Quantum Feature Maps And Classical Data In Quantum Space
Quantum Feature Maps
Iterative quantum feature mappings (IQFMs) are a quantum machine learning (QML) innovation that introduces a hybrid classical-quantum architecture that solves some of the primary issues with implementing quantum models on conventional hardware. Fujitsu Research researchers Nasa Matsumoto, Quoc Hoan Tran, Koki Chinzei, Yasuhiro Endo, and Hirotaka Oshima designed this framework. Quantum News published “Quantum-enhanced Machine Learning Boosts Performance with Iterative Feature Maps” on June 25, 2025, detailing their research's benefits and results.
IQFMs build on Quantum Feature Maps. QFMs convert conventional data into quantum states using quantum computers' growing Hilbert space. The transformation makes QML models universal approximators of continuous functions and may speed up classification problems exponentially. Classical machine learning (ML) methods that map input data into new feature spaces improve separability.
Practitioners face various challenges when using deep QFMs. Current quantum technology is limited and susceptible to circuit noise. The conventional variational quantum algorithms (VQAs) used to train these models often experience computational bottlenecks, especially when obtaining precise gradient estimation, which requires substantial quantum resources and can lead to local minima or “barren plateaus” in the optimisation landscape.
IQFMs generate deep learning systems by iteratively integrating shallow quantum feature maps (QFMs) with classically derived augmentation weights to address these difficulties. This hybrid design intentionally reduces learning quantum resources.
Hybrid Architecture: IQFMs connect shallow QFMs via measurement outputs, which are processed by classical augmentation, in place of deep quantum circuits. This form promotes expressiveness and flexibility for near-term quantum computers.
A key feature of IQFMs is that they optimise just the classical augmentation weights between QFMs, not the quantum circuits' variational characteristics. This technique avoids a major shortcoming of standard QML algorithms and reduces quantum computational runtime by offloading gradient estimates to classical processors. The classical augmentation parameters (𝑾_l) can be taught, while the quantum circuit parameters (𝜽_l) are often fixed to random values.
IQFMs use contrastive learning, an important representation learning strategy. The model is trained to produce similar representations with similar inputs and divergent representations with unrelated inputs. By focussing on key data similarities and differences, contrastive learning stabilises feature extraction across noisy quantum circuits and reduces variability caused by hardware faults or quantum measurements in IQFMs.
Using supervised contrastive-learning, a “anchor” feature vector is produced for an input. A “negative” sample (one with a different label) is processed to yield a representation farther from the anchor than a “positive” sample (one with the same label). This is done by minimising a contrastive loss function.
Layer-wise Training: IQFMs supplement contrastive learning with layer-by-layer training. Instead of optimising every parameter, which would demand a lot of quantum resources, this method trains classical augmentation weights for each QFM layer. It also avoids the "barren plateaus" phenomenon in VQAs where gradients disappear in long quantum circuits, reducing computational complexity.
QFM block characteristics are extracted via quantum measurements in many bases. The approach involves transferring classical features into a quantum state using an embedding circuit (𝒰_𝚿), entangling and mixing data with a preprocessing circuit (P_l), and adjusting the measurement basis with a parameterised circuit (Ω_l). The process creates a feature vector (𝒈_l) based on measurement operator expectations. To improve the feature set, measurements in bases other than the computational (Pauli-Z) basis concatenate feature vectors. This multi-basis strategy improves classification and prevents classical simulation of some quantum correlations.
Flexibility and Performance: IQFMs can categorise classical and quantum data.
Quantum Data Classification: IQFMs consistently outperform Quantum Convolutional Neural Networks (QCNN) in quantum phase recognition tasks (Task A and Task B, which categorise Hamiltonians' ground states into discrete quantum phases). This suggests that random measurement bases and typical post-processing are effective without QFM circuit optimisation.
Robustness to Noise: IQFMs beat QCNN in the presence of statistical errors from a small number of measurement shots and physical RX noise (random data rotations). At higher noise levels, IQFMs outperformed QCNN in accuracy. Visualisations reveal that contrastive learning strengthened discriminative representations by forming more coherent feature space clusters.
Classification: On the Fashion-MNIST test, IQFMs fared comparably to classical neural networks with similar designs. Classical data was processed using modular IQFMs to handle large datasets. Multiple QFMs process classical data simultaneously in this configuration. This modular design, which only allows subcircuits on quantum devices, allows large-scale tasks on near-term quantum devices with constrained qubits.
Future Outlook: IQFMs are a promising step towards quantum-enhanced machine learning's full potential, making them ideal for practical applications with limited computational resources and uneven data quality. The researchers note that IQFMs' architecture avoids the incompatibility of back-propagation with quantum circuits, which lack intermediate states for gradient computation, and that Direct Feedback Alignment (DFA) may be investigated as a training method.