FlowQ-Net: A Generative Framework for Automated Quantum Circuit Design

TL;DR

FlowQ-Net reframes quantum circuit design as a sequential, generative problem solved by Generative Flow Networks to produce a diverse ensemble of high-quality, resource-efficient ansätze. By separating outer discrete architecture search from inner continuous parameter optimization, the framework achieves circuits that maintain accuracy under noise while dramatically reducing circuit depth, gate count, and parameters across quantum chemistry, quantum neural networks, and Max-Cut tasks. The key contribution is a trainable, reward-proportional sampling process that favors compact yet expressive designs, enabling robust performance on NISQ devices. The approach holds promise for scalable, automated quantum algorithm design and could accelerate practical quantum computing across chemistry, optimization, and machine learning applications.

Abstract

Designing efficient quantum circuits is a central bottleneck to exploring the potential of quantum computing, particularly for noisy intermediate-scale quantum (NISQ) devices, where circuit efficiency and resilience to errors are paramount. The search space of gate sequences grows combinatorially, and handcrafted templates often waste scarce qubit and depth budgets. We introduce \textsc{FlowQ-Net} (Flow-based Quantum design Network), a generative framework for automated quantum circuit synthesis based on Generative Flow Networks (GFlowNets). This framework learns a stochastic policy to construct circuits sequentially, sampling them in proportion to a flexible, user-defined reward function that can encode multiple design objectives such as performance, depth, and gate count. This approach uniquely enables the generation of a diverse ensemble of high-quality circuits, moving beyond single-solution optimization. We demonstrate the efficacy of \textsc{FlowQ-Net} through an extensive set of simulations. We apply our method to Variational Quantum Algorithm (VQA) ansatz design for molecular ground state estimation, Max-Cut, and image classification, key challenges in near-term quantum computing. Circuits designed by \textsc{FlowQ-Net} achieve significant improvements, yielding circuits that are 10$\times$-30$\times$ more compact in terms of parameters, gates, and depth compared to commonly used unitary baselines, without compromising accuracy. This trend holds even when subjected to error profiles from real-world quantum devices. Our results underline the potential of generative models as a general-purpose methodology for automated quantum circuit design, offering a promising path towards more efficient quantum algorithms and accelerating scientific discovery in the quantum domain.

Figures (6)

• Figure 1: GFlowNet-guided VQA ansatz design. Top band: For each candidate architecture $\mathcal{G}_i$ generated by FlowQ-Net, the quantum‐processing unit (QPU) executes the circuits to obtain measurement outcomes, which are post‐processed to obtain a loss. If parameters are present, a classical optimizer optimizes continuous parameters $\boldsymbol{\theta}$ to minimize the loss $\mathcal{L}(\boldsymbol{\theta};\mathcal{G}_i)$, while parameter-free circuits are evaluated directly. The process returns the minimal loss $\mathcal{L}(\boldsymbol{\theta}^*;\mathcal{G}_i)$. Bottom band: The resulting loss is mapped to a reward $R(\mathcal{G}_i)$, which updates the GFlowNet component of FlowQ-Net. then a new circuit architecture $\mathcal{G}_i$ is constructed step by step by sampling actions $a_t\!\sim\!\pi(a_t\mid s_t)$ from the GFlowNet. The terminal sample is finally passed to the QPU. The outer GFlowNet learning loop and the inner (optional) continuous parameter optimization loop iterate until high-reward (low-loss) circuit architectures are sampled with high probability.
• Figure 2: Learning dynamics of the FlowQ-Net on four independent $\mathrm{H}_2$ (4-qubit) runs. Left panel shows the reward approaching its theoretical optimum after roughly $10^{3}$ epochs. A running mean over 50 epochs smooths the raw reward. Right panel shows a steady expansion in circuit diversity. The two plots indicate that exploration and exploitation progress yielding high-quality and diverse circuit families.
• Figure 3: Quantum resource comparison across problem instances and noise models. Stacked bars report the number of circuit parameters ($P$), gate count ($G$), and circuit depth ($D$) on a log-scale $y$-axis for four molecular VQE benchmarks, $\mathrm{H}_2$ with 2, 3, and 4 qubits, and $\mathrm{LiH}$ with 4 qubits. Each colour grouping corresponds to a different execution context: noiseless simulation, IBM Mumbai backend, IBM Ourense backend, and a single-qubit depolarizing noise model.
• Figure 4: Comparison of our approach with quantum and classical baselines on four data encoding setups. Left Panel: Test accuracy. Right Panel: Average number of parameters.
• Figure 5: Optimal Max-Cut solutions. Vertices are split into light-purple and deep-purple sets. Black edges cross the cut, light-gray edges lie within a set.