qcr:2604.63041.1

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.

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https://github.com/AngshulMajumdar/quantum-dsdl-kaczmarz

README.md

Quantum-Compatible Doubly Sparse Dictionary Learning (DSDL)

This repository contains a flat, minimal implementation of a quantum-compatible doubly sparse dictionary learning (DSDL) algorithm.

There is no package structure and no paper material here by design. This repo exists only to host working code that demonstrates the algorithmic idea.

What this code does

Uses a doubly sparse model: D = Phi A
Solves both sparse coding and dictionary update via ridge-stabilized randomized Kaczmarz
Uses Qiskit only for quantum inner products
No OMP, no SVD, no QRAM assumptions
Fully hybrid quantum–classical, NISQ-compatible

Files

dsdl_qiskit.py : main algorithm (paste the final Block 5 here)
requirements.txt : minimal dependencies
LICENSE : MIT

Dependencies

numpy
qiskit

Install with:

pip install -r requirements.txt

Philosophy

This is a structural algorithmic demonstration, not a benchmarking suite and not a paper repository.

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