Quantum-Compatible Dictionary Learning via Doubly Sparse Models

Dictionary learning (DL) is a core tool in signal processing and machine learning for discovering sparse representations of data. In contrast with classical successes, there is currently no practical quantum dictionary learning algorithm. We argue that this absence stems from structural mismatches between classical DL formulations and the operational constraints of quantum computing. We identify the fundamental bottlenecks that prevent efficient quantum realization of classical DL and show how a structurally restricted model, doubly sparse dictionary learning (DSDL), naturally avoids these problems. We present a simple, hybrid quantum-classical algorithm based on projection-based randomized Kaczmarz iterations with Qiskit-compatible quantum inner products. We outline practical considerations and share an open-source implementation at https://github.com/AngshulMajumdar/quantum-dsdl-kaczmarz. The goal is not to claim exponential speedups, but to realign dictionary learning with the realities of near-term quantum devices.