Quantum LEGO Learning: A Modular Design Principle for Hybrid Artificial Intelligence

TL;DR

Quantum LEGO Learning presents a modular, architecture-agnostic framework for hybrid quantum–classical models that partitions learning into a frozen classical feature block and a trainable VQC head, formalized as $f_{ m lg} = \widehat{f}_{v} \circ f_{c}$. The authors derive block-wise generalization bounds $\mathcal{L}(f_{\rm lg}) = \epsilon_{\rm app} + \epsilon_{\rm est} + \epsilon_{\rm opt}$, showing the approximation error depends chiefly on the classical encoder while estimation and optimization relate to the quantum block, enabling qubit-count independence in the approximation term. They demonstrate noise resilience and hardware viability through gradient estimation on quantum hardware and experiments on quantum dot classification and genome TFBS tasks, including IBM Heron hardware. The work offers a scalable, interpretable blueprint for near-term quantum learning, outlining explicit trade-offs and conditions under which quantum blocks provide advantages, and suggesting extensions to adaptive classical blocks and structured quantum heads.

Abstract

Hybrid quantum-classical learning models increasingly integrate neural networks with variational quantum circuits (VQCs) to exploit complementary inductive biases. However, many existing approaches rely on tightly coupled architectures or task-specific encoders, limiting conceptual clarity, generality, and transferability across learning settings. In this work, we introduce Quantum LEGO Learning, a modular and architecture-agnostic learning framework that treats classical and quantum components as reusable, composable learning blocks with well-defined roles. Within this framework, a pre-trained classical neural network serves as a frozen feature block, while a VQC acts as a trainable adaptive module that operates on structured representations rather than raw inputs. This separation enables efficient learning under constrained quantum resources and provides a principled abstraction for analyzing hybrid models. We develop a block-wise generalization theory that decomposes learning error into approximation and estimation components, explicitly characterizing how the complexity and training status of each block influence overall performance. Our analysis generalizes prior tensor-network-specific results and identifies conditions under which quantum modules provide representational advantages over comparably sized classical heads. Empirically, we validate the framework through systematic block-swap experiments across frozen feature extractors and both quantum and classical adaptive heads. Experiments on quantum dot classification demonstrate stable optimization, reduced sensitivity to qubit count, and robustness to realistic noise.

Figures (4)

• Figure 1: Quantum LEGO Learning Architecture. A pre-trained classical neural network (frozen) serves as the feature block, transforming the input $\textbf{x} \in \mathbb{R}^D$ into a structured embedding $\widehat{f}_{c}(\textbf{x}) \in \mathbb{R}^U$. This embedding is then encoded into a quantum state via a Tensor Product Encoder using single-qubit $R_{Y}(\frac{\pi}{2}\phi(\widehat{f}^{(u)}_{c}(\textbf{x})))$ rotations. A trainable VQC acts as the quantum block, applying layers of parameterized $R_{X}(\alpha_u)$, $R_{Y}(\beta_u)$, and $R_{Z}(\gamma_u)$ gates, highlighted by a green dashed box. Measurement of Pauli-Z observables $\langle \sigma_{z}^{(u)}\rangle$ produces classical outputs that are passed through a softmax layer for prediction. During training, only the quantum block parameters are updated, while the classical feature block remains fixed. This modular design exemplifies Quantum LEGO Learning, in which classical and quantum components serve as reusable, composable blocks.
• Figure 2: Illustration of single and double quantum dot charge stability diagrams. (a) labeled clean charge stability diagrams containing the transition lines without noise; (b) labeled noisy charge stability diagrams mixed with realistic noise effects on the transition lines. Label:$0$ and Label:$1$ denote charge stability diagrams of single and double quantum dots. By detecting transition lines using the QML approach, we aim to determine whether the charge stability diagram corresponds to single- or double-quantum-dot behavior. In particular, we use noiseless data to evaluate the models' representational power and noisy data to assess their generalization power.
• Figure 3: Empirical evaluation of Quantum LEGO Learning on quantum dot classification. Classification accuracy over training epochs under different hybrid architectures, noise conditions, and deployment settings. (a) Noise-free simulation with 20 qubits and 6 VQC layers, comparing ResNet18/50 + VQC with PCA + VQC and TTN + VQC; (b) comparison between quantum (VQC) and classical (FC) heads trained on identical frozen ResNet features; (c) sensitivity to qubit count under noise-free simulation, showing stable performance as qubit number decreases; (d) performance under realistic quantum noise (depolarizing, dephasing, two-qubit Pauli, and readout errors); (e) robustness of ResNet18 + VQC under increasing single-qubit noise strength; (f) execution on the IBM Heron quantum processor (20 qubits, depth 6), demonstrating practical robustness.
• Figure 4: Empirical results of genome TFBS prediction on IBM quantum hardware. Classification accuracy (left) and cross-entropy loss (right) as a function of training epochs for genome TFBS prediction using hybrid Quantum LEGO models executed on the 156-qubit IBM Heron r2 processor. We compare a hybrid TTN+VQC model against a classical TTN+NN baseline and a PCA+VQC model, in which the pre-trained TTN feature block is frozen, and only the VQC parameters are optimized during training. Results show that Pre-TTN+VQC achieves higher accuracy and lower loss, demonstrating improved generalization and robustness under realistic quantum hardware conditions.

Theorems & Definitions (4)

• Theorem 1: Approximation Error
• Theorem 2: Estimation Error
• Theorem 3: Optimization Error
• Theorem 4