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arXiv:2607.06058

SQGen: Structured Quantum Image Generation with Latent-Modulated Quantized Tensor Trains

Guang Lin, Qibin Zhao

quant-phSubmitted Jul 7, 2026• Announced Jul 8, 2026• 0 citations• Revised Jul 14, 2026 (v2)
v1 · Jul 7, 2026v2 · Jul 14, 2026
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Abstract

Generating images directly from quantum systems is an attractive but unresolved goal on NISQ hardware. Existing quantum generators face several coupled obstacles: barren plateaus that block trainability, expensive quantum circuit preparation, and hardware noise that erodes quantum information with depth. A further difficulty is producing image-scale output without a classical decoder, whose use would otherwise break the end-to-end quantum advantage. We propose SQGen, a full quantum generator built on a quantized tensor train (QTT) with a latent modulation architecture. Specifically, SQGen promotes the QTT bond index of the target pixel distribution to ancilla bond qubits, so that each circuit site operates locally on a bond register plus the two physical qubits that carry the row- and column-bit of one image scale. We further introduce latent modulation: each re-uploading rotation is factorized at the angle level into a trainable main path plus an additive latent term, reducing to the trainable main path when the latent term is disabled. During training, we create a differentiable model in the classical system under gate-compatibility constraints, with a torus prior as the latent distribution. After training, every operator maps one-to-one to a native quantum gate, yielding a compact, deployable quantum circuit with no classical decoder in the inference path. Together, these design choices address the obstacles raised above. Extensive experiments on image datasets and synthetic data demonstrate that SQGen trains stably, generates images end-to-end from a shallow circuit with no classical decoder, and shows promising feasibility on real quantum hardware.

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•Nov 28, 2019•3 citations
Generating images directly from quantum systems is an attractive but unresolved goal on NISQ hardware. Existing quantum generators face several coupled obstacles: barren plateaus that block trainability, expensive quantum circuit preparation, and hardware noise that erodes quantum information with depth. A further difficulty is producing image-scale output without a classical decoder, whose use would otherwise break the end-to-end quantum advantage. We propose SQGen, a full quantum generator built on a quantized tensor train (QTT) with a latent modulation architecture. Specifically, SQGen promotes the QTT bond index of the target pixel distribution to ancilla bond qubits, so that each circuit site operates locally on a bond register plus the two physical qubits that carry the row- and column-bit of one image scale. We further introduce latent modulation: each re-uploading rotation is factorized at the angle level into a trainable main path plus an additive latent term, reducing to the trainable main path when the latent term is disabled. During training, we create a differentiable model in the classical system under gate-compatibility constraints, with a torus prior as the latent distribution. After training, every operator maps one-to-one to a native quantum gate, yielding a compact, deployable quantum circuit with no classical decoder in the inference path. Together, these design choices address the obstacles raised above. Extensive experiments on image datasets and synthetic data demonstrate that SQGen trains stably, generates images end-to-end from a shallow circuit with no classical decoder, and shows promising feasibility on real quantum hardware.
Quantum Generative Adversarial Networks (QGANs) offer a promising path for learning data distributions on near-term quantum devices. However, existing QGANs for image synthesis avoid direct full-image generation, relying on classical post-processing or patch-based methods. These approaches dilute the quantum generator's role and struggle to capture global image semantics. To address this, we propose ReQGAN, an end-to-end framework that synthesizes an entire N=2^D-pixel image using a single D-qubit quantum circuit. ReQGAN overcomes two fundamental bottlenecks hindering direct pixel generation: (1) the rigid classical-to-quantum noise interface and (2) the output mismatch between normalized quantum statistics and the desired pixel-intensity space. We introduce a learnable Neural Noise Encoder for adaptive state preparation and a differentiable Intensity Calibration module to map measurements to a stable, visually meaningful pixel domain. Experiments on MNIST and Fashion-MNIST demonstrate that ReQGAN achieves stable training and effective image synthesis under stringent qubit budgets, with ablation studies verifying the contribution of each component.
Quantum generative modeling is among the promising candidates for achieving a practical advantage in data analysis. Nevertheless, one key challenge is to generate large-size images comparable to those generated by their classical counterparts. In this work, we take an initial step in this direction and introduce the Latent Style-based Quantum GAN (LaSt-QGAN), which employs a hybrid classical-quantum approach in training Generative Adversarial Networks (GANs) for arbitrary complex data generation. This novel approach relies on powerful classical auto-encoders to map a high-dimensional original image dataset into a latent representation. The hybrid classical-quantum GAN operates in this latent space to generate an arbitrary number of fake features, which are then passed back to the auto-encoder to reconstruct the original data. Our LaSt-QGAN can be successfully trained on realistic computer vision datasets beyond the standard MNIST, namely Fashion MNIST (fashion products) and SAT4 (Earth Observation images) with 10 qubits, resulting in a comparable performance (and even better in some metrics) with the classical GANs. Moreover, we analyze the barren plateau phenomena within this context of the continuous quantum generative model using a polynomial depth circuit and propose a method to mitigate the detrimental effect during the training of deep-depth networks. Through empirical experiments and theoretical analysis, we demonstrate the potential of LaSt-QGAN for the practical usage in the context of image generation and open the possibility of applying it to a larger dataset in the future.
We propose an approach to generative quantum machine learning that overcomes the fundamental scaling issues of variational quantum circuits. The core idea is to use a class of generative models based on instantaneous quantum polynomial circuits, which we show can be trained efficiently on classical hardware. Although training is classically efficient, sampling from these circuits is widely believed to be classically hard, and so computational advantages are possible when sampling from the trained model on quantum hardware. By combining our approach with a data-dependent parameter initialisation strategy, we do not encounter issues of barren plateaus and successfully circumvent the poor scaling of gradient estimation that plagues traditional approaches to quantum circuit optimisation. We investigate and evaluate our approach on a number of real and synthetic datasets, training models with up to one thousand qubits and hundreds of thousands of parameters. We find that the quantum models can successfully learn from high dimensional data, and perform surprisingly well compared to simple energy-based classical generative models trained with a similar amount of hyperparameter optimisation. Overall, our work demonstrates that a path to scalable quantum generative machine learning exists and can be investigated today at large scales.
Quantum generative adversarial networks (QGANs) have attracted increasing attention for image generation using parameterized quantum circuits. Existing amplitude-based approaches face two key limitations: pixel locations are typically encoded by computational-basis indices or address qubits, causing quantum resources to grow with image resolution; meanwhile, jointly decoding many pixels from normalized quantum states introduces probability competition among pixels and limits precise pixel-wise control. To address these issues, we reformulate quantum image generation as coordinate-conditioned implicit function learning. Our method takes spatial coordinates and latent variables as inputs, uses a classical embedding network to generate input-dependent circuit parameters, and evaluates a variational quantum circuit at each coordinate. Pixel intensities are directly obtained from the expectation value of a dedicated color qubit, and a complete image is generated by querying all spatial coordinates. This design decouples image resolution from address-qubit requirements and avoids shared probability-normalization constraints across pixels. We further design a specialized variational quantum circuit to provide structural inductive bias for coordinate-conditioned generation. Simulated experiments on two benchmark datasets show that our method outperforms FRQI-based generation and PQWGAN in visual and quantitative quality while using fewer qubits, and also achieves better generation quality than the corresponding classical baseline.
High-fidelity circuit execution on noisy intermediate-scale quantum devices is bottlenecked by compilation pipelines that disregard complex, correlated noise. To address this, this methodology article proposes a quantum machine learning control (QMLC) framework for generative quantum circuit synthesis from gate-set tomography (GST) data that bypasses the traditional two-step pipeline of characterizing native quantum gates via GST followed by unitary decomposition algorithms. Instead, a generative concept space is directly learnt from GST data, enabling conditional synthesis of quantum circuits on a desired output distribution. Our approach tokenizes GST germ circuits and embeds them into a structured latent space using a curriculum-learning-motivated strategy, starting with short circuits and progressively incorporating longer ones with diverse output statistics. The embedded sequences are processed by a set-vision transformer with permutation-invariant pooling, producing k-seed vectors that represent the learned concept space of the quantum device. Aggregating data across multiple circuits makes this latent representation inherently context-aware, capturing the shared physical noise environment (e.g., crosstalk, drift) that isolated gate metrics miss. We propose an unconditional diffusion model to sample from the concept space. During inference, a user provides a target measurement distribution, and the model generates a corresponding circuit. To ensure fidelity and robustness, the output is denoised using a diffusion model that operates on the target conditional covariance matrix. This end-to-end framework is a step towards context-aware, hardware-native circuit synthesis directly from raw GST data, which offers a new paradigm for integrating quantum control and compilation. The QMLC framework is particularly suited for near-term quantum devices with complex calibration procedures.
The combination of quantum and classical computational resources towards more effective algorithms is one of the most promising research directions in computer science. In such a hybrid framework, existing quantum computers can be used to their fullest extent and for practical applications. Generative modeling is one of the applications that could benefit the most, either by speeding up the underlying sampling methods or by unlocking more general models. In this work, we design a number of hybrid generative models and validate them on real hardware and datasets. The quantum-assisted Boltzmann machine is trained to generate realistic artificial images on quantum annealers. Several challenges in state-of-the-art annealers shall be overcome before one can assess their actual performance. We attack some of the most pressing challenges such as the sparse qubit-to-qubit connectivity, the unknown effective-temperature, and the noise on the control parameters. In order to handle datasets of realistic size and complexity, we include latent variables and obtain a more general model called the quantum-assisted Helmholtz machine. In the context of gate-based computers, the quantum circuit Born machine is trained to encode a target probability distribution in the wavefunction of a set of qubits. We implement this model on a trapped ion computer using low-depth circuits and native gates. We use the generative modeling performance on the canonical Bars-and-Stripes dataset to design a benchmark for hybrid systems. It is reasonable to expect that quantum data, i.e., datasets of wavefunctions, will become available in the future. We derive a quantum generative adversarial network that works with quantum data. Here, two circuits are optimized in tandem: one tries to generate suitable quantum states, the other tries to distinguish between target and generated states.