Conquer: Modular Quantum Generative Models Enable Precise Control and Mitigate Bias in IQP Circuits

Quantum generative models based on instantaneous polynomial circuits offer a promising route to learning complex data patterns while remaining computationally manageable, but existing systems struggle with controlling the generated outputs and exhibit strong biases towards predictable results. To address these limitations, Xiaocheng Zou and Shijin Duan from Northeastern University, alongside Charles Fleming, Gaowen Liu, Ramana Rao Kompella from Cisco Research, and Shaolei Ren from the University of California, Riverside, present ConQuER, a Controllable Generative Framework. This new approach utilises a modular circuit architecture, embedding a lightweight controller that precisely shapes the output distribution without requiring complete retraining of the underlying model, and achieves precise control over characteristics like data density with minimal computational cost. Furthermore, the team extends this modular design through data-driven optimisation, embedding implicit control mechanisms directly into the quantum circuit, which significantly reduces generation bias when working with structured datasets, bridging a critical gap between theoretical potential and practical application in controllable generation modelling.

Controllability, trainability and scalability of quantum models

The research team introduces ConQER, a new framework for controllable quantum generation that tackles key limitations in current quantum generative models. These limitations include difficulties in controlling the type of outputs generated, challenges in training quantum neural networks due to vanishing gradients, and the need for models that scale effectively with increasing numbers of qubits for practical applications. ConQER utilizes a modular design built around instantaneous polynomial (IQP) circuits, known for their mathematical properties that facilitate efficient training and scalability. Lightweight controllers are integrated into the framework to provide conditional generation, offering precise control without adding significant computational overhead.

Experiments demonstrate that ConQER enables precise control over generated outputs and achieves an 18% reduction in bias within the generated data. The framework inherits the scalability benefits of IQP circuits, potentially allowing it to function effectively with a large number of qubits. Importantly, the lightweight controllers introduce minimal overhead, adding less than 5% to the total number of parameters. This approach allows for polynomial-time classical training, a significant advantage over many other quantum generative modelling techniques. The team suggests future research could focus on developing more sophisticated control mechanisms to manipulate specific quantum correlations, such as entanglement patterns. Combining IQP circuits with other types of quantum gates could also enhance the model’s expressiveness, while exploring different quantum correlations could unlock new possibilities for generating data with specific quantum properties.

Controllable Quantum Generation via Data-Driven Optimisation

Scientists have developed ConQuER, a novel framework for controllable quantum generation that addresses limitations in existing quantum models. This work demonstrates that precise control over generated outputs and reduction of generation bias are achievable using instantaneous polynomial (IQP) circuits. The team embedded a lightweight controller circuit into pre-trained IQP circuits, allowing for precise control of the output distribution without complete retraining of the model. This controller introduces minimal parameter and gate overhead, enabling fine-grained control over properties like the Hamming Weight distribution.

To mitigate generation bias, the researchers pioneered a data-driven architecture optimization strategy. This method analyzes the trained parameters of the controller to identify key gate patterns and then implicitly embeds control structures directly into the original IQP circuits. By redistributing gates based on empirical importance, the team achieved over a 40% reduction in pattern imbalance on structured datasets compared to baseline IQP circuits, all while maintaining computational complexity. This preserves the quantum computational advantages and classical training efficiency inherent in IQP circuits.

Experiments involving training and evaluating ConQuER on both 2D Ising models and binary blob datasets, scaling the system from 16 to 25 qubits, demonstrated excellent scalability. The IQP circuits employed a three-layer structure consisting of Hadamard gates, parameterized diagonal gates in the X-basis, and final Hadamard gates before measurement. This unique structure allows simultaneous application of all gates without temporal ordering constraints. The team utilized the Maximum Mean Discrepancy (MMD) to efficiently estimate the distance between the model and target distributions, decomposing the loss into a weighted sum of Pauli-Z expectation values computable using IQP’s structure. This enabled training on datasets requiring circuits with over 1000 qubits, a scale unattainable with conventional quantum machine learning approaches.

Controllable Quantum Generation Reduces Output Bias

Scientists have developed ConQuER, a new framework for controllable quantum generation that overcomes limitations in existing quantum generative models. This work demonstrates that precise control over generated outputs and reduction of generation bias are achievable using a modular circuit architecture based on instantaneous polynomial (IQP) circuits. The team embedded a lightweight controller circuit directly into pre-trained IQP circuits, allowing for precise control of the output distribution without requiring full retraining of the model. Experiments reveal that ConQuER significantly improves the uniformity of generated patterns, particularly on structured datasets.

Specifically, the team measured an 18. 1% reduction in pattern standard deviation, indicating a more balanced generation across all eight patterns tested. Furthermore, the max/min ratio, which reflects the disparity between the most and least frequent patterns, improved by 17. 6%, and the total deviation from ideal uniform distribution decreased by 10. 7%.

These results validate the hypothesis that architectural choices, rather than fundamental limitations, drive generation bias in quantum circuits. The controller’s efficiency is remarkable, adding only 45 parameters to a 16-qubit system containing 14,892 parameters in the base IQP circuit, resulting in a mere 0. 3% overhead. Deploying three, five, or seven control modes adds only 135, 225, or 315 parameters respectively. The controller converges in approximately 500 iterations, achieving a 4× training speedup compared to the base model.

Scalability tests demonstrate that the percentage overhead decreases logarithmically with system size; even with seven control modes, a 25-qubit system experienced less than a 1. 5% overhead increase. Predictions suggest that this trend continues, with overhead dropping below 0. 1% for a 30×30 system. This high scalability is due to the linear growth of controller parameters while the underlying IQP parameters grow polynomially.

Controllable Quantum Generation with Minimal Bias

This work presents ConQuER, a novel framework for controllable quantum generation that addresses limitations in existing quantum generative models. Current approaches often lack precise control over generated outputs and exhibit biases towards certain patterns; ConQuER overcomes these challenges through a modular circuit architecture. By embedding lightweight controller circuits within pre-trained instantaneous polynomial (IQP) circuits, the framework achieves precise control over output distributions with minimal parameter overhead, demonstrated through accurate control of Hamming weight distributions. The researchers demonstrate that ConQuER retains the efficient classical training properties and scalability benefits of IQP circuits, while significantly reducing generation bias on structured datasets.

Experimental validation across multiple datasets shows superior control accuracy and balanced generation performance, achieved with less than five percent parameter overhead. The scalability of the framework is particularly noteworthy, as controller parameters grow linearly while underlying IQP parameters grow polynomially, ensuring efficiency even for larger systems. The authors acknowledge that future work could explore more fine-grained control mechanisms to manipulate specific quantum correlations beyond Hamming weight, such as entanglement patterns. Additionally, enhancing the expressive power of IQP circuits through hybrid architectures incorporating non-commuting gates may enable the capture of more complex quantum phenomena while preserving scalability for practical quantum machine learning applications.