the violation of this inequality. The method is general and could be used to classify entanglement for continuous measurement results.

quant-ph↗