arXiv subjects

Xusheng Xu

Publications and source records attributed to Xusheng Xu.

16 recordsLinked to original sources

arXiv2026

Trainable Quantum Channels as Computational Primitives for Quantum Learning

Variational quantum learning is traditionally constrained to unitary dynamics, often treating quantum channels as detrimental noise. In this work, we reformulate the quantum channels as trainable computational primitives and establish a non-unitary quantum machine learning framework grounded in open-system dynamics. We demonstrate that the outputs of channel-enhanced quantum models form a structured superposition of multiple functional components. Each component is governed by an effective observable whose spectrum can be adaptively modulated during training, a significant departure from the spectral invariance in unitary transformations. Moreover, the proposed framework generalizes conventional unitary quantum models by retaining them as a special case while introducing additional non-unitary degrees of freedom. Furthermore, we reveal that trainable quantum channels enrich the optimization geometry through ensemble-averaged gradient and additional optimization directions induced by the Kraus operators. Extensive experiments on classification tasks using trainable amplitude-damping and phase-damping channels confirm enhanced optimization dynamics and predictive performance. In addition, we experimentally validate the proposed framework through hardware inference using ten-qubit quantum models implemented on the superconducting quantum processor, confirming its practical feasibility and hardware compatibility. Our work provides a principled approach for leveraging quantum channels as trainable resources and advances the design of high-performance quantum learning architectures.

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arXiv2026

Variational simulation of higher-spin systems on qubit-based quantum simulators

Qubit-based quantum simulators naturally target two-level systems, whereas many quantum many-body problems are intrinsically $d$ level. Encodings from qudits to qubits then enlarge the Hilbert space and can introduce unphysical states that interfere with variational optimization. We formulate a variational framework for encoded $d$-level models that suppresses these illegitimate states with penalty terms and benchmark it for spin-1 and spin-3/2 bilinear-biquadratic Heisenberg chains. We compare binary encoding, which minimizes the qubit overhead, with symmetry encoding, which preserves the relevant spin symmetries and enables symmetry-conserving ansätze. Although binary encoding is more qubit efficient, its hardware-efficient ansatz is harder to train and less effective at exploiting conserved quantities. In contrast, symmetry encoding requires more qubits but reaches substantially higher fidelities, converges faster, and exhibits better trainability than the binary hardware-efficient ansatz. These results identify symmetry-preserving encodings as a practical route to simulating higher-spin models on existing qubit platforms.

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arXiv2026

Bayesian Optimization by Kernel Regression and Density-based Exploration

Bayesian optimization is highly effective for optimizing expensive-to-evaluate black-box functions, but it faces significant computational challenges due to the cubic per-iteration cost of Gaussian processes, which results in a total time complexity that is quartic with respect to the number of iterations. To address this limitation, we propose a novel algorithm, Bayesian optimization by kernel regression and density-based exploration (BOKE). BOKE uses kernel regression for efficient function approximation, kernel density for exploration, and integrates them into the confidence bound criteria to guide the optimization process, thus reducing computational costs to quadratic. Our theoretical analysis rigorously establishes the global convergence of BOKE under noisy evaluations. Through extensive numerical experiments on both synthetic and real-world optimization tasks, we demonstrate that BOKE not only performs competitively compared to Gaussian process-based methods and several other baseline methods but also exhibits superior computational efficiency. These results highlight BOKE's effectiveness in resource-constrained environments, providing a practical approach for optimization problems in engineering applications.

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arXiv2024

MindSpore Quantum: A User-Friendly, High-Performance, and AI-Compatible Quantum Computing Framework

We introduce MindSpore Quantum, a pioneering hybrid quantum-classical framework with a primary focus on the design and implementation of noisy intermediate-scale quantum (NISQ) algorithms. Leveraging the robust support of MindSpore, an advanced open-source deep learning training/inference framework, MindSpore Quantum exhibits exceptional efficiency in the design and training of variational quantum algorithms on both CPU and GPU platforms, delivering remarkable performance. Furthermore, this framework places a strong emphasis on enhancing the operational efficiency of quantum algorithms when executed on real quantum hardware. This encompasses the development of algorithms for quantum circuit compilation and qubit mapping, crucial components for achieving optimal performance on quantum processors. In addition to the core framework, we introduce QuPack, a meticulously crafted quantum computing acceleration engine. QuPack significantly accelerates the simulation speed of MindSpore Quantum, particularly in variational quantum eigensolver (VQE), quantum approximate optimization algorithm (QAOA), and tensor network simulations, providing astonishing speed. This combination of cutting-edge technologies empowers researchers and practitioners to explore the frontiers of quantum computing with unprecedented efficiency and performance.

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arXiv2024

Distributed Exact Generalized Grover's Algorithm

Distributed quantum computation has garnered immense attention in the noisy intermediate-scale quantum (NISQ) era, where each computational node necessitates fewer qubits and quantum gates. In this paper, we focus on a generalized search problem involving multiple targets within an unordered database and propose a Distributed Exact Generalized Grover's Algorithm (DEGGA) to address this challenge by decomposing it into arbitrary $t$ components, where $2 \leq t \leq n$. Specifically, (1) our algorithm ensures accuracy, with a theoretical probability of identifying the target states at $100\%$; (2) if the number of targets is fixed, the pivotal factor influencing the circuit depth of DEGGA is the partitioning strategy, rather than the magnitude of $n$; (3) our method requires a total of $n$ qubits, eliminating the need for auxiliary qubits; (4) we elucidate the resolutions (two-node and three-node) of a particular generalized search issue incorporating two goal strings (000000 and 111111) by applying DEGGA. The feasibility and effectiveness of our suggested approach is further demonstrated by executing the quantum circuits on MindSpore Quantum (a quantum simulation software). Eventually, through the decomposition of multi-qubit gates, DEGGA diminishes the utilization of quantum gates by $90.7\%$ and decreases the circuit depth by $91.3\%$ in comparison to the modified Grover's algorithm by Long. It is increasingly evident that distributed quantum algorithms offer augmented practicality.

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arXiv2024

Quantum Resonant Dimensionality Reduction and Its Application in Quantum Machine Learning

Quantum computing is a promising candidate for accelerating machine learning tasks. Limited by the control accuracy of current quantum hardware, reducing the consumption of quantum resources is the key to achieving quantum advantage. Here, we propose a quantum resonant dimension reduction (QRDR) algorithm based on the quantum resonant transition to reduce the dimension of input data and accelerate the quantum machine learning algorithms. After QRDR, the dimension of input data $N$ can be reduced into desired scale $R$, and the effective information of the original data will be preserved correspondingly, which will reduce the computational complexity of subsequent quantum machine learning algorithms or quantum storage. QRDR operates with polylogarithmic time complexity and reduces the error dependency from the order of $1/ε^3$ to the order of $1/ε$, compared to existing algorithms. We demonstrate the performance of our algorithm combining with two types of quantum classifiers, quantum support vector machines and quantum convolutional neural networks, for classifying underwater detection targets and quantum many-body phase respectively. The simulation results indicate that reduced data improved the processing efficiency and accuracy following the application of QRDR. As quantum machine learning continues to advance, our algorithm has the potential to be utilized in a variety of computing fields.

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arXiv2024

Exploring Ground States of Fermi-Hubbard Model on Honeycomb Lattices with Counterdiabaticity

Exploring the ground state properties of many-body quantum systems conventionally involves adiabatic processes, alongside exact diagonalization, in the context of quantum annealing or adiabatic quantum computation. Shortcuts to adiabaticity by counter-diabatic driving serve to accelerate these processes by suppressing energy excitations. Motivated by this, we develop variational quantum algorithms incorporating the auxiliary counterdiabatic interactions, comparing them with digitized adiabatic algorithms. These algorithms are then implemented on gate-based quantum circuits to explore the ground states of the Fermi-Hubbard model on honeycomb lattices, utilizing systems with up to 26 qubits. The comparison reveals that the counter-diabatic inspired ansatz is superior to traditional Hamiltonian variational ansatz. Furthermore, the number and duration of Trotter steps are analyzed to understand and mitigate errors. Given the model's relevance to materials in condensed matter, our study paves the way for using variational quantum algorithms with counterdiabaticity to explore quantum materials in the noisy intermediate-scale quantum era.

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arXiv2024

Variational Quantum Circuits Enhanced Generative Adversarial Network

Generative adversarial network (GAN) is one of the widely-adopted machine-learning frameworks for a wide range of applications such as generating high-quality images, video, and audio contents. However, training a GAN could become computationally expensive for large neural networks. In this work, we propose a hybrid quantum-classical architecture for improving GAN (denoted as QC-GAN). The performance was examed numerically by benchmarking with a classical GAN using MindSpore Quantum on the task of hand-written image generation. The generator of the QC-GAN consists of a quantum variational circuit together with a one-layer neural network, and the discriminator consists of a traditional neural network. Leveraging the entangling and expressive power of quantum circuits, our hybrid architecture achieved better performance (Frechet Inception Distance) than the classical GAN, with much fewer training parameters and number of iterations for convergence. We have also demonstrated the superiority of QC-GAN over an alternative quantum GAN, namely pathGAN, which could hardly generate 16$\times$16 or larger images. This work demonstrates the value of combining ideas from quantum computing with machine learning for both areas of Quantum-for-AI and AI-for-Quantum.

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arXiv2024

Benchmarking hybrid digitized-counterdiabatic quantum optimization

Hybrid digitized-counterdiabatic quantum computing (DCQC) is a promising approach for leveraging the capabilities of near-term quantum computers, utilizing parameterized quantum circuits designed with counterdiabatic protocols. However, the classical aspect of this approach has received limited attention. In this study, we systematically analyze the convergence behavior and solution quality of various classical optimizers when used in conjunction with the digitized-counterdiabatic approach. We demonstrate the effectiveness of this hybrid algorithm by comparing its performance to the traditional QAOA on systems containing up to 28 qubits. Furthermore, we employ principal component analysis to investigate the cost landscape and explore the crucial influence of parameterization on the performance of the counterdiabatic ansatz. Our findings indicate that fewer iterations are required when local cost landscape minima are present, and the SPSA-based BFGS optimizer emerges as a standout choice for the hybrid DCQC paradigm.

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arXiv2024

Matrix product state ansatz for the variational quantum solution of the Heisenberg model on Kagome geometries

The Variational Quantum Eigensolver (VQE) algorithm, as applied to finding the ground state of a Hamiltonian, is particularly well-suited for deployment on noisy intermediate-scale quantum (NISQ) devices. Here we utilize the VQE algorithm with a quantum circuit ansatz inspired by the Density Matrix Renormalization Group (DMRG) algorithm. To ameliorate the impact of realistic noise on the performance of the method we employ zero-noise extrapolation. We find that, with realistic error rates, our DMRG-VQE hybrid algorithm delivers good results for strongly correlated systems. We illustrate our approach with the Heisenberg model on a Kagome lattice patch and demonstrate that DMRG-VQE hybrid methods can locate, and faithfully represent the physics of, the ground state of such systems. Moreover, the parameterized ansatz circuit used in this work is low-depth and requires a reasonably small number of parameters, so is efficient for NISQ devices.

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arXiv2023

Variational quantum circuit learning of entanglement purification in multiple degrees of freedom

Entanglement purification is a crucial technique for promising the effective entanglement channel in noisy large-scale quantum networks, yet complicated in designing protocols in multi-degree of freedom (DoF). To execute the above tasks easily and effectively, developing a learning framework for designing the entanglement purification with multi-DoF is a promising way and still an open research question. Inspired by variational quantum circuit (VQC) with remarkable advantage in learning optimal quantum operations with near-term quantum devices, in this paper we propose an effective VQC framework for the entanglement purification in multi-DoF and exploit it to learn the optimal purification protocols of the objective function which are based on postselection. By properly introducing additional circuit lines for representing each of the ancillary DoFs of all the particles, e.g., space and time, the parametrized quantum circuit can effectively simulate scalable entanglement purification. To verify our framework, the well-known protocols in linear optics are learned well with alternative operations in low-depth quantum circuit. Moreover, we simulate the multipair cases with multi-DoF to show the scalability and discover one-round protocols. Our work provides an effective way for exploring the entanglement purification protocols in multi-DoF and multipair with near-term quantum devices.

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arXiv2023

Variational quantum simulation of long-range interacting systems

Current quantum simulators suffer from multiple limitations such as short coherence time, noisy operations, faulty readout and restricted qubit connectivity in some platforms. Variational quantum algorithms are the most promising approach in near-term quantum simulation to achieve practical quantum advantage over classical computers. Here, we explore variational quantum algorithms, with different levels of qubit connectivity, for digital simulation of the ground state of long-range interacting systems as well as generation of spin squeezed states. We find that as the interaction becomes more long-ranged, the variational algorithms become less efficient, achieving lower fidelity and demanding more optimization iterations. In particular, when the system is near its criticality the efficiency is even lower. Increasing the connectivity between distant qubits improves the results, even with less quantum and classical resources. Our results show that by mixing circuit layers with different levels of connectivity one can sensibly improve the performance. Interestingly, the order of layers becomes very important and grouping the layers with long-distance connectivity at the beginning of the circuit outperforms other permutations. The same design of circuits can also be used to variationally produce spin squeezed states, as a resource for quantum metrology.

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arXiv2023

A sequentially generated variational quantum circuit with polynomial complexity

Variational quantum algorithms have been a promising candidate to utilize near-term quantum devices to solve real-world problems. The powerfulness of variational quantum algorithms is ultimately determined by the expressiveness of the underlying quantum circuit ansatz for a given problem. In this work, we propose a sequentially generated circuit ansatz, which naturally adapts to 1D, 2D, 3D quantum many-body problems. Specifically, in 1D our ansatz can efficiently generate any matrix product states with a fixed bond dimension, while in 2D our ansatz generates the string-bond states. As applications, we demonstrate that our ansatz can be used to accurately reconstruct unknown pure and mixed quantum states which can be represented as matrix product states, and that our ansatz is more efficient compared to several alternatives in finding the ground states of some prototypical quantum many-body systems as well as quantum chemistry systems, in terms of the number of quantum gate operations.

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arXiv2023

Circuit-Depth Reduction of Unitary-Coupled-Cluster Ansatz by Energy Sorting

Quantum computation represents a revolutionary approach for solving problems in quantum chemistry. However, due to the limited quantum resources in the current noisy intermediate-scale quantum (NISQ) devices, quantum algorithms for large chemical systems remains a major task. In this work, we demonstrate that the circuit depth of the unitary coupled cluster (UCC) and UCC-based ansatzes in the algorithm of variational quantum eigensolver can be significantly reduced by an energy-sorting strategy. Specifically, subsets of excitation operators are first pre-screened from the operator pool according to its contribution to the total energy. The quantum circuit ansatz is then iteratively constructed until the convergence of the final energy to a typical accuracy. For demonstration, this method has been successfully applied to molecular and periodic systems. Particularly, a reduction of 50\%$\sim$98\% in the number of operators is observed while retaining the accuracy of the origin UCCSD operator pools. This method can be straightforwardly extended to general parametric variational ansatzes.

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arXiv2023

Symmetry enhanced variational quantum spin eigensolver

The variational quantum-classical algorithms are the most promising approach for achieving quantum advantage on near-term quantum simulators. Among these methods, the variational quantum eigensolver has attracted a lot of attention in recent years. While it is very effective for simulating the ground state of many-body systems, its generalization to excited states becomes very resource demanding. Here, we show that this issue can significantly be improved by exploiting the symmetries of the Hamiltonian. The improvement is even more effective for higher energy eigenstates. We introduce two methods for incorporating the symmetries. In the first approach, called hardware symmetry preserving, all the symmetries are included in the design of the circuit. In the second approach, the cost function is updated to include the symmetries. The hardware symmetry preserving approach indeed outperforms the second approach. However, integrating all symmetries in the design of the circuit could be extremely challenging. Therefore, we introduce hybrid symmetry preserving method in which symmetries are divided between the circuit and the classical cost function. This allows to harness the advantage of symmetries while preventing sophisticated circuit design.

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arXiv2022

Towards a Larger Molecular Simulation on the Quantum Computer: Up to 28 Qubits Systems Accelerated by Point Group Symmetry

The exact evaluation of the molecular ground state in quantum chemistry requires an exponentially increasing computational cost. Quantum computation is a promising way to overcome the exponential problem using polynomial-time quantum algorithms. A quantum-classical hybrid optimization scheme known as the variational quantum eigensolver(VQE) is preferred for noisy intermediate-scale quantum devices. However, the circuit depth becomes one of the bottlenecks of its application to large molecules of more than 20 qubits. In this work, we employ the point group symmetry to reduce the number of operators in constructing ansatz so as to achieve a more compact quantum circuit. We illustrate this methodology with a series of molecules ranging from LiH(12 qubits) to C2H4(28 qubits). A significant reduction of up to 82% of the operator numbers is reached on C2H4, which enables the largest molecule ever numerically simulated by VQE-UCC to the best of our knowledge. This also shed light into the further work of this direction to construct even shallower ansatz with enough expressive power and simulate even larger scale system.

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