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HVIA: A Hybrid Variational Ising Architecture for Quantum Language Modeling

Chengang Mao, Haisheng Li

Published Jun 12, 2026• 0 citations
Publisher

Abstract

Abstract Language modeling in natural language processing has predominantly relied on large-scale classical neural architectures, yet constructing expressive and resource-efficient models compatible with Noisy Intermediate-Scale Quantum (NISQ) devices remains a fundamental open challenge. In this work, two Ising-inspired variational quantum-classical architectures are proposed to enhance representational capacity by leveraging spin-coupling mechanisms and Ising-type Hamiltonian evolution within hybrid classical-quantum layers. Specifically, a quantum Ising Ansatz circuit parameterized by an Ising Hamiltonian is constructed, and a quantum approximate optimization algorithm (QAOA) is incorporated to reduce the number of trainable circuit parameters while enabling learnable quantum evolution of hidden states. To achieve stable and efficient hybrid training under NISQ constraints, a joint optimization strategy is introduced that combines the Adam optimizer with quantum simultaneous perturbation stochastic approximation (SPSA), yielding convergence acceleration of up to $64\%$ relative to parameter-shift rule and Adam-only baselines. Empirical evaluations on the WikiText-2 benchmark demonstrate that the proposed architectures effectively capture long-range semantic dependencies, achieving a competitive perplexity of $\text{PPL} = 39.8$ (lower values indicate stronger language modeling performance). This result surpasses existing quantum language models, including Quixer, Quantum LSTM, and Quantum GRU, and approaches the performance of the classical NanoGPT baseline ($\text{PPL} = 40.5$). Collectively, these findings establish the viability of Ising-based hybrid quantum-classical networks as a promising direction for practical quantum natural language processing.

DOI
10.21203/rs.3.rs-9030361/v1

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Abstract Language modeling in natural language processing has predominantly relied on large-scale classical neural architectures, yet constructing expressive and resource-efficient models compatible with Noisy Intermediate-Scale Quantum (NISQ) devices remains a fundamental open challenge. In this work, two Ising-inspired variational quantum-classical architectures are proposed to enhance representational capacity by leveraging spin-coupling mechanisms and Ising-type Hamiltonian evolution within hybrid classical-quantum layers. Specifically, a quantum Ising Ansatz circuit parameterized by an Ising Hamiltonian is constructed, and a quantum approximate optimization algorithm (QAOA) is incorporated to reduce the number of trainable circuit parameters while enabling learnable quantum evolution of hidden states. To achieve stable and efficient hybrid training under NISQ constraints, a joint optimization strategy is introduced that combines the Adam optimizer with quantum simultaneous perturbation stochastic approximation (SPSA), yielding convergence acceleration of up to 64%64\%64% relative to parameter-shift rule and Adam-only baselines. Empirical evaluations on the WikiText-2 benchmark demonstrate that the proposed architectures effectively capture long-range semantic dependencies, achieving a competitive perplexity of PPL=39.8\text{PPL} = 39.8PPL=39.8 (lower values indicate stronger language modeling performance). This result surpasses existing quantum language models, including Quixer, Quantum LSTM, and Quantum GRU, and approaches the performance of the classical NanoGPT baseline (PPL=40.5\text{PPL} = 40.5PPL=40.5). Collectively, these findings establish the viability of Ising-based hybrid quantum-classical networks as a promising direction for practical quantum natural language processing.
Quantum Natural Language Processing (QNLP) represents a novel interdisciplinaryparadigm that integrates Quantum Computing with Natural Language Processing toenhance semantic modeling and computational efficiency. Despite the remarkable successof transformer-based architectures such as BERT and GPT, classical NLP systems requirelarge-scale computational resources and extensive parameter tuning. This paper proposesa hybrid quantum–classical architecture employing parameterized quantum circuits (PQCs)integrated with classical embedding layers for text classification tasks. The frameworkutilizes classical preprocessing, quantum state encoding, variational optimization, andclassical post-measurement classification. Experimental results on benchmark sentimentanalysis datasets demonstrate competitive accuracy with significantly reduced parametercomplexity. The findings indicate that hybrid QNLP models provide enhanced semanticcompositionality and efficient representation in Hilbert space while remaining feasiblewithin Noisy Intermediate-Scale Quantum (NISQ) constraints
Combining variational quantum circuits with classical neural network models is a potential direction for quantum natural language processing (QNLP) in the NISQ (Noisy Intermediate-Scale Quantum) era. We propose a hybrid classical-quantum neural network that enhances a transformer architecture in two key ways: first, by incorporating optimized variational quantum circuits into the self-attention and multilayer perceptron components, and second, by integrating a hybrid convolutional module for effective dimensionality reduction which can reduce the quantum resources required for subsequent layers and enhances the model’s trainability by mitigating issues like the barren plateau phenomenon, thus making it feasible to construct a deeper and more powerful network architecture. Our experiments on three widely-used sentiment analysis datasets demonstrate that the proposed model achieves comparable or even superior performance in terms of accuracy and F1 score compared to classical transformer-based sentiment classification models with similar structures, while reducing the number of parameters through the utilization of quantum advantages.
Hybrid quantum-classical models represent a crucial step toward leveraging near-term quantum devices for sequential data processing. We present Quantum Recurrent Neural Networks (QRNNs) and Quantum Convolutional Neural Networks (QCNNs) as hybrid quantum language models, reporting the first empirical demonstration of generative language modeling trained and evaluated end-to-end on real quantum hardware. Our architecture combines hardware-optimized parametric quantum circuits with a lightweight classical projection layer, utilizing a multi-sample SPSA strategy to efficiently train quantum parameters despite hardware noise. To characterize the capabilities of these models, we introduce a synthetic dataset designed to isolate syntactic dependencies in a controlled, low-resource environment. Experiments on IBM Quantum processors reveal the critical trade-offs between circuit depth and trainability, demonstrating that while noise remains a significant factor, observable-based readout enables the successful learning of sequential patterns on NISQ devices. These results establish a rigorous engineering baseline for generative quantum natural language processing, validating the feasibility of training complex sequence models on current quantum hardware.
Variational quantum learning faces practical challenges in the noisy intermediate-scale quantum (NISQ) era. Parameterized quantum circuit (PQC) models suffer from statistical uncertainty due to finite-shot measurements and are highly sensitive to quantum noise, while purely classical approximations like neural quantum states (NQS) lack access to genuine quantum correlations and are limited in scalability. This work introduces Hybrid Parameterized Quantum States (HPQS), a general-purpose modeling framework that interpolates between quantum and classical parameterizations. HPQS combines PQC-based measurements with neural estimators via a blending mechanism and postprocessing functions, enabling enhanced, shot-efficient evaluation under hardware constraints. We demonstrate HPQS across three representative quantum learning tasks: (1) Expectation-based QML, where HPQS yields higher classification accuracy than PQC-only and NQS-only baselines under limited quantum measurements. (2) Quantum-Train, where HPQS generates the entire parameter set of classical networks using polylogarithmic trainable variables; and (3) Quantum Parameter Adaptation (QPA), where HPQS produces LoRA adapter parameters for fine-tuning large language models like GPT-2 and Gemma-2 with improved perplexity under low-shot conditions; Together, these results position HPQS as a scalable, noise-resilient approach for variational quantum learning, compatible with both current NISQ hardware and future fault-tolerant architectures.
Significant computational challenges exist in the training of large language models (LLMs), specifically for the efficient convergence. This paper discusses a hybrid quantum-classical framework designed to address these challenges. With the integration of quantum computing principles, like the superposition, entanglement, and tunneling, into the classical deep learning methods, an approach is studied to accelerate convergence, enhance optimization efficiency, and improve model generalization. A quantum feature mapping is used to project classical data into high-dimensional Hilbert spaces, enhancing data representation and revealing more complex feature patterns in the data. The quantum-assisted optimization algorithms, like Quantum Approximate Optimization Algorithm (QAOA) and Variational Quantum Eigensolver (VQE), can efficiently find optimal solutions within complex, non-convex loss landscapes and mitigate the issues of local minima encountered by classical methods. Furthermore, the quantum-accelerated matrix operations, with the use of Harrow-Hassidim-Lloyd (HHL) algorithm or Quantum Fourier Transform (QFT) etc., can provide computational speed-ups for the LLM training. Quantum measurement introduces inherent randomness, similar to the dropout in deep neural networks, where certain neurons are randomly deactivated during training. In the noisy intermediate-scale quantum (NISQ) era, our quantum-classical framework and conceptual analyses demonstrate the feasibility and potential advantages. This work lays the foundation for future research in this area.
Hybrid Quantum Deep Learning (HQDL) models have emerged as a pragmatic bridge between the algorithmic richness of deep learning and the computational advantages of near-term quantum devices. Rather than seeking full quantum replacement of neural architectures, current research favours layered or modular integration-where variational quantum circuits, quantum kernels, or quantum-enhanced feature embeddings operate alongside classical neural networks. This convergence has yielded promising results in domains such as classification, generative modelling, molecular simulation, and combinatorial optimization. However, performance varies significantly depending on data encoding strategies, circuit expressivity, and training stability under hardware noise. This review synthesizes the taxonomy of existing HQDL architectures, evaluates their empirical benefits over purely classical baselines, and contextualizes their feasibility within current Noisy Intermediate-Scale Quantum (NISQ) constraints. Furthermore, it highlights reproducibility challenges, benchmarking inconsistencies, and open questions surrounding optimization landscapes and scalability. The analysis concludes that while HQDL remains in an early experimental phase, its trajectory is rapidly transitioning from proof-of-concept demonstrations toward targeted domain specialization in finance, materials discovery, and strategic decision-making.