Adaptive interpolating quantum transform: A quantum-native framework for efficient transform learning

Machine learning on quantum computers has attracted attention for its potential to deliver computational speedups in different tasks. However, deep variational quantum circuits require a large number of trainable parameters that grows with both qubit count and circuit depth, often rendering training infeasible. In this study we introduce the adaptive interpolating quantum transform (AIQT), a quantum-native framework for flexible and efficient learning. The AIQT defines a trainable unitary that interpolates between quantum transforms, such as the Hadamard and quantum Fourier transforms. This approach enables expressive quantum state manipulation while controlling parameter overhead. When built upon efficient quantum circuits such as the quantum Fourier transform, the AIQT achieves polynomial scaling of the number of gates with respect to the number of qubits. Our results show that the AIQT achieves high performance with minimal parameter count, offering a scalable and interpretable alternative to deep variational circuits.